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Playing the cup-and-ball game is an intriguing task for robotics research since it abstracts important problem characteristics including system nonlinearity, contact forces and precise positioning as terminal goal. In this paper, we present a learning model based control strategy for the cup-and-ball game, where a Universal Robots UR5e manipulator arm learns to catch a ball in one of the cups on a Kendama. Our control problem is divided into two sub-tasks, namely $(i)$ swinging the ball up in a constrained motion, and $(ii)$ catching the free-falling ball. The swing-up trajectory is computed offline, and applied in open-loop to the arm. Subsequently, a convex optimization problem is solved online during the ball's free-fall to control the manipulator and catch the ball. The controller utilizes noisy position feedback of the ball from an Intel RealSense D435 depth camera. We propose a novel iterative framework, where data is used to learn the support of the camera noise distribution iteratively in order to update the control policy. The probability of a catch with a fixed policy is computed empirically with a user specified number of roll-outs. Our design guarantees that probability of the catch increases in the limit, as the learned support nears the true support of the camera noise distribution. High-fidelity Mujoco simulations and preliminary experimental results support our theoretical analysis., Comment: Final paper for IEEE CASE, Hong Kong, August, 2020. First three authors contributed equally

We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with additive disturbance. Set bounds for the system matrices and the additive uncertainty are assumed to be known. We formulate a novel optimization-based constraint tightening strategy around a predicted nominal trajectory which utilizes these bounds. With an appropriately designed terminal cost function and constraint set, we prove robust satisfaction of the imposed constraints by the resulting MPC in closed-loop with the uncertain system, and Input to State Stability of the origin. We highlight the efficacy of our proposed approach via a numerical example., Comment: Dimension of matrices in the MPC problem fixed. Shortened and slightly altered version of this draft published as a full paper in Automatica

This paper presents a distributed learning model predictive control (DLMPC) scheme for distributed linear time invariant systems with coupled dynamics and state constraints. The proposed solution method is based on an online distributed optimization scheme with nearest-neighbor communication. If the control task is iterative and data from previous feasible iterations are available, local data are exploited by the subsystems in order to construct the local terminal set and terminal cost, which guarantee recursive feasibility and asymptotic stability, as well as performance improvement over iterations. In case a first feasible trajectory is difficult to obtain, or the task is non-iterative, we further propose an algorithm that efficiently explores the state-space and generates the data required for the construction of the terminal cost and terminal constraint in the MPC problem in a safe and distributed way. In contrast to other distributed MPC schemes which use structured positive invariant sets, the proposed approach involves a control invariant set as the terminal set, on which we do not impose any distributed structure. The proposed iterative scheme converges to the global optimal solution of the underlying infinite horizon optimal control problem under mild conditions. Numerical experiments demonstrate the effectiveness of the proposed DLMPC scheme.

This work presents a distributed method for multi-vehicle coordination based on nonlinear model predictive control (NMPC) and dual decomposition. Our approach allows the vehicles to coordinate in tight spaces (e.g., busy highway lanes or parking lots) by using a polytopic description of each vehicle's shape and formulating collision avoidance as a dual optimization problem. Our method accommodates heterogeneous teams of vehicles (i.e., vehicles with different polytopic shapes and dynamic models can be part of the same team). Our method allows the vehicles to share their intentions in a distributed fashion without relying on a central coordinator and efficiently provides collision-free trajectories for the vehicles. In addition, our method decouples the individual-vehicles' trajectory optimization from their collision-avoidance objectives enhancing the scalability of the method and allowing one to exploit parallel hardware architectures. All these features are particularly important for vehicular applications, where the systems operate at high-frequency rates in dynamic environments. To validate our method, we apply it in a vehicular application, that is, the autonomous lane-merging of a team of connected vehicles to form a platoon. We compare our design with the centralized NMPC design to show the computational benefits of the proposed distributed algorithm.

In this paper we present a model-predictive control (MPC) based approach for vehicle platooning in an urban traffic setting. Our primary goal is to demonstrate that vehicle platooning has the potential to significantly increase throughput at intersections, which can create bottlenecks in the traffic flow. To do so, our approach relies on vehicle connectivity: vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication. In particular, we introduce a customized V2V message set which features a velocity forecast, i.e. a prediction on the future velocity trajectory, which enables platooning vehicles to accurately maintain short following distances, thereby increasing throughput. Furthermore, V2I communication allows platoons to react immediately to changes in the state of nearby traffic lights, e.g. when the traffic phase becomes green, enabling additional gains in traffic efficiency. We present our design of the vehicle platooning system, and then evaluate performance by estimating the potential gains in terms of throughput using our results from simulation, as well as experiments conducted with real test vehicles on a closed track. Lastly, we briefly overview our demonstration of vehicle platooning on public roadways in Arcadia, CA., Comment: 14 pages, 11 figures, 4 tables

