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In limbed robotics, end-effectors must serve dual functions, such as both feet for locomotion and grippers for grasping, which presents design challenges. This paper introduces a multi-modal end-effector capable of transitioning between flat and line foot configurations while providing grasping capabilities. MAGPIE integrates 8-axis force sensing using proposed mechanisms with hall effect sensors, enabling both contact and tactile force measurements. We present a computational design framework for our sensing mechanism that accounts for noise and interference, allowing for desired sensitivity and force ranges and generating ideal inverse models. The hardware implementation of MAGPIE is validated through experiments, demonstrating its capability as a foot and verifying the performance of the sensing mechanisms, ideal models, and gated network-based models.

This paper presents a novel approach through the design and implementation of Cycloidal Quasi-Direct Drive actuators for legged robotics. The cycloidal gear mechanism, with its inherent high torque density and mechanical robustness, offers significant advantages over conventional designs. By integrating cycloidal gears into the Quasi-Direct Drive framework, we aim to enhance the performance of legged robots, particularly in tasks demanding high torque and dynamic loads, while still keeping them lightweight. Additionally, we develop a torque estimation framework for the actuator using an Actuator Network, which effectively reduces the sim-to-real gap introduced by the cycloidal drive's complex dynamics. This integration is crucial for capturing the complex dynamics of a cycloidal drive, which contributes to improved learning efficiency, agility, and adaptability for reinforcement learning.

Mixed integer bilinear programs (MIBLPs) offer tools to resolve robotics motion planning problems with orthogonal rotation matrices or static moment balance, but require long solving times. Recent work utilizing data-driven methods has shown potential to overcome this issue allowing for applications on larger scale problems. To solve mixed-integer bilinear programs online with data-driven methods, several re-formulations exist including mathematical programming with complementary constraints (MPCC), and mixed-integer programming (MIP). In this work, we compare the data-driven performances of various MIBLP reformulations using a book placement problem that has discrete configuration switches and bilinear constraints. The success rate, cost, and solving time are compared along with non-data-driven methods. Our results demonstrate the advantage of using data-driven methods to accelerate the solving speed of MIBLPs, and provide references for users to choose the suitable re-formulation., Comment: UR 2024 accepted. arXiv admin note: substantial text overlap with arXiv:2208.13158

This article introduces the development and implementation of the Yummy Operations Robot Initiative (YORI), an innovative, autonomous robotic cooking system. YORI marks a major advancement in culinary automation, adept at handling a diverse range of cooking tasks, capable of preparing multiple dishes simultaneously, and offering the flexibility to adapt to an extensive array of culinary activities. This versatility is achieved through the use of custom tools and appliances operated by a dual arm manipulator utilizing proprioceptive actuators. The use of proprioceptive actuators enables fast yet precise movements, while allowing for accurate force control and effectively mitigating the inevitable impacts encountered in cooking. These factors underscore this technology's boundless potential. A key to YORI's adaptability is its modular kitchen design, which allows for easy adaptations to accommodate a continuously increasing range of culinary tasks. This article provides a comprehensive look at YORI's design process, and highlights its role in revolutionizing the culinary world by enhancing efficiency, consistency, and versatility in food preparation., Comment: This manuscript is 13 pages long, includes 10 figures, and cites 20 references. It is to be submitted

State estimation for legged robots is challenging due to their highly dynamic motion and limitations imposed by sensor accuracy. By integrating Kalman filtering, optimization, and learning-based modalities, we propose a hybrid solution that combines proprioception and exteroceptive information for estimating the state of the robot's trunk. Leveraging joint encoder and IMU measurements, our Kalman filter is enhanced through a single-rigid body model that incorporates ground reaction force control outputs from convex Model Predictive Control optimization. The estimation is further refined through Gated Recurrent Units, which also considers semantic insights and robot height from a Vision Transformer autoencoder applied on depth images. This framework not only furnishes accurate robot state estimates, including uncertainty evaluations, but can minimize the nonlinear errors that arise from sensor measurements and model simplifications through learning. The proposed methodology is evaluated in hardware using a quadruped robot on various terrains, yielding a 65% improvement on the Root Mean Squared Error compared to our VIO SLAM baseline. Code example: https://github.com/AlexS28/OptiState, Comment: Accepted to the 2024 IEEE International Conference on Robotics and Automation (ICRA), May 13-17, in Yokohama, Japan. 7 pages, 5 figures, 1 table

