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Visibility is a crucial aspect of planning and control of autonomous vehicles (AV), particularly when navigating environments with occlusions. However, when an AV follows a trajectory with multiple occlusions, existing methods evaluate each occlusion individually, calculate a visibility cost for each, and rely on the planner to minimize the overall cost. This can result in conflicting priorities for the planner, as individual occlusion costs may appear to be in opposition. We solve this problem by creating an alternate perspective cost map that allows for an aggregate view of the occlusions in the environment. The value of each cell on the cost map is a measure of the amount of visual information that the vehicle can gain about the environment by visiting that location. Our proposed method identifies observation locations and occlusion targets drawn from both map data and sensor data. We show how to estimate an alternate perspective for each observation location and then combine all estimates into a single alternate perspective cost map for motion planning., Comment: This work has been submitted to the IEEE-RAL for possible publication

Adaptive task planning is fundamental to ensuring effective and seamless human-robot collaboration. This paper introduces a robot task planning framework that takes into account both human leading/following preferences and performance, specifically focusing on task allocation and scheduling in collaborative settings. We present a proactive task allocation approach with three primary objectives: enhancing team performance, incorporating human preferences, and upholding a positive human perception of the robot and the collaborative experience. Through a user study, involving an autonomous mobile manipulator robot working alongside participants in a collaborative scenario, we confirm that the task planning framework successfully attains all three intended goals, thereby contributing to the advancement of adaptive task planning in human-robot collaboration. This paper mainly focuses on the first two objectives, and we discuss the third objective, participants' perception of the robot, tasks, and collaboration in a companion paper.

Achieving effective and seamless human-robot collaboration requires two key outcomes: enhanced team performance and fostering a positive human perception of both the robot and the collaboration. This paper investigates the capability of the proposed task planning framework to realize these objectives by integrating human leading/following preference and performance into its task allocation and scheduling processes. We designed a collaborative scenario wherein the robot autonomously collaborates with participants. The outcomes of the user study indicate that the proactive task planning framework successfully attains the aforementioned goals. We also explore the impact of participants' leadership and followership styles on their collaboration. The results reveal intriguing relationships between these factors, which warrant further investigation in future studies.

We propose a data-driven receding-horizon control method dealing with the chance-constrained output-tracking problem of unknown stochastic linear time-invariant (LTI) systems with partial state observation. The proposed method takes into account the statistics of the process noise, the measurement noise and the uncertain initial condition, following an analogous framework to Stochastic Model Predictive Control (SMPC), but does not rely on the use of a parametric system model. As such, our receding-horizon algorithm produces a sequence of closed-loop control policies for predicted time steps, as opposed to a sequence of open-loop control actions. Under certain conditions, we establish that our proposed data-driven control method produces identical control inputs as that produced by the associated model-based SMPC. Simulation results on a grid-connected power converter are provided to illustrate the performance benefits of our methodology., Comment: 20 pages, 4 figures. The extended version of a submission to IEEE Transactions on Automatic Control

When designing a motion planner for autonomous robots there are usually multiple objectives to be considered. However, a cost function that yields the desired trade-off between objectives is not easily obtainable. A common technique across many applications is to use a weighted sum of relevant objective functions and then carefully adapt the weights. However, this approach may not find all relevant trade-offs even in simple planning problems. Thus, we study an alternative method based on a weighted maximum of objectives. Such a cost function is more expressive than the weighted sum, and we show how it can be deployed in both continuous- and discrete-space motion planning problems. We propose a novel path planning algorithm for the proposed cost function and establish its correctness, and present heuristic adaptations that yield a practical runtime. In extensive simulation experiments, we demonstrate that the proposed cost function and algorithm are able to find a wider range of trade-offs between objectives (i.e., Pareto-optimal solutions) for various planning problems, showcasing its advantages in practice.

Robotic-based compact storage and retrieval systems provide high-density storage in distribution center and warehouse applications. In the system, items are stored in bins, and the bins are organized inside a three-dimensional grid. Robots move on top of the grid to retrieve and deliver bins. To retrieve a bin, a robot removes all bins above one by one with its gripper, called bin digging. The closer the target bin is to the top of the grid, the less digging is required to retrieve the bin. In this paper, we propose a policy to optimally arrange the bins in the grid while processing bin requests so that the most frequently accessed bins remain near the top of the grid. This improves the performance of the system and makes it responsive to changes in bin demand. Our solution approach identifies the optimal bin arrangement in the storage facility, initiates a transition to this optimal set-up, and subsequently ensures the ongoing maintenance of this arrangement for optimal performance. We perform extensive simulations on a custom-built discrete event model of the system. Our simulation results show that under the proposed policy more than half of the bins requested are located on top of the grid, reducing bin digging compared to existing policies. Compared to existing approaches, the proposed policy reduces the retrieval time of the requested bins by over 30% and the number of bin requests that exceed certain time thresholds by nearly 50%., Comment: 35 pages, 16 figures, submitted to Transportation Science (INFORMS)