We propose a control design method for linear time-invariant systems that iteratively learns to satisfy unknown polyhedral state constraints. At each iteration of a repetitive task, the method constructs an estimate of the unknown environment constraints using collected closed-loop trajectory data. This estimated constraint set is improved iteratively upon collection of additional data. An MPC controller is then designed to robustly satisfy the estimated constraint set. This paper presents the details of the proposed approach, and provides robust and probabilistic guarantees of constraint satisfaction as a function of the number of executed task iterations. We demonstrate the safety of the proposed framework and explore the safety vs. performance trade-off in a detailed numerical example., Comment: Long version of the published paper for IEEE-CDC 2020. First two authors contributed equally. Added some very relevant citations that were missing

This paper presents a data-driven supervisory energy management strategy (EMS) for plug-in hybrid electric vehicles which leverages Vehicle-to-Cloud connectivity to increase energy efficiency by learning control policies from completed trips. The proposed EMS consists of two layers, a cloud layer and an on-board layer. The cloud layer has two main tasks: the first task is to learn EMS policy parameters from historical trip data, and the second task is to provide the policy parameters along a certain route requested from the vehicle. The on-board layer receives the learned policy parameters from the cloud layer and computes a real-time solution to the powertrain energy management problem, using a model predictive control scheme. The proposed EMS is evaluated on more than 3000 miles (48 independent driving cycles) of real-world trip data, collected along three commuting routes in California. For the routes, the proposed algorithm shows 3.3%, 7.3%, and 6.5% improvement in average MPGe when compared to a baseline EMS., Comment: To appear at the 21st International Federation of Automatic Control (IFAC2020)

We propose a hierarchical learning architecture for predictive control in unknown environments. We consider a constrained nonlinear dynamical system and assume the availability of state-input trajectories solving control tasks in different environments. A parameterized environment model generates state constraints specific to each task, which are satisfied by the stored trajectories. Our goal is to find a feasible trajectory for a new task in an unknown environment. From stored data, we learn strategies in the form of target sets in a reduced-order state space. These strategies are applied to the new task in real-time using a local forecast of the new environment, and the resulting output is used as a terminal region by a low-level receding horizon controller. We show how to i) design the target sets from past data and then ii) incorporate them into a model predictive control scheme with shifting horizon that ensures safety of the closed-loop system when performing the new task. We prove the feasibility of the resulting control policy, and verify the proposed method in a robotic path planning application.

A Task Decomposition method for iterative learning Model Predictive Control (TDMPC) for linear time-varying systems is presented. We consider the availability of state-input trajectories which solve an original task T1, and design a feasible MPC policy for a new task, T2, using stored data from T1. Our approach applies to tasks T2 which are composed of subtasks contained in T1. In this paper we formally define the task decomposition problem, and provide a feasibility proof for the resulting policy. The proposed algorithm reduces the computational burden for linear time-varying systems with piecewise convex constraints. Simulation results demonstrate the improved efficiency of the proposed method on a robotic path-planning task.

We investigate the problem of predicting driver behavior in parking lots, an environment which is less structured than typical road networks and features complex, interactive maneuvers in a compact space. Using the CARLA simulator, we develop a parking lot environment and collect a dataset of human parking maneuvers. We then study the impact of model complexity and feature information by comparing a multi-modal Long Short-Term Memory (LSTM) prediction model and a Convolution Neural Network LSTM (CNN-LSTM) to a physics-based Extended Kalman Filter (EKF) baseline. Our results show that 1) intent can be estimated well (roughly 85% top-1 accuracy and nearly 100% top-3 accuracy with the LSTM and CNN-LSTM model); 2) knowledge of the human driver's intended parking spot has a major impact on predicting parking trajectory; and 3) the semantic representation of the environment improves long term predictions., Comment: * Indicates equal contribution. Accepted at IEEE Intelligent Vehicles Symposium (IV) 2020

We propose a computationally efficient Learning Model Predictive Control (LMPC) scheme for constrained optimal control of a class of nonlinear systems where the state and input can be reconstructed using lifted outputs. For the considered class of systems, we show how to use historical trajectory data collected during iterative tasks to construct a convex value function approximation along with a convex safe set in a lifted space of virtual outputs. These constructions are iteratively updated with historical data and used to synthesize predictive control policies. We show that the proposed strategy guarantees recursive constraint satisfaction, asymptotic stability and non-decreasing closed-loop performance at each policy update. Finally, simulation results demonstrate the effectiveness of the proposed strategy on a piecewise affine (PWA) system, kinematic unicycle and bilinear DC motor.