This paper presents SCALER, a versatile free-climbing multi-limbed robot that is designed to achieve tightly coupled simultaneous locomotion and dexterous grasping. Although existing quadruped-limbed robots have shown impressive dexterous skills such as object manipulation, it is essential to balance power-intensive locomotion and dexterous grasping capabilities. We design a torso linkage and a parallel-serial limb to meet such conflicting skills that pose unique challenges in the hardware designs. SCALER employs underactuated two-fingered GOAT grippers that can mechanically adapt and offer 7 modes of grasping, enabling SCALER to traverse extreme terrains with multi-modal grasping strategies. We study the whole-body approach, where SCALER uses its body and limbs to generate additional forces for stable grasping with environments, further enhancing versatility. Furthermore, we improve the GOAT gripper actuation speed to realize more dynamic climbing in a closed-loop control fashion. With these proposed technologies, SCALER can traverse vertical, overhang, upside-down, slippery terrains, and bouldering walls with non-convex-shaped climbing holds under the Earth's gravity.

Domain randomization (DR), which entails training a policy with randomized dynamics, has proven to be a simple yet effective algorithm for reducing the gap between simulation and the real world. However, DR often requires careful tuning of randomization parameters. Methods like Bayesian Domain Randomization (Bayesian DR) and Active Domain Randomization (Adaptive DR) address this issue by automating parameter range selection using real-world experience. While effective, these algorithms often require long computation time, as a new policy is trained from scratch every iteration. In this work, we propose Adaptive Bayesian Domain Randomization via Strategic Fine-tuning (BayRnTune), which inherits the spirit of BayRn but aims to significantly accelerate the learning processes by fine-tuning from previously learned policy. This idea leads to a critical question: which previous policy should we use as a prior during fine-tuning? We investigated four different fine-tuning strategies and compared them against baseline algorithms in five simulated environments, ranging from simple benchmark tasks to more complex legged robot environments. Our analysis demonstrates that our method yields better rewards in the same amount of timesteps compared to vanilla domain randomization or Bayesian DR.

Generating dynamic jumping motions on legged robots remains a challenging control problem as the full flight phase and large landing impact are expected. Compared to quadrupedal robots or other multi-legged robots, bipedal robots place higher requirements for the control strategy given a much smaller footprint. To solve this problem, a novel heuristic landing planner is proposed in this paper. With the momentum feedback during the flight phase, landing locations can be updated to minimize the influence of uncertainties from tracking errors or external disturbances when landing. To the best of our knowledge, this is the first approach to take advantage of the flight phase to reduce the impact of the jump landing which is implemented in the actual robot. By integrating it with a modified kino-dynamics motion planner with centroidal momentum and a low-level controller which explores the whole-body dynamics to hierarchically handle multiple tasks, a complete and versatile jumping control framework is designed in this paper. Extensive results of simulation and hardware jumping experiments on a miniature bipedal robot with proprioceptive actuation are provided to demonstrate that the proposed framework is able to achieve human-like efficient and robust jumping tasks, including directional jump, twisting jump, step jump, and somersaults.

The light and soft characteristics of Buoyancy Assisted Lightweight Legged Unit (BALLU) robots have a great potential to provide intrinsically safe interactions in environments involving humans, unlike many heavy and rigid robots. However, their unique and sensitive dynamics impose challenges to obtaining robust control policies in the real world. In this work, we demonstrate robust sim-to-real transfer of control policies on the BALLU robots via system identification and our novel residual physics learning method, Environment Mimic (EnvMimic). First, we model the nonlinear dynamics of the actuators by collecting hardware data and optimizing the simulation parameters. Rather than relying on standard supervised learning formulations, we utilize deep reinforcement learning to train an external force policy to match real-world trajectories, which enables us to model residual physics with greater fidelity. We analyze the improved simulation fidelity by comparing the simulation trajectories against the real-world ones. We finally demonstrate that the improved simulator allows us to learn better walking and turning policies that can be successfully deployed on the hardware of BALLU.