In this paper, we propose a method to replan coverage paths for a robot operating in an environment with initially unknown static obstacles. Existing coverage approaches reduce coverage time by covering along the minimum number of coverage lines (straight-line paths). However, recomputing such paths online can be computationally expensive resulting in robot stoppages that increase coverage time. A naive alternative is greedy detour replanning, i.e., replanning with minimum deviation from the initial path, which is efficient to compute but may result in unnecessary detours. In this work, we propose an anytime coverage replanning approach named OARP-Replan that performs near-optimal replans to an interrupted coverage path within a given time budget. We do this by solving linear relaxations of integer linear programs (ILPs) to identify sections of the interrupted path that can be optimally replanned within the time budget. We validate OARP-Replan in simulation and perform comparisons against a greedy detour replanner and other state-of-the-art coverage planners. We also demonstrate OARP-Replan in experiments using an industrial-level autonomous robot., Comment: 16 pages, 18 figures, Paper submitted to IEEE T-RO

This paper addresses the challenge of enabling a single robot to effectively assist multiple humans in decision-making for task planning domains. We introduce a comprehensive framework designed to enhance overall team performance by considering both human expertise in making the optimal decisions and robot influence on human decision-making. Our model integrates these factors seamlessly within the task-planning domain, formulating the problem as a partially observable Markov decision process (POMDP) while treating expertise and influence as unobservable components of the system state. To solve for the robot's actions in such systems, we propose an efficient Attention-Switching policy. This policy capitalizes on the inherent structure of such systems, solving multiple smaller POMDPs to generate heuristics for prioritizing interactions with different human teammates, thereby reducing the state space and improving scalability. Our empirical results on a simulated kit fulfillment task demonstrate improved team performance when the robot's policy accounts for both expertise and influence. This research represents a significant step forward in the field of adaptive robot assistance, paving the way for integration into cost-effective small and mid-scale industries, where substantial investments in robotic infrastructure may not be economically viable., Comment: 7 pages, 5 figures

With the introduction of collaborative robots, humans and robots can now work together in close proximity and share the same workspace. However, this collaboration presents various challenges that need to be addressed to ensure seamless cooperation between the agents. This paper focuses on task planning for human-robot collaboration, taking into account the human's performance and their preference for following or leading. Unlike conventional task allocation methods, the proposed system allows both the robot and human to select and assign tasks to each other. Our previous studies evaluated the proposed framework in a computer simulation environment. This paper extends the research by implementing the algorithm in a real scenario where a human collaborates with a Fetch mobile manipulator robot. We briefly describe the experimental setup, procedure and implementation of the planned user study. As a first step, in this paper, we report on a system evaluation study where the experimenter enacted different possible behaviours in terms of leader/follower preferences that can occur in a user study. Results show that the robot can adapt and respond appropriately to different human agent behaviours, enacted by the experimenter. A future user study will evaluate the system with human participants.

This paper presents a solution for the problem of optimal planning for a robot in a collaborative human-robot team, where the human supervisor is intermittently available to assist the robot in completing tasks more quickly. Specifically, we address the challenge of computing the fastest path between two configurations in an environment with time constraints on how long the robot can wait for assistance. To solve this problem, we propose a novel approach that utilizes the concepts of budget and critical departure times, which enables us to obtain optimal solutions while scaling to larger problem instances than existing methods. We demonstrate the effectiveness of our approach by comparing it with several baseline algorithms on a city road network and analyzing the quality of the solutions obtained. Our work contributes to the field of robot planning by addressing the critical issue of incorporating human assistance and environmental restrictions, which has significant implications for real-world applications., Comment: 9 pages, 7 figures, IEEE ROMAN 2023

We study the problem of deploying a fleet of mobile robots to service tasks that arrive stochastically over time and at random locations in an environment. This is known as the Dynamic Vehicle Routing Problem (DVRP) and requires robots to allocate incoming tasks among themselves and find an optimal sequence for each robot. State-of-the-art approaches only consider average wait times and focus on high-load scenarios where the arrival rate of tasks approaches the limit of what can be handled by the robots while keeping the queue of unserviced tasks bounded, i.e., stable. To ensure stability, these approaches repeatedly compute minimum distance tours over a set of newly arrived tasks. This paper is aimed at addressing the missing policies for moderate-load scenarios, where quality of service can be improved by prioritizing long-waiting tasks. We introduce a novel DVRP policy based on a cost function that takes the $p$-norm over accumulated wait times and show it guarantees stability even in high-load scenarios. We demonstrate that the proposed policy outperforms the state-of-the-art in both mean and $95^{th}$ percentile wait times in moderate-load scenarios through simulation experiments in the Euclidean plane as well as using real-world data for city scale service requests., Comment: Accepted for publication in IEEE Robotics and Automation Letters (RA-L)

Human supervisors in multi-robot systems are primarily responsible for monitoring robots, but can also be assigned with secondary tasks. These tasks can act as interruptions and can be categorized as either intrinsic, i.e., being directly related to the monitoring task, or extrinsic, i.e., being unrelated. In this paper, we investigate the impact of these two types of interruptions through a user study ($N=39$), where participants monitor a number of remote mobile robots while intermittently being interrupted by either a robot fault correction task (intrinsic) or a messaging task (extrinsic). We find that task performance of participants does not change significantly with the interruptions but depends greatly on the number of robots. However, interruptions result in an increase in perceived workload, and extrinsic interruptions have a more negative effect on workload across all NASA-TLX scales. Participants also reported switching between extrinsic interruptions and the primary task to be more difficult compared to the intrinsic interruption case. Statistical significance of these results is confirmed using ANOVA and one-sample t-test. These findings suggest that when deciding task assignment in such supervision systems, one should limit interruptions from secondary tasks, especially extrinsic ones, in order to limit user workload., Comment: 7 pages, 10 figures, 2 tables, ICRA 2023