We present a Model Predictive Control (MPC) strategy for unknown input-affine nonlinear dynamical systems. A non-parametric method is used to estimate the nonlinear dynamics from observed data. The estimated nonlinear dynamics are then linearized over time varying regions of the state space to construct an Affine Time Varying (ATV) model. Error bounds arising from the estimation and linearization procedure are computed by using sampling techniques. The ATV model and the uncertainty sets are used to design a robust Model Predictive Control (MPC) problem which guarantees safety for the unknown system with high probability. A simple nonlinear example demonstrates the effectiveness of the approach where commonly used linearization methods fail., Comment: Fixed double citation in section 4, typos and combined two propositions into one

We present a decentralized minimum-time trajectory optimization scheme based on learning model predictive control for multi-agent systems with nonlinear decoupled dynamics and coupled state constraints. By performing the same task iteratively, data from previous task executions is used to construct and improve local time-varying safe sets and an approximate value function. These are used in a decoupled MPC problem as terminal sets and terminal cost functions. Our framework results in a decentralized controller, which requires no communication between agents over each iteration of task execution, and guarantees persistent feasibility, finite-time closed-loop convergence, and non-decreasing performance of the global system over task iterations. Numerical experiments of a multi-vehicle collision avoidance scenario demonstrate the effectiveness of the proposed scheme., Comment: 8 pages, 2 figures, accepted at Conference on Decision and Control 2020

Advances in vehicular communication technologies are expected to facilitate cooperative driving. Connected and Automated Vehicles (CAVs) are able to collaboratively plan and execute driving maneuvers by sharing their perceptual knowledge and future plans. In this paper, an architecture for autonomous navigation of tight multi-lane platoons travelling on public roads is presented. Using the proposed approach, CAVs are able to form single or multi-lane platoons of various geometrical configurations. They are able to reshape and adjust their configurations according to changes in the environment. The proposed architecture consists of two main components: an offline motion planner system and an online hierarchical control system. The motion planner uses an optimization-based approach for cooperative formation and reconfiguration in tight spaces. A constrained optimization scheme is used to plan smooth, dynamically feasible and collision-free trajectories for all the vehicles within the platoon. The paper addresses online computation limitations by employing a family of maneuvers precomputed offline and stored on a look-up table on the vehicles. The online hierarchical control system is composed of three levels: a traffic operation system (TOS), a decision-maker, and a path-follower. The TOS determines the desired platoon reconfiguration. The decision-maker checks the feasibility of the reconfiguration plan. The reconfiguration maneuver is executed by a low-level path-following feedback controller in real-time. The effectiveness of the approach is demonstrated through simulations of three case studies: 1) formation reconfiguration 2) obstacle avoidance, and 3) benchmarking against behavior-based planning in which the desired formation is achieved using a sequence of motion primitives. Videos and software can be found online https://github.com/RoyaFiroozi/Centralized-Planning.

In this paper, we propose a novel framework for approximating the explicit MPC policy for linear parameter-varying systems using supervised learning. Our learning scheme guarantees feasibility and near-optimality of the approximated MPC policy with high probability. Furthermore, in contrast to most existing approaches that only learn the MPC policy, we also learn the "dual policy", which enables us to keep a check on the approximated MPC's optimality online during the control process. If the check deems the control input from the approximated MPC policy safe and near-optimal, then it is applied to the plant, otherwise a backup controller is invoked, thus filtering out (severely) suboptimal control inputs. The backup controller is only invoked with a bounded (low) probability, where the exact probability level can be chosen by the user. Since our framework does not require solving any optimization problem during the control process, it enables the deployment of MPC on resource-constrained systems. Specifically, we illustrate the utility of the proposed framework on a vehicle dynamics control problem. Compared to online optimization methods, we demonstrate a speedup of up to 62x on a desktop computer and 10x on an automotive-grade electronic control unit, while maintaining a high control performance., Comment: First two authors contributed equally. arXiv admin note: text overlap with arXiv:1906.08257