Humans can effortlessly perform very complex, dexterous manipulation tasks by reacting to sensor observations. In contrast, robots can not perform reactive manipulation and they mostly operate in open-loop while interacting with their environment. Consequently, the current manipulation algorithms either are inefficient in performance or can only work in highly structured environments. In this paper, we present closed-loop control of a complex manipulation task where a robot uses a tool to interact with objects. Manipulation using a tool leads to complex kinematics and contact constraints that need to be satisfied for generating feasible manipulation trajectories. We first present an open-loop controller design using Non-Linear Programming (NLP) that satisfies these constraints. In order to design a closed-loop controller, we present a pose estimator of objects and tools using tactile sensors. Using our tactile estimator, we design a closed-loop controller based on Model Predictive Control (MPC). The proposed algorithm is verified using a 6 DoF manipulator on tasks using a variety of objects and tools. We verify that our closed-loop controller can successfully perform tool manipulation under several unexpected contacts. Video summarizing this work and hardware experiments are found https://youtu.be/VsClK04qDhk., Comment: Accepted to ICRA2023. Video: https://youtu.be/VsClK04qDhk

Achieving highly accurate dynamic or simulator models that are close to the real robot can facilitate model-based controls (e.g., model predictive control or linear-quadradic regulators), model-based trajectory planning (e.g., trajectory optimization), and decrease the amount of learning time necessary for reinforcement learning methods. Thus, the objective of this work is to learn the residual errors between a dynamic and/or simulator model and the real robot. This is achieved using a neural network, where the parameters of a neural network are updated through an Unscented Kalman Filter (UKF) formulation. Using this method, we model these residual errors with only small amounts of data -- a necessity as we improve the simulator/dynamic model by learning directly from real-world operation. We demonstrate our method on robotic hardware (e.g., manipulator arm, and a wheeled robot), and show that with the learned residual errors, we can further close the reality gap between dynamic models, simulations, and actual hardware., Comment: Accepted to Ubiquitous Robotics 2023, Honolulu, Hawaii

Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines data-driven methods on solver heuristics has shown potential to overcome this issue allowing for applications on larger scale practical problems. To solve mixed-integer bilinear programs online with data-driven methods, several formulations exist including mathematical programming with complementary constraints (MPCC), mixed-integer programming (MIP). In this work, we benchmark the performances of those data-driven schemes on a bookshelf organization problem that has discrete mode switch and collision avoidance constraints. The success rate, optimal cost and solving time are compared along with non-data-driven methods. Our proposed methods are demonstrated as a high level planner for a robotic arm for the bookshelf problem., Comment: arXiv admin note: substantial text overlap with arXiv:2110.00666

The logistics of transporting a package from a storage facility to the consumer's front door usually employs highly specialized robots often times splitting sub-tasks up to different systems, e.g., manipulator arms to sort and wheeled vehicles to deliver. More recent endeavors attempt to have a unified approach with legged and humanoid robots. These solutions, however, occupy large amounts of space thus reducing the number of packages that can fit into a delivery vehicle. As a result, these bulky robotic systems often reduce the potential for scalability and task parallelization. In this paper, we introduce LIMMS (Latching Intelligent Modular Mobility System) to address both the manipulation and delivery portion of a typical last-mile delivery while maintaining a minimal spatial footprint. LIMMS is a symmetrically designed, 6 degree of freedom (DoF) appendage-like robot with wheels and latching mechanisms at both ends. By latching onto a surface and anchoring at one end, LIMMS can function as a traditional 6-DoF manipulator arm. On the other hand, multiple LIMMS can latch onto a single box and behave like a legged robotic system where the package is the body. During transit, LIMMS folds up compactly and takes up much less space compared to traditional robotic systems. A large group of LIMMS units can fit inside of a single delivery vehicle, opening the potential for new delivery optimization and hybrid planning methods never done before. In this paper, the feasibility of LIMMS is studied and presented using a hardware prototype as well as simulation results for a range of sub-tasks in a typical last-mile delivery.