We consider a general form of the sensor scheduling problem for state estimation of linear dynamical systems, which involves selecting sensors that minimize the trace of the Kalman filter error covariance (weighted by a positive semidefinite matrix) subject to polyhedral constraints on the selected sensors. This general form captures several well-studied problems including sensor placement, sensor scheduling with budget constraints, and Linear Quadratic Gaussian (LQG) control and sensing co-design. We present a mixed integer optimization approach that is derived by exploiting the optimality of the Kalman filter. While existing work has focused on approximate methods to specific problem variants, our work provides a unified approach to computing optimal solutions to the general version of sensor scheduling. In simulation, we show this approach finds optimal solutions for systems with 30 to 50 states in seconds.

In this paper we study multi-robot path planning for persistent monitoring tasks. We consider the case where robots have a limited battery capacity with a discharge time $D$. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum allowable time between robot visits, called the latency. The objective is to find the minimum number of robots that can satisfy these latency constraints while also ensuring that the robots periodically charge at a recharging depot. The decision version of this problem is known to be PSPACE-complete. We present a $O(\frac{\log D}{\log \log D}\log \rho)$ approximation algorithm for the problem where $\rho$ is the ratio of the maximum and the minimum latency constraints. We also present an orienteering based heuristic to solve the problem and show empirically that it typically provides higher quality solutions than the approximation algorithm. We extend our results to provide an algorithm for the problem of minimizing the maximum weighted latency given a fixed number of robots. We evaluate our algorithms on large problem instances in a patrolling scenario and in a wildfire monitoring application. We also compare the algorithms with an existing solver on benchmark instances., Comment: 13 pages, 10 fiugres. arXiv admin note: substantial text overlap with arXiv:1903.06105

Vessel transit in ice-covered waters poses unique challenges in safe and efficient motion planning. When the concentration of ice is high, it may not be possible to find collision-free trajectories. Instead, ice can be pushed out of the way if it is small or if contact occurs near the edge of the ice. In this work, we propose a real-time navigation framework that minimizes collisions with ice and distance travelled by the vessel. We exploit a lattice-based planner with a cost that captures the ship interaction with ice. To address the dynamic nature of the environment, we plan motion in a receding horizon manner based on updated vessel and ice state information. Further, we present a novel planning heuristic for evaluating the cost-to-go, which is applicable to navigation in a channel without a fixed goal location. The performance of our planner is evaluated across several levels of ice concentration both in simulated and in real-world experiments., Comment: 7 pages, 8 figures

This article presents a survey of literature in the area of Human-Robot Interaction (HRI), specifically on systems containing more than two agents (i.e., having multiple humans and/or multiple robots). We identify three core aspects of ``Multi-agent" HRI systems that are useful for understanding how these systems differ from dyadic systems and from one another. These are the Team structure, Interaction style among agents, and the system's Computational characteristics. Under these core aspects, we present five attributes of HRI systems, namely Team size, Team composition, Interaction model, Communication modalities, and Robot control. These attributes are used to characterize and distinguish one system from another. We populate resulting categories with examples from recent literature along with a brief discussion of their applications and analyze how these attributes differ from the case of dyadic human-robot systems. We summarize key observations from the current literature, and identify challenges and promising areas for future research in this domain. In order to realize the vision of robots being part of the society and interacting seamlessly with humans, there is a need to expand research on multi-human -- multi-robot systems. Not only do these systems require coordination among several agents, they also involve multi-agent and indirect interactions which are absent from dyadic HRI systems. Adding multiple agents in HRI systems requires advanced interaction schemes, behavior understanding and control methods to allow natural interactions among humans and robots. In addition, research on human behavioral understanding in mixed human-robot teams also requires more attention. This will help formulate and implement effective robot control policies in HRI systems with large numbers of heterogeneous robots and humans; a team composition reflecting many real-world scenarios., Comment: 23 pages, 7 figures

We study the sample placement and shortest tour problem for robots tasked with mapping environmental phenomena modeled as stationary random fields. The objective is to minimize the resources used (samples or tour length) while guaranteeing estimation accuracy. We give approximation algorithms for both problems in convex environments. These improve previously known results, both in terms of theoretical guarantees and in simulations. In addition, we disprove an existing claim in the literature on a lower bound for a solution to the sample placement problem.

In this paper, we consider the problem of allocating human operator assistance in a system with multiple autonomous robots. Each robot is required to complete independent missions, each defined as a sequence of tasks. While executing a task, a robot can either operate autonomously or be teleoperated by the human operator to complete the task at a faster rate. We show that the problem of creating a teleoperation schedule that minimizes makespan of the system is NP-Hard. We formulate our problem as a Mixed Integer Linear Program, which can be used to optimally solve small to moderate sized problem instances. We also develop an anytime algorithm that makes use of the problem structure to provide a fast and high-quality solution of the operator scheduling problem, even for larger problem instances. Our key insight is to identify blocking tasks in greedily-created schedules and iteratively remove those blocks to improve the quality of the solution. Through numerical simulations, we demonstrate the benefits of the proposed algorithm as an efficient and scalable approach that outperforms other greedy methods.

Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the weighted sum of the individual objectives. Solutions to this scalarized optimization problem are Pareto optimal solutions to the original multi-objective problem. However, finding an accurate representation of a Pareto front remains an important challenge. Using uniformly spaced weight vectors is often inefficient and does not provide error bounds. Thus, we address the problem of computing a finite set of weight vectors such that for any other weight vector, there exists an element in the set whose error compared to optimal is minimized. To this end, we prove fundamental properties of the optimal cost as a function of the weight vector, including its continuity and concavity. Using these, we propose an algorithm that greedily adds the weight vector least-represented by the current set, and provide bounds on the error. Finally, we illustrate that the proposed approach significantly outperforms uniformly distributed weights for different robot planning problems with varying numbers of objective functions.

Control barrier functions are widely used to synthesize safety-critical controls. The existence of Gaussian-type noise may lead to unsafe actions and result in severe consequences. While studies are widely done in safety-critical control for stochastic systems, in many real-world applications, we do not have the knowledge of the stochastic component of the dynamics. In this paper, we study safety-critical control of stochastic systems with an unknown diffusion part and propose a data-driven method to handle these scenarios. More specifically, we propose a data-driven stochastic control barrier function (DDSCBF) framework and use supervised learning to learn the unknown stochastic dynamics via the DDSCBF scheme. Under some reasonable assumptions, we provide guarantees that the DDSCBF scheme can approximate the It\^{o} derivative of the stochastic control barrier function (SCBF) under partially unknown dynamics using the universal approximation theorem. We also show that we can achieve the same safety guarantee using the DDSCBF scheme as with SCBF in previous work without requiring the knowledge of stochastic dynamics. We use two non-linear stochastic systems to validate our theory in simulations.

We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum error over a finite set of prediction locations. The problem is known to be NP-hard. However, we strive to compute optimal solutions by leveraging advances in mixed integer optimization. Our approach is based on expanding the search space so we optimize not only over the collected measurement subset, but also over the class of all linear estimators. This allows us to formulate a mixed integer quadratic program that is convex in the continuous variables. The formulations are general and are not restricted to any covariance structure of the field. In simulations, we demonstrate the effectiveness of our approach over previous branch and bound algorithms.

In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements can be taken at any location in the continuous field, and the covariance between the field values at different points is given by the widely used squared exponential covariance function. One approach for observation selection is to perform a grid discretization of the space and obtain an approximate solution using the greedy algorithm. The solution quality improves with a finer grid resolution but at the cost of increased computation. We propose a method to reduce the computational complexity, or conversely to increase solution quality, of the greedy algorithm by considering a search space consisting only of prediction locations and centroids of cliques formed by the prediction locations. We demonstrate the effectiveness of our proposed approach in simulation, both in terms of solution quality and runtime., Comment: Accepted for publication at European Control Conference, 2022

We consider the problem of data-driven predictive control for an unknown discrete-time linear time-periodic (LTP) system of known period. Our proposed strategy generalizes both Data-enabled Predictive Control (DeePC) and Subspace Predictive Control (SPC), which are established data-driven control techniques for linear time-invariant (LTI) systems. The approach is supported by an extensive theoretical development of behavioral systems theory for LTP systems, culminating in a generalization of the fundamental lemma. Our algorithm produces results identical to standard Model Predictive Control (MPC) for deterministic LTP systems. Robustness of the algorithm to noisy data is illustrated via simulation of a regularized version of the algorithm applied to a stochastic multi-input multi-output LTP system., Comment: 12 pages, 7 figures, the extended version of a CDC 2022 paper

We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker can observe only pairwise information, i.e., can evaluate the objective function on sets of size two. We begin with a negative result that no algorithm using only $k$-wise information can guarantee performance better than $k/n$. We present two algorithms that utilize only pairwise information about the function and characterize their performance relative to the optimal, which depends on the curvature of the submodular function. Additionally, if the submodular function possess a property called supermodularity of conditioning, then we can provide a method to bound the performance based purely on pairwise information. The proposed algorithms offer significant computational speedups over a traditional greedy strategy. A by-product of our study is the introduction of two new notions of curvature, the $k$-Marginal Curvature and the $k$-Cardinality Curvature. Finally, we present experiments highlighting the performance of our proposed algorithms in terms of approximation and time complexity., Comment: 14 pages, 8 figures

In this paper, we study the well-known team orienteering problem where a fleet of robots collects rewards by visiting locations. Usually, the rewards are assumed to be known to the robots; however, in applications such as environmental monitoring or scene reconstruction, the rewards are often subjective and specifying them is challenging. We propose a framework to learn the unknown preferences of the user by presenting alternative solutions to them, and the user provides a ranking on the proposed alternative solutions. We consider the two cases for the user: 1) a deterministic user which provides the optimal ranking for the alternative solutions, and 2) a noisy user which provides the optimal ranking according to an unknown probability distribution. For the deterministic user we propose a framework to minimize a bound on the maximum deviation from the optimal solution, namely regret. We adapt the approach to capture the noisy user and minimize the expected regret. Finally, we demonstrate the importance of learning user preferences and the performance of the proposed methods in an extensive set of experimental results using real world datasets for environmental monitoring problems.