We propose an approach to design a Model Predictive Controller (MPC) for constrained Linear Time Invariant systems performing an iterative task. The system is subject to an additive disturbance, and the goal is to learn to satisfy state and input constraints robustly. Using disturbance measurements after each iteration, we construct Confidence Support sets, which contain the true support of the disturbance distribution with a given probability. As more data is collected, the Confidence Supports converge to the true support of the disturbance. This enables design of an MPC controller that avoids conservative estimate of the disturbance support, while simultaneously bounding the probability of constraint violation. The efficacy of the proposed approach is then demonstrated with a detailed numerical example., Comment: Added a set of important references that were missing

A robust Learning Model Predictive Controller (LMPC) for uncertain systems performing iterative tasks is presented. At each iteration of the control task the closed-loop state, input and cost are stored and used in the controller design. This paper first illustrates how to construct robust invariant sets and safe control policies exploiting historical data. Then, we propose an iterative LMPC design procedure, where data generated by a robust controller at iteration $j$ are used to design a robust LMPC at the next $j+1$ iteration. We show that this procedure allows us to iteratively enlarge the domain of the control policy and it guarantees recursive constraints satisfaction, input to state stability and performance bounds for the certainty equivalent closed-loop system. The use of an adaptive prediction horizon is the key element of the proposed design. The effectiveness of the proposed control scheme is illustrated on a linear system subject to bounded additive disturbance.

In this paper we present a Learning Model Predictive Control (LMPC) strategy for linear and nonlinear time optimal control problems. Our work builds on existing LMPC methodologies and it guarantees finite time convergence properties for the closed-loop system. We show how to construct a time varying safe set and terminal cost function using closed-loop data. The resulting LMPC policy is time varying and it guarantees recursive constraint satisfaction and non-decreasing performance. Computational efficiency is obtained by convexifing the safe set and terminal cost function. We demonstrate that, for a class of nonlinear system and convex constraints, the convex LMPC formulation guarantees recursive constraint satisfaction and non-decreasing performance. Finally, we illustrate the effectiveness of the proposed strategies on minimum time obstacle avoidance and racing examples.

We propose a reference-free learning model predictive controller for periodic repetitive tasks. We consider a problem in which dynamics, constraints and stage cost are periodically time-varying. The controller uses the closed-loop data to construct a time-varying terminal set and a time-varying terminal cost. We show that the proposed strategy in closed-loop with linear and nonlinear systems guarantees recursive constraints satisfaction, non-increasing open-loop cost, and that the open-loop and closed-loop cost are the same at convergence. Simulations are presented for different repetitive tasks, both for linear and nonlinear systems., Comment: 2020 European Control Conference, Saint Petersburg, Russia. Extended version of the conference paper

We propose an Adaptive MPC framework for uncertain linear systems to achieve robust satisfaction of state and input constraints. The uncertainty in the system is assumed additive, state dependent, and globally Lipschitz with a known Lipschitz constant. We use a non-parametric technique for online identification of the system uncertainty by approximating its graph via envelopes defined by quadratic constraints. At any given time, by solving a set of convex optimization problems, the MPC controller guarantees robust constraint satisfaction for the closed loop system for all possible values of system uncertainty modeled by the envelope. The uncertainty envelope is refined with data using Set Membership Methods. We highlight the efficacy of the proposed framework via a detailed numerical example., Comment: Accepted for European Control Conference (ECC), May 2020, Saint Petersburg, Russia

In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using envelopes described by quadratic constraints. The proposed approach is then demonstrated on two control applications: (i) computation of tractable bounds for unmodeled dynamics, and (ii) computation of positive invariant sets. We further highlight the efficacy of the proposed approach via a detailed numerical example.

The problem of autonomous parking of vehicle fleets is addressed in this paper. We present a system-level modeling and control framework which allows investigating different vehicle parking strategies while taking into account path planning and collision avoidance. The proposed approach decouples the problem into a centralized parking spot allocation and path generation, and a decentralized collision avoidance control. This paper presents the hierarchical framework and algorithmic details. Extensive simulations are used to assess several allocation strategies in terms of total fleet parking time and queue length. In particular, we describe how Braess's paradox can be observed for parking vehicle fleets., Comment: Accepted at IEEE American Control Conference (ACC), Denver, CO, USA, July 2020