In this paper we present a motion planner for LIMMS, a modular multi-agent, multi-modal package delivery platform. A single LIMMS unit is a robot that can operate as an arm or leg depending on how and what it is attached to, e.g., a manipulator when it is anchored to walls within a delivery vehicle or a quadruped robot when 4 are attached to a box. Coordinating amongst multiple LIMMS, when each one can take on vastly different roles, can quickly become complex. For such a planning problem we first compose the necessary logic and constraints. The formulation is then solved for skill exploration and can be implemented on hardware after refinement. To solve this optimization problem we use alternating direction method of multipliers (ADMM). The proposed planner is experimented under various scenarios which shows the capability of LIMMS to enter into different modes or combinations of them to achieve their goal of moving shipping boxes., Comment: IROS 2022

Convex model predictive controls (MPCs) with a single rigid body model have demonstrated strong performance on real legged robots. However, convex MPCs are limited by their assumptions such as small rotation angle and pre-defined gait, limiting the richness of potential solutions. We remove those assumptions and solve the complete mixed-integer non-convex programming with single rigid body model. We first collect datasets of pre-solved problems offline, then learn the problem-solution map to solve this optimization fast for MPC. If warm-starts can be found, offline problems can be solved close to the global optimality. The proposed controller is tested by generating various gaits and behaviors depending on the initial conditions. Hardware test demonstrates online gait generation and adaptation running at more than 50 Hz based on sensor feedback.

While motion planning of locomotion for legged robots has shown great success, motion planning for legged robots with dexterous multi-finger grasping is not mature yet. We present an efficient motion planning framework for simultaneously solving locomotion (e.g., centroidal dynamics), grasping (e.g., patch contact), and contact (e.g., gait) problems. To accelerate the planning process, we propose distributed optimization frameworks based on Alternating Direction Methods of Multipliers (ADMM) to solve the original large-scale Mixed-Integer NonLinear Programming (MINLP). The resulting frameworks use Mixed-Integer Quadratic Programming (MIQP) to solve contact and NonLinear Programming (NLP) to solve nonlinear dynamics, which are more computationally tractable and less sensitive to parameters. Also, we explicitly enforce patch contact constraints from limit surfaces with micro-spine grippers. We demonstrate our proposed framework in the hardware experiments, showing that the multi-limbed robot is able to realize various motions including free-climbing at a slope angle 45{\deg} with a much shorter planning time., Comment: Accepted for the 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2022). Hardware implementation videos: https://youtu.be/QLH1shghqQ0

This paper introduces SCALER, a quadrupedal robot that demonstrates climbing on bouldering walls, overhangs, ceilings and trotting on the ground. SCALER is one of the first high-degrees of freedom four-limbed robots that can free-climb under the Earth's gravity and one of the most mechanically efficient quadrupeds on the ground. Where other state-of-the-art climbers specialize in climbing, SCALER promises practical free-climbing with payload \textit{and} ground locomotion, which realizes true versatile mobility. A new climbing gait, SKATE gait, increases the payload by utilizing the SCALER body linkage mechanism. SCALER achieves a maximum normalized locomotion speed of $1.87$ /s, or $0.56$ m/s on the ground and $1.0$ /min, or $0.35$ m/min in bouldering wall climbing. Payload capacity reaches $233$ % of the SCALER weight on the ground and $35$ % on the vertical wall. Our GOAT gripper, a mechanically adaptable underactuated two-finger gripper, successfully grasps convex and non-convex objects and supports SCALER., Comment: Proceeding to IROS 2022, Preprint and not a final version