In this paper, we consider the problem of allocating human operators in a system with multiple semi-autonomous robots. Each robot is required to perform an independent sequence of tasks, subjected to a chance of failing and getting stuck in a fault state at every task. If and when required, a human operator can assist or teleoperate a robot. Conventional MDP techniques used to solve such problems face scalability issues due to exponential growth of state and action spaces with the number of robots and operators. In this paper we derive conditions under which the operator allocation problem is indexable, enabling the use of the Whittle index heuristic. The conditions can be easily checked to verify indexability, and we show that they hold for a wide range of problems of interest. Our key insight is to leverage the structure of the value function of individual robots, resulting in conditions that can be verified separately for each state of each robot. We apply these conditions to two types of transitions commonly seen in remote robot supervision systems. Through numerical simulations, we demonstrate the efficacy of Whittle index policy as a near-optimal and scalable approach that outperforms existing scalable methods., Comment: 11 pages + 4 page Appendix, 7 Figures

Today's robots are increasingly interacting with people and need to efficiently learn inexperienced user's preferences. A common framework is to iteratively query the user about which of two presented robot trajectories they prefer. While this minimizes the users effort, a strict choice does not yield any information on how much one trajectory is preferred. We propose scale feedback, where the user utilizes a slider to give more nuanced information. We introduce a probabilistic model on how users would provide feedback and derive a learning framework for the robot. We demonstrate the performance benefit of slider feedback in simulations, and validate our approach in two user studies suggesting that scale feedback enables more effective learning in practice., Comment: 16 pages, 15 figures, 3 tables. Published at Conference on Robot Learning (CoRL) 2021

In this paper, we tackle the problem of planning an optimal coverage path for a robot operating indoors. Many existing approaches attempt to discourage turns in the path by covering the environment along the least number of coverage lines, i.e., straight-line paths. This is because turning not only slows down the robot but also negatively affects the quality of coverage, e.g., tools like cameras and cleaning attachments commonly have poor performance around turns. The problem of minimizing coverage lines however is typically solved using heuristics that do not guarantee optimality. In this work, we propose a turn-minimizing coverage planning method that computes the optimal number of axis-parallel (horizontal/vertical) coverage lines for the environment in polynomial time. We do this by formulating a linear program (LP) that optimally partitions the environment into axis-parallel ranks (non-intersecting rectangles of width equal to the tool width). We then generate coverage paths for a set of real-world indoor environments and compare the results with state-of-the-art coverage approaches., Comment: 8 pages, 9 figures, submitted to RA-L with IROS 2022 option

Lattice-based planning techniques simplify the motion planning problem for autonomous vehicles by limiting available motions to a pre-computed set of primitives. These primitives are then combined online to generate more complex maneuvers. A set of motion primitives t-span a lattice if, given a real number t at least 1, any configuration in the lattice can be reached via a sequence of motion primitives whose cost is no more than a factor of t from optimal. Computing a minimal t-spanning set balances a trade-off between computed motion quality and motion planning performance. In this work, we formulate this problem for an arbitrary lattice as a mixed integer linear program. We also propose an A*-based algorithm to solve the motion planning problem using these primitives. Finally, we present an algorithm that removes the excessive oscillations from planned motions -- a common problem in lattice-based planning. Our method is validated for autonomous driving in both parking lot and highway scenarios., Comment: 12 pages, 9 figures, 2 tables, accepted to IEEE Transactions on Intelligent Transportation Systems (preprint)

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods., Comment: 13 pages, 11 figures, submitted to IEEE Transactions on Intelligent Vehicles

Control barrier functions have been widely used for synthesizing safety-critical controls, often via solving quadratic programs. However, the existence of Gaussian-type noise may lead to unsafe actions and result in severe consequences. In this paper, we study systems modeled by stochastic differential equations (SDEs) driven by Brownian motions. We propose a notion of stochastic control barrier functions (SCBFs)and show that SCBFs can significantly reduce the control efforts, especially in the presence of noise, compared to stochastic reciprocal control barrier functions (SRCBFs), and offer a less conservative estimation of safety probability, compared to stochastic zeroing control barrier functions (SZCBFs). Based on this less conservative probabilistic estimation for the proposed notion of SCBFs, we further extend the results to handle high relative degree safety constraints using high-order SCBFs. We demonstrate that the proposed SCBFs achieve good trade-offs of performance and control efforts, both through theoretical analysis and numerical simulations.

Mobile robots are often tasked with repeatedly navigating through an environment whose traversability changes over time. These changes may exhibit some hidden structure, which can be learned. Many studies consider reactive algorithms for online planning, however, these algorithms do not take advantage of the past executions of the navigation task for future tasks. In this paper, we formalize the problem of minimizing the total expected cost to perform multiple start-to-goal navigation tasks on a roadmap by introducing the Learned Reactive Planning Problem. We propose a method that captures information from past executions to learn a motion policy to handle obstacles that the robot has seen before. We propose the LAMP framework, which integrates the generated motion policy with an existing navigation stack. Finally, an extensive set of experiments in simulated and real-world environments show that the proposed method outperforms the state-of-the-art algorithms by 10% to 40% in terms of expected time to travel from start to goal. We also evaluate the robustness of the proposed method in the presence of localization and mapping errors on a real robot.