This paper deals with the problem of formulating an adaptive Model Predictive Control strategy for constrained uncertain systems. We consider a linear system, in presence of bounded time varying additive uncertainty. The uncertainty is decoupled as the sum of a process noise with known bounds, and a time varying offset that we wish to identify. The time varying offset uncertainty is assumed unknown point-wise in time. Its domain, called the Feasible Parameter Set, and its maximum rate of change are known to the control designer. As new data becomes available, we refine the Feasible Parameter Set with a Set Membership Method based approach, using the known bounds on process noise. We consider two separate cases of robust and probabilistic constraints on system states, with hard constraints on actuator inputs. In both cases, we robustly satisfy the imposed constraints for all possible values of the offset uncertainty in the Feasible Parameter Set. By imposing adequate terminal conditions, we prove recursive feasibility and stability of the proposed algorithms. The efficacy of the proposed robust and stochastic Adaptive MPC algorithms is illustrated with detailed numerical examples., Comment: Corrected Figure 4, and added a missing compactness and containment of origin assumption for the constraint sets. The brief version of this will been published as a technical note in IEEE Transactions on Automatic Control, Vol 66, June 2021

We present a hardware-in-the-loop (HIL) simulation setup for repeatable testing of Connected Automated Vehicles (CAVs) in dynamic, real-world scenarios. Our goal is to test control and planning algorithms and their distributed implementation on the vehicle hardware and, possibly, in the cloud. The HIL setup combines PreScan for perception sensors, road topography, and signalized intersections; Vissim for traffic micro-simulation; ETAS DESK-LABCAR/a dynamometer for vehicle and powertrain dynamics; and on-board electronic control units for CAV real time control. Models of traffic and signalized intersections are driven by real-world measurements. To demonstrate this HIL simulation setup, we test a Model Predictive Control approach for maximizing energy efficiency of CAVs in urban environments., Comment: This work was presented at the 14th International Symposium in Advanced Vehicle Control (AVEC '18)

We present a predictive cruise controller which iteratively improves the fuel economy of a vehicle traveling along the same route every day. Our approach uses historical data from previous trip iterations to improve vehicle performance while guaranteeing a desired arrival time. The proposed predictive cruise controller is based on the recently developed Learning Model Predictive Control (LMPC) framework, which is extended in this paper to include time constraints. Moreover, we reformulate the modified LMPC with time constraint into a computationally tractable form. Our method is presented in detail, applied to the predictive cruise control problem, and validated through simulations., Comment: This work was presented at the 14th International Symposium in Advanced Vehicle Control (AVEC '18)

In this paper, we propose a novel framework for approximating the explicit MPC law for linear parameter-varying systems using supervised learning. In contrast to most existing approaches, we not only learn the control policy, but also a "certificate policy", that allows us to estimate the sub-optimality of the learned control policy online, during execution-time. We learn both these policies from data using supervised learning techniques, and also provide a randomized method that allows us to guarantee the quality of each learned policy, measured in terms of feasibility and optimality. This in turn allows us to bound the probability of the learned control policy of being infeasible or suboptimal, where the check is performed by the certificate policy. Since our algorithm does not require the solution of an optimization problem during run-time, it can be deployed even on resource-constrained systems. We illustrate the efficacy of the proposed framework on a vehicle dynamics control problem where we demonstrate a speedup of up to two orders of magnitude compared to online optimization with minimal performance degradation., Comment: IEEE American Control Conference (ACC) 2019, July 9-12, Philadelphia, PA, USA

Reinforcement learning (RL) for robotics is challenging due to the difficulty in hand-engineering a dense cost function, which can lead to unintended behavior, and dynamical uncertainty, which makes exploration and constraint satisfaction challenging. We address these issues with a new model-based reinforcement learning algorithm, Safety Augmented Value Estimation from Demonstrations (SAVED), which uses supervision that only identifies task completion and a modest set of suboptimal demonstrations to constrain exploration and learn efficiently while handling complex constraints. We then compare SAVED with 3 state-of-the-art model-based and model-free RL algorithms on 6 standard simulation benchmarks involving navigation and manipulation and a physical knot-tying task on the da Vinci surgical robot. Results suggest that SAVED outperforms prior methods in terms of success rate, constraint satisfaction, and sample efficiency, making it feasible to safely learn a control policy directly on a real robot in less than an hour. For tasks on the robot, baselines succeed less than 5% of the time while SAVED has a success rate of over 75% in the first 50 training iterations. Code and supplementary material is available at https://tinyurl.com/saved-rl., Comment: Robotics and Automation Letters and International Conference on Robotics and Automation 2020. First two authors contributed equally