In multi-point contact systems, precise force control is crucial for achieving stable and safe interactions between robots and their environment. Thus, we demonstrate an admittance controller with auto-tuning that can be applied for these systems. The controller's objective is to track the target wrench profiles of each contact point while considering the additional torque due to rotational friction. Our admittance controller is adaptive during online operation by using an auto-tuning method that tunes the gains of the controller while following user-specified training objectives. These objectives include facilitating controller stability, such as tracking the wrench profiles as closely as possible, ensuring control outputs are within force limits that minimize slippage, and avoiding configurations that induce kinematic singularity. We demonstrate the robustness of our controller on hardware for both manipulation and locomotion tasks using a multi-limbed climbing robot., Comment: Accepted to IEEE RAS International Conference on Humanoid Robots 2023, December 12-14 in Austin, Texas, USA

Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines learning methods on solver heuristics has shown potential to overcome this issue allowing for applications on larger scale practical problems. Gathering sufficient training data to employ these methods still present a challenge since getting data from traditional solvers are slow and newer learning approaches still require large amounts of data. In order to scale up and make these hybrid learning approaches more manageable we propose ReDUCE, a method that exploits structure within small to medium size datasets. We also introduce the bookshelf organization problem as an MINLP as a way to measure performance of solvers with ReDUCE. Results show that existing algorithms with ReDUCE can solve this problem within a few seconds, a significant improvement over the original formulation. ReDUCE is demonstrated as a high level planner for a robotic arm for the bookshelf problem.

Current rigid linkage grippers are limited in flexibility, and gripper design optimality relies on expertise, experiments, or arbitrary parameters. Our proposed rigid gripper can accommodate irregular and off-center objects through a whippletree mechanism, improving adaptability. We present a whippletree-based rigid under-actuated gripper and its parametric design multi-objective optimization for a one-wall climbing task. Our proposed objective function considers kinematics and grasping forces simultaneously with a mathematical metric based on a model of an object environment. Our multi-objective problem is formulated as a single kinematic objective function with auto-tuning force-based weight. Our results indicate that our proposed objective function determines optimal parameters and kinematic ranges for our under-actuated gripper in the task environment with sufficient grasping forces., Comment: Accepted for IROS 2021

For multi-limbed robots, motion planning with posture and force constraints tends to be a difficult optimization problem due to nonlinearities, which also present extended solve times. We propose a multi-stage optimization framework with data-driven inter-stage coupling constraints to address the nonlinearity. Both clustering and evolutionary approaches to find the McCormick envelope relaxations are used to find the problem-specific parameters. The learned constraints are then used in the prior stages, which provides advanced knowledge of the following stages. This leads to improved solve times and interpretability of the results. The planner is validated through multiple walking and climbing tasks on a 10 kg hexapod robot.

We present an end-to-end online motion planning framework that uses a data-driven approach to navigate a heterogeneous robot team towards a global goal while avoiding obstacles in uncertain environments. First, we use stochastic model predictive control (SMPC) to calculate control inputs that satisfy robot dynamics, and consider uncertainty during obstacle avoidance with chance constraints. Second, recurrent neural networks are used to provide a quick estimate of future state uncertainty considered in the SMPC finite-time horizon solution, which are trained on uncertainty outputs of various simultaneous localization and mapping algorithms. When two or more robots are in communication range, these uncertainties are then updated using a distributed Kalman filtering approach. Lastly, a Deep Q-learning agent is employed to serve as a high-level path planner, providing the SMPC with target positions that move the robots towards a desired global goal. Our complete methods are demonstrated on a ground and aerial robot simultaneously (code available at: https://github.com/AlexS28/SABER)., Comment: Accepted to IEEE Robotics and Automation Letters (RA-L) 2021. Pre-print version. The video link of the paper is: https://www.youtube.com/watch?v=EKCCQtN5Z6A