Control barrier functions have shown great success in addressing control problems with safety guarantees. These methods usually find the next safe control input by solving an online quadratic programming problem. However, model uncertainty is a big challenge in synthesizing controllers. This may lead to the generation of unsafe control actions, resulting in severe consequences. In this paper, we develop a learning framework to deal with system uncertainty. Our method mainly focuses on learning the dynamics of the control barrier function, especially for high relative degree with respect to a system. We show that for each order, the time derivative of the control barrier function can be separated into the time derivative of the nominal control barrier function and a remainder. This implies that we can use a neural network to learn the remainder so that we can approximate the dynamics of the real control barrier function. We show by simulation that our method can generate safe trajectories under parametric uncertainty using a differential drive robot model.

When a robot learns from human examples, most approaches assume that the human partner provides examples of optimal behavior. However, there are applications in which the robot learns from non-expert humans. We argue that the robot should learn not only about the human's objectives, but also about their expertise level. The robot could then leverage this joint information to reduce or increase the frequency at which it provides assistance to its human's partner or be more cautious when learning new skills from novice users. Similarly, by taking into account the human's expertise, the robot would also be able of inferring a human's true objectives even when the human's fails to properly demonstrate these objectives due to a lack of expertise. In this paper, we propose to jointly infer the expertise level and objective function of a human given observations of their (possibly) non-optimal demonstrations. Two inference approaches are proposed. In the first approach, inference is done over a finite, discrete set of possible objective functions and expertise levels. In the second approach, the robot optimizes over the space of all possible hypotheses and finds the objective function and expertise level that best explain the observed human behavior. We demonstrate our proposed approaches both in simulation and with real user data., Comment: 17 pages, TRO Submission

We study active preference learning as a framework for intuitively specifying the behaviour of autonomous robots. In active preference learning, a user chooses the preferred behaviour from a set of alternatives, from which the robot learns the user's preferences, modeled as a parameterized cost function. Previous approaches present users with alternatives that minimize the uncertainty over the parameters of the cost function. However, different parameters might lead to the same optimal behaviour; as a consequence the solution space is more structured than the parameter space. We exploit this by proposing a query selection that greedily reduces the maximum error ratio over the solution space. In simulations we demonstrate that the proposed approach outperforms other state of the art techniques in both learning efficiency and ease of queries for the user. Finally, we show that evaluating the learning based on the similarities of solutions instead of the similarities of weights allows for better predictions for different scenarios.

In this paper, we revisit the distributed coverage control problem with multiple robots on both metric graphs and in non-convex continuous environments. Traditionally, the solutions provided for this problem converge to a locally optimal solution with no guarantees on the quality of the solution. We consider sub-additive sensing functions, which capture the scenarios where sensing an event requires the robot to visit the event location. For these sensing functions, we provide the first constant factor approximation algorithms for the distributed coverage problem. The approximation results require twice the conventional communication range in the existing coverage algorithms. However, we show through extensive simulation results that the proposed approximation algorithms outperform several existing algorithms in convex, non-convex continuous, and discrete environments even with the conventional communication ranges. Moreover, the proposed algorithms match the state-of-the-art centralized algorithms in the solution quality.

In this paper, we propose a model-free reinforcement learning method to synthesize control policies for motion planning problems with continuous states and actions. The robot is modelled as a labeled discrete-time Markov decision process (MDP) with continuous state and action spaces. Linear temporal logics (LTL) are used to specify high-level tasks. We then train deep neural networks to approximate the value function and policy using an actor-critic reinforcement learning method. The LTL specification is converted into an annotated limit-deterministic B\"uchi automaton (LDBA) for continuously shaping the reward so that dense rewards are available during training. A na\"ive way of solving a motion planning problem with LTL specifications using reinforcement learning is to sample a trajectory and then assign a high reward for training if the trajectory satisfies the entire LTL formula. However, the sampling complexity needed to find such a trajectory is too high when we have a complex LTL formula for continuous state and action spaces. As a result, it is very unlikely that we get enough reward for training if all sample trajectories start from the initial state in the automata. In this paper, we propose a method that samples not only an initial state from the state space, but also an arbitrary state in the automata at the beginning of each training episode. We test our algorithm in simulation using a car-like robot and find out that our method can learn policies for different working configurations and LTL specifications successfully.

This paper characterizes safe following distances for on-road driving when vehicles can avoid collisions by either braking or by swerving into an adjacent lane. In particular, we focus on safety as defined in the Responsibility-Sensitive Safety (RSS) framework. We extend RSS by introducing swerve manoeuvres as a valid response in addition to the already present brake manoeuvre. These swerve manoeuvres use the more realistic kinematic bicycle model rather than the double integrator model of RSS. When vehicles are able to swerve and brake, it is shown that their required safe following distance at higher speeds is less than that required through braking alone. In addition, when all vehicles follow this new distance, they are provably safe. The use of the kinematic bicycle model is then validated by comparing these swerve manoeuvres to that of a dynamic single-track model.