Robust estimation of vehicle sideslip angle is essential for stability control applications. However, the direct measurement of sideslip angle is expensive for production vehicles. This paper presents a novel sideslip estimation algorithm which relies only on sensors available on passenger and commercial vehicles. The proposed method uses both kinematics and dynamics vehicle models to construct extended Kalman filter observers. The estimate relies on the results provided from the dynamics model observer where the tire cornering stiffness parameters are updated using the information provided from the kinematics model observer. The stability property of the proposed algorithm is discussed and proven. Finally, multiple experimental tests are conducted to verify its performance in practice. The results show that the proposed approach provides smooth and accurate sideslip angle estimation. In addition, our novel algorithm provides reliable estimates of bank angles and lateral acceleration sensor bias., Comment: 13 pages, 20 figures, IEEE Transaction on Vehicular Technology

In this paper we propose a distributed model predictive control architecture to coordinate the longitudinal motion of a vehicle platoon at a signalized intersection. Our control approach is cooperative; we use vehicle-to-vehicle (V2V) communication in order to maintain small inter-vehicle distances and correspondingly achieve large vehicle throughput at an intersection. We study the trade-off between safety and road throughput for this problem. In particular, we present the link between traffic efficiency gains in terms of throughput, and safety of the connected platoon measured as trust on the predicted speed profile of other vehicles in the network., Comment: 6 pages, 4 figures, 2 tables

We present a sample-based Learning Model Predictive Controller (LMPC) for constrained uncertain linear systems subject to bounded additive disturbances. The proposed controller builds on earlier work on LMPC for deterministic systems. First, we introduce the design of the safe set and value function used to guarantee safety and performance improvement. Afterwards, we show how these quantities can be approximated using noisy historical data. The effectiveness of the proposed approach is demonstrated on a numerical example. We show that the proposed LMPC is able to safely explore the state space and to iteratively improve the worst-case closed-loop performance, while robustly satisfying state and input constraints.

This paper presents the design of an ecological adaptive cruise controller (ECO-ACC) for a plug-in hybrid vehicle (PHEV) which exploits automated driving and connectivity. Most existing papers for ECO-ACC focus on a short-sighted control scheme. A two-level control framework for long-sighted ECO-ACC was only recently introduced. However, that work is based on a deterministic traffic signal phase and timing (SPaT) over the entire route. In practice, connectivity with traffic lights may be limited by communication range, e.g. just one upcoming traffic light. We propose a two-level receding-horizon control framework for long-sighted ECO-ACC that exploits deterministic SPaT for the upcoming traffic light, and utilizes historical SPaT for other traffic lights within a receding control horizon. We also incorporate a powertrain control mechanism to enhance PHEV energy prediction accuracy. Hardware-in-the-loop simulation results validate the energy savings of the receding-horizon control framework in various traffic scenarios., Comment: To appear at 2019 IEEE Conference on Decision and Control

A task decomposition method for iterative learning model predictive control is presented. We consider a constrained nonlinear dynamical system and assume the availability of state-input pair datasets which solve a task T1. Our objective is to find a feasible model predictive control policy for a second task, T2, using stored data from T1. Our approach applies to tasks T2 which are composed of subtasks contained in T1. In this paper we propose a formal definition of subtasks and the task decomposition problem, and provide proofs of feasibility and iteration cost improvement over simple initializations. We demonstrate the effectiveness of the proposed method on autonomous racing and robotic manipulation experiments.

As autonomous vehicles (AVs) inch closer to reality, a central requirement for acceptance will be earning the trust of humans in everyday driving situations. In particular, the interaction between AVs and pedestrians is of high importance, as every human is a pedestrian at some point of the day. This paper considers the interaction of a pedestrian and an autonomous vehicle at a mid-block, unsignalized intersection where there is ambiguity over when the pedestrian should cross and when and how the vehicle should yield. By modeling pedestrian behavior through the concept of gap acceptance, the authors show that a hybrid controller with just four distinct modes allows an autonomous vehicle to successfully interact with a pedestrian across a continuous spectrum of possible crosswalk entry behaviors. The controller is validated through extensive simulation and compared to an alternate POMDP solution and experimental results are provided on a research vehicle for a virtual pedestrian.

In this paper we present a Learning Model Predictive Controller (LMPC) for autonomous racing. We model the autonomous racing problem as a minimum time iterative control task, where an iteration corresponds to a lap. In the proposed approach at each lap the race time does not increase compared to the previous lap. The system trajectory and input sequence of each lap are stored and used to systematically update the controller for the next lap. The first contribution of the paper is to propose a LMPC strategy which reduces the computational burden associated with existing LMPC strategies. In particular, we show how to construct a safe set and an approximation to the value function, using a subset of the stored data. The second contribution is to present a system identification strategy for the autonomous racing iterative control task. We use data from previous iterations and the vehicle's kinematics equations to build an affine time-varying prediction model. The effectiveness of the proposed strategy is demonstrated by experimental results on the Berkeley Autonomous Race Car (BARC) platform.

This paper presents the design and implementation results of an ecological adaptive cruise controller (ECO-ACC) which exploits driving automation and connectivity. The controller avoids front collisions and traffic light violations, and is designed to reduce the energy consumption of connected automated vehicles by utilizing historical and real-time signal phase and timing data of traffic lights that adapt to the current traffic conditions. We propose an optimization-based generation of a reference velocity, and a velocity-tracking model predictive controller that avoids front collisions and violations. We present an experimental setup encompassing the real vehicle and controller in the loop, and an environment simulator in which the traffic flow and the traffic light patterns are calibrated on real-world data. We present and analyze simulation and experimental results, finding a significant potential for energy consumption reduction, even in the presence of traffic., Comment: Submitted to 2019 American Control Conference

We present the design of a safe Adaptive Cruise Control (ACC) which uses road grade and lead vehicle motion preview. The ACC controller is designed by using a Model Predictive Control (MPC) framework to optimize comfort, safety, energy-efficiency and speed tracking accuracy. Safety is achieved by computing a robust invariant terminal set. The paper presents a novel approach to compute such set which is less conservative than existing methods. The proposed controller ensures safe inter-vehicle spacing at all times despite changes in the road grade and uncertainty in the predicted motion of the lead vehicle. Simulation results compare the proposed controller with a controller that does not incorporate prior grade knowledge on two scenarios including car-following and autonomous intersection crossing. The results demonstrate the effectiveness of the proposed control algorithm.

A data-based policy for iterative control task is presented. The proposed strategy is model-free and can be applied whenever safe input and state trajectories of a system performing an iterative task are available. These trajectories, together with a user-defined cost function, are exploited to construct a piecewise affine approximation to the value function. Approximated value functions are then used to evaluate the control policy by solving a linear program. We show that for linear system subject to convex cost and constraints, the proposed strategy guarantees closed-loop constraint satisfaction and performance bounds on the closed-loop trajectory. We evaluate the proposed strategy in simulations and experiments, the latter carried out on the Berkeley Autonomous Race Car (BARC) platform. We show that the proposed strategy is able to reduce the computation time by one order of magnitude while achieving the same performance as our model-based control algorithm., Comment: submitted for conference publication

In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional decision variables. In particular, given a metric for adjusting the uncertainty sets, we address the question of determining the optimal size and shape of those uncertainty sets, while ensuring robust constraint satisfaction. The focus of this paper is on ensuring constraint satisfaction over an infinite horizon, also known as persistent feasibility. We show that, similar as in standard Robust MPC, persistent feasibility can be guaranteed if the terminal set is an invariant set with respect to both the state of the system and the adjustable uncertainty set. We also present an algorithm for computing such invariant sets, and illustrate the effectiveness of our approach in a cooperative adaptive cruise control application., Comment: Full version of the eponymous work at CDC 2018

We propose a map-aided vehicle localization method for GPS-denied environments. This approach exploits prior knowledge of the road grade map and vehicle on-board sensor measurements to accurately estimate the longitudinal position of the vehicle. Real-time localization is crucial to systems that utilize position-dependent information for planning and control. We validate the effectiveness of the localization method on a hierarchical control system. The higher level planner optimizes the vehicle velocity to minimize the energy consumption for a given route by employing traffic condition and road grade data. The lower level is a cruise control system that tracks the position-dependent optimal reference velocity. Performance of the proposed localization algorithm is evaluated using both simulations and experiments.

This paper proposes an Adaptive Robust Model Predictive Control strategy for lateral control in lane keeping problems, where we continuously learn an unknown, but constant steering angle offset present in the steering system. Longitudinal velocity is assumed constant. The goal is to minimize the outputs, which are distance from lane center line and the steady state heading angle error, while satisfying respective safety constraints. We do not assume perfect knowledge of the vehicle lateral dynamics model and estimate and adapt in real-time the maximum possible bound of the steering angle offset from data using a robust Set Membership Method based approach. Our approach is even well-suited for scenarios with sharp curvatures on high speed, where obtaining a precise model bias for constrained control is difficult, but learning from data can be helpful. We ensure persistent feasibility using a switching strategy during change of lane curvature. The proposed methodology is general and can be applied to more complex vehicle dynamics problems., Comment: 14th International Symposium on Advanced Vehicle Control (AVEC), Beijing, China, July 2018

This paper proposes an Adaptive Learning Model Predictive Control strategy for uncertain constrained linear systems performing iterative tasks. The additive uncertainty is modeled as the sum of a bounded process noise and an unknown constant offset. As new data becomes available, the proposed algorithm iteratively adapts the believed domain of the unknown offset after each iteration. An MPC strategy robust to all feasible offsets is employed in order to guarantee recursive feasibility. We show that the adaptation of the feasible offset domain reduces conservatism of the proposed strategy, compared to classical robust MPC strategies. As a result, the controller performance improves. Performance is measured in terms of following trajectories with lower associated costs at each iteration. Numerical simulations highlight the main advantages of the proposed approach.