Accurate early diagnosis and monitoring of neurodegenerative conditions is essential for effective disease management and delivery of medication and treatment. This research develops automatic methods for detecting brain imaging preclinical biomarkers for Parkinson's disease (PD) by considering the novel application of evolutionary algorithms. A fundamental novel element of this work is the use of evolutionary algorithms to both map and predict the functional connectivity in patients using resting state functional MRI data taken from the PPMI to identify PD progression biomarkers. Specifically, Cartesian Genetic Programming was used to classify DCM data as well as time-series data. The findings were validated using two other commonly used classification methods (Artificial Neural Networks and Support Vector Machines) and by employing k-fold cross-validation. Across DCM and time-series analyses, findings revealed maximum accuracies of 75.21% for early stage (prodromal) PD patients versus healthy controls, 85.87% for PD patients versus prodromal PD patients, and 92.09% for PD patients versus healthy controls. Prodromal PD patients were classified from healthy controls with high accuracy - this is notable and represents the key finding of this research since current methods of diagnosing prodromal PD have both low reliability and low accuracy. Furthermore, Cartesian Genetic Programming provided comparable performance accuracy relative to ANN and SVM. Evolutionary algorithms enable us to decode the classifier in terms of understanding the data inputs that are used, more easily than in ANN and SVM. Hence, these findings underscore the relevance of both DCM analyses for classification and CGP as a novel classification tool for brain imaging data with medical implications for disease diagnosis, particularly in early and asymptomatic stages.

This paper focuses on the problem of controlling self-interested drivers in ride-sourcing applications. Each driver has the objective of maximizing its profit, while the ride-sourcing company focuses on customer experience by seeking to minimizing the expected wait time for pick-up. These objectives are not usually aligned, and the company has no direct control on the waiting locations of the drivers. In this paper, we provide two indirect control methods to optimize the set of waiting locations of the drivers, thereby minimizing the expected wait time of the customers: 1) sharing the location of all drivers with a subset of drivers, and 2) paying the drivers to relocate. We show that finding the optimal control for each method is NP-hard and we provide algorithms to find near-optimal control in each case. We evaluate the performance of the proposed control methods on real-world data and show that we can achieve between 20% to 80% improvement in the expected response., Comment: 8 pages

In this paper we investigate the problem of using a UAV to provide current map information of the environment in front of a moving ground vehicle. We propose a simple coverage plan called a conformal lawn mower plan that enables a UAV to scan the route ahead of the ground vehicle. The plan requires only limited knowledge of the ground vehicle's future path. For a class of curvature-constrained ground vehicle paths, we show that the proposed plan requires a UAV velocity that is no more than twice the velocity required to cover the optimal plan. We also establish necessary and sufficient UAV velocities, relative to the ground vehicle velocity, required to successfully cover any path in the curvature restricted set. In simulation, we validate the proposed plan, showing that the required velocity to provide coverage is strongly related to the curvature of the ground vehicle's path. Our results also illustrate the relationship between mapping requirements and the relative velocities of the UAV and ground vehicle., Comment: Detailed version of the 2019 IEEE Conference on Decision and Control paper

An important challenge in human-robot interaction (HRI) is enabling non-expert users to specify complex tasks for autonomous robots. Recently, active preference learning has been applied in HRI to interactively shape a robot's behavior. We study a framework where users specify constraints on allowable robot movements on a graphical interface, yielding a robot task specification. However, users may not be able to accurately assess the impact of such constraints on the performance of a robot. Thus, we revise the specification by iteratively presenting users with alternative solutions where some constraints might be violated, and learn about the importance of the constraints from the users' choices between these alternatives. We demonstrate our framework in a user study with a material transport task in an industrial facility. We show that nearly all users accept alternative solutions and thus obtain a revised specification through the learning process, and that the revision leads to a substantial improvement in robot performance. Further, the learning process reduces the variances between the specifications from different users and, thus, makes the specifications more similar. As a result, the users whose initial specifications had the largest impact on performance benefit the most from the interactive learning., Comment: The International Journal of Robotics Research, Mar. 2020

In this paper we consider the problem of computing an optimal set of motion primitives for a lattice planner. The objective we consider is to compute a minimal set of motion primitives that t-span a configuration space lattice. A set of motion primitives t-span a lattice if, given a real number t greater or equal to one, any configuration in the lattice can be reached via a sequence of motion primitives whose cost is no more than t times the cost of the optimal path to that configuration. Determining the smallest set of t-spanning motion primitives allows for quick traversal of a state lattice in the context of robotic motion planning, while maintaining a t-factor adherence to the theoretically optimal path. While several heuristics exist to determine a t-spanning set of motion primitives, these are presented without guarantees on the size of the set relative to optimal. This paper provides a proof that the minimal t-spanning control set problem for a lattice defined over an arbitrary robot configuration space is NP-complete, and presents a compact mixed integer linear programming formulation to compute an optimal t-spanner. We show that solutions obtained by the mixed integer linear program have significantly fewer motion primitives than state of the art heuristic algorithms, and out perform a set of standard primitives used in robotic path planning., Comment: 8 pages, 5 figures, 2 tables

In this paper we study a multi-robot path planning problem for persistent monitoring of an environment. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum time spent by the robots between visits to that vertex, called the latency, and the objective is to find the minimum number of robots that can satisfy these latency constraints. The decision version of this problem is known to be PSPACE-complete. We present a $O(\log \rho)$ approximation algorithm for the problem where $\rho$ is the ratio of the maximum and the minimum latency constraints. We also present an orienteering based heuristic to solve the problem and show through simulations that in most of the cases the heuristic algorithm gives better solutions than the approximation algorithm. We evaluate our algorithms on large problem instances in a patrolling scenario and in a persistent scene reconstruction application. We also compare the algorithms with an existing solver on benchmark instances., Comment: Detailed version of the 2019 American Control Conference paper

This paper introduces a method to compute a sparse lattice planner control set that is suited to a particular task by learning from a representative dataset of vehicle paths. To do this, we use a scoring measure similar to the Fr\'echet distance and propose an algorithm for evaluating a given control set according to the scoring measure. Control actions are then selected from a dense control set according to an objective function that rewards improvements in matching the dataset while also encouraging sparsity. This method is evaluated across several experiments involving real and synthetic datasets, and it is shown to generate smaller control sets when compared to the previous state-of-the-art lattice control set computation technique, with these smaller control sets maintaining a high degree of manoeuvrability in the required task. This results in a planning time speedup of up to 4.31x when using the learned control set over the state-of-the-art computed control set. In addition, we show the learned control sets are better able to capture the driving style of the dataset in terms of path curvature., Comment: Accepted to the 2019 IEEE Intelligent Vehicles Symposium

Specifying complex task behaviours while ensuring good robot performance may be difficult for untrained users. We study a framework for users to specify rules for acceptable behaviour in a shared environment such as industrial facilities. As non-expert users might have little intuition about how their specification impacts the robot's performance, we design a learning system that interacts with the user to find an optimal solution. Using active preference learning, we iteratively show alternative paths that the robot could take on an interface. From the user feedback ranking the alternatives, we learn about the weights that users place on each part of their specification. We extend the user model from our previous work to a discrete Bayesian learning model and introduce a greedy algorithm for proposing alternative that operates on the notion of equivalence regions of user weights. We prove that with this algorithm the revision active learning process converges on the user-optimal path. In simulations on realistic industrial environments, we demonstrate the convergence and robustness of our approach.

We consider a class of distributed submodular maximization problems in which each agent must choose a single strategy from its strategy set. The global objective is to maximize a submodular function of the strategies chosen by each agent. When choosing a strategy, each agent has access to only a limited number of other agents' choices. For each of its strategies, an agent can evaluate its marginal contribution to the global objective given its information. The main objective is to investigate how this limitation of information about the strategies chosen by other agents affects the performance when agents make choices according to a local greedy algorithm. In particular, we provide lower bounds on the performance of greedy algorithms for submodular maximization, which depend on the clique number of a graph that captures the information structure. We also characterize graph-theoretic upper bounds in terms of the chromatic number of the graph. Finally, we demonstrate how certain graph properties limit the performance of the greedy algorithm. Simulations on several common models for random networks demonstrate our results., Comment: 11 pages, 8 figures

In this paper we consider discrete robot path planning problems on metric graphs. We propose a clustering method, Gamma-Clustering for the planning graph that significantly reduces the number of feasible solutions, yet retains a solution within a constant factor of the optimal. By increasing the input parameter Gamma, the constant factor can be decreased, but with less reduction in the search space. We provide a simple polynomial- time algorithm for finding optimal Gamma-Clusters, and show that for a given Gamma, this optimal is unique. We demonstrate the effectiveness of the clustering method on traveling salesman instances, showing that for many instances we obtain significant reductions in computation time with little to no reduction in solution quality., Comment: 11 pages, 6 figures, 1 table, ACC 2016

In this paper, we address the problem of computing optimal paths through three consecutive points for the curvature-constrained forward moving Dubins vehicle. Given initial and final configurations of the Dubins vehicle, and a midpoint with an unconstrained heading, the objective is to compute the midpoint heading that minimizes the total Dubins path length. We provide a novel geometrical analysis of the optimal path, and establish new properties of the optimal Dubins' path through three points. We then show how our method can be used to quickly refine Dubins TSP tours produced using state-of-the-art techniques. We also provide extensive simulation results showing the improvement of the proposed approach in both runtime and solution quality over the conventional method of uniform discretization of the heading at the mid-point, followed by solving the minimum Dubins path for each discrete heading., Comment: Extended version of IEEE CDC 2016 paper

In this paper we consider a robot patrolling problem in which events arrive randomly over time at the vertices of a graph. When an event arrives it remains active for a random amount of time. If that time active exceeds a certain threshold, then we say that the event is a true event; otherwise it is a false event. The robot(s) can traverse the graph to detect newly arrived events, and can revisit these events in order to classify them as true or false. The goal is to plan robot paths that maximize the number of events that are correctly classified, with the constraint that there are no false positives. We show that the offline version of this problem is NP-hard. We then consider a simple patrolling policy based on the traveling salesman tour, and characterize the probability of correctly classifying an event. We investigate the problem when multiple robots follow the same path, and we derive the optimal (and not necessarily uniform) spacing between robots on the path., Comment: Extended version of IEEE CDC 2014 paper