This paper proposes an adaptive stochastic Model Predictive Control (MPC) strategy for stable linear time invariant systems in the presence of bounded disturbances. We consider multi-input multi-output systems that can be expressed by a finite impulse response model, whose parameters we estimate using a linear Recursive Least Squares algorithm. Building on the work of [1],[2], our approach is able to handle hard input constraints and probabilistic output constraints. By using tools from distributionally robust optimization, we formulate our MPC design task as a convex optimization problem that can be solved using existing tools. Furthermore, we show that our adaptive stochastic MPC algorithm is persistently feasible. The efficacy of the developed algorithm is demonstrated in a numerical example and the results are compared with the adaptive robust MPC algorithm of [2].

Autonomous driving technology pledges safety, convenience, and energy efficiency. Challenges include the unknown intentions of other road users: communication between vehicles and with the road infrastructure is a possible approach to enhance awareness and enable cooperation. Connected and automated vehicles (CAVs) have the potential to disrupt mobility, extending what is possible with driving automation and connectivity alone. Applications include real-time control and planning with increased awareness, routing with micro-scale traffic information, coordinated platooning using traffic signals information, eco-mobility on demand with guaranteed parking. This paper introduces a control and planning architecture for CAVs, and surveys the state of the art on each functional block therein; the main focus is on techniques to improve energy efficiency. We provide an overview of existing algorithms and their mutual interactions, we present promising optimization-based approaches to CAVs control and identify future challenges.

This paper proposes a new adaptation methodology to find the control inputs for a class of nonlinear systems with time-varying bounded uncertainties. The proposed method does not require any prior knowledge of the uncertainties including their bounds. The main idea is developed under the structure of adaptive sliding mode control; an update law decreases the gain inside and increases the gain outside a vicinity of the sliding surface. The semi-global stability of the closed-loop system and the adaptation error are guaranteed by Lyapunov theory. The simulation results show that the proposed adaptation methodology can reduce the magnitude of the controller gain to the minimum possible value and smooth out the chattering., Comment: 8 pages, 20 figures, 2018 American Control Conference

This paper focuses on the speed planning problem for connected and automated vehicles (CAVs) communicating to traffic lights. The uncertainty of traffic signal timing for signalized intersections on the road is considered. The eco-driving problem is formulated as a data-driven chance constrained robust optimization problem. Effective red light duration (ERD) is defined as a random variable, and describes the feasible passing time through the signalized intersections. In practice, the true probability distribution for ERD is usually unknown. Consequently, a data-driven approach is adopted to formulate chance constraints based on empirical sample data. This incorporates robustness into the eco-driving control problem with respect to uncertain signal timing. Dynamic programming (DP) is employed to solve the optimization problem. Simulation results demonstrate that the proposed method can generate optimal speed reference trajectories with 40% less vehicle fuel consumption, while maintaining the arrival time at a similar level when compared to a modified intelligent driver model (IDM). The proposed control approach significantly improves the controller robustness in the face of uncertain signal timing, without requiring to know the distribution of the random variable a priori., Comment: I want to withdraw the paper to make some revision and corrections

This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid obstacles while moving in an n-dimensional space. The proposed reformulation does not introduce approximations, and applies to general obstacles and controlled objects that can be represented in an n-dimensional space as the finite union of convex sets. Furthermore, we connect our results with the notion of signed distance, which is widely used in traditional trajectory generation algorithms. Our method can be used in generic navigation and trajectory planning tasks, and the smoothness property allows the use of general-purpose gradient- and Hessian-based optimization algorithms. Finally, in case a collision cannot be avoided, our framework allows us to find "least-intrusive" trajectories, measured in terms of penetration. We demonstrate the efficacy of our framework on a quadcopter navigation and automated parking problem, and our numerical experiments suggest that the proposed methods enable real-time optimization-based trajectory planning problems in tight environments. Source code of our implementation is provided at https://github.com/XiaojingGeorgeZhang/OBCA., Comment: 27 pages, 9 figures, 2 tables