In order to achieve autonomous vertical wall climbing, the transition phase from the ground to the wall requires extra consideration inevitably. This paper focuses on the contact sequence planner to transition between flat terrain and vertical surfaces for multi-limbed climbing robots. To overcome the transition phase, it requires planning both multi-contact and contact wrenches simultaneously which makes it difficult. Instead of using a predetermined contact sequence, we consider various motions on different environment setups via modeling contact constraints and limb switchability as complementarity conditions. Two safety factors for toe sliding and motor over-torque are the main tuning parameters for different contact sequences. By solving as a nonlinear program (NLP), we can generate several feasible sequences of foot placements and contact forces to avoid failure cases. We verified feasibility with demonstrations on the hardware SiLVIA, a six-legged robot capable of vertically climbing between two walls by bracing itself in-between using only friction., Comment: ICRA 2021 Accepted. Optimization, Climbing motion planning, Complementarity Constraints

Although Trajectory Optimization (TO) is one of the most powerful motion planning tools, it suffers from expensive computational complexity as a time horizon increases in cluttered environments. It can also fail to converge to a globally optimal solution. In this paper, we present Lazy Trajectory Optimization (LTO) that unifies local short-horizon TO and global Graph-Search Planning (GSP) to generate a long-horizon global optimal trajectory. LTO solves TO with the same constraints as the original long-horizon TO with improved time complexity. We also propose a TO-aware cost function that can balance both solution cost and planning time. Since LTO solves many nearly identical TO in a roadmap, it can provide an informed warm-start for TO to accelerate the planning process. We also present proofs of the computational complexity and optimality of LTO. Finally, we demonstrate LTO's performance on motion planning problems for a 2 DOF free-flying robot and a 21 DOF legged robot, showing that LTO outperforms existing algorithms in terms of its runtime and reliability., Comment: Accepted for 2021 IEEE International Conference on Robotics and Automation (2021 ICRA). You can find a summary video here: https://youtu.be/o5zDEKc2HPU

In this paper, we propose an online path planning architecture that extends the model predictive control (MPC) formulation to consider future location uncertainties for safer navigation through cluttered environments. Our algorithm combines an object detection pipeline with a recurrent neural network (RNN) which infers the covariance of state estimates through each step of our MPC's finite time horizon. The RNN model is trained on a dataset that comprises of robot and landmark poses generated from camera images and inertial measurement unit (IMU) readings via a state-of-the-art visual-inertial odometry framework. To detect and extract object locations for avoidance, we use a custom-trained convolutional neural network model in conjunction with a feature extractor to retrieve 3D centroid and radii boundaries of nearby obstacles. The robustness of our methods is validated on complex quadruped robot dynamics and can be generally applied to most robotic platforms, demonstrating autonomous behaviors that can plan fast and collision-free paths towards a goal point., Comment: Accepted to the 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Las Vegas, USA. First two authors contributed equally. For supplementary video, see https://www.youtube.com/watch?v=td4K55Tj-U8

We present a motion planning algorithm with probabilistic guarantees for limbed robots with stochastic gripping forces. Planners based on deterministic models with a worst-case uncertainty can be conservative and inflexible to consider the stochastic behavior of the contact, especially when a gripper is installed. Our proposed planner enables the robot to simultaneously plan its pose and contact force trajectories while considering the risk associated with the gripping forces. Our planner is formulated as a nonlinear programming problem with chance constraints, which allows the robot to generate a variety of motions based on different risk bounds. To model the gripping forces as random variables, we employ Gaussian Process regression. We validate our proposed motion planning algorithm on an 11.5 kg six-limbed robot for two-wall climbing. Our results show that our proposed planner generates various trajectories (e.g., avoiding low friction terrain under the low risk bound, choosing an unstable but faster gait under the high risk bound) by changing the probability of risk based on various specifications., Comment: IEEE Robotics and Automation Letters (RA-L). Pre-print Version. The video of this paper is: https://youtu.be/ZDqvf1J4nS4

Practitioners often rely on compute-intensive domain randomization to ensure reinforcement learning policies trained in simulation can robustly transfer to the real world. Due to unmodeled nonlinearities in the real system, however, even such simulated policies can still fail to perform stably enough to acquire experience in real environments. In this paper we propose a novel method that guarantees a stable region of attraction for the output of a policy trained in simulation, even for highly nonlinear systems. Our core technique is to use "bias-shifted" neural networks for constructing the controller and training the network in the simulator. The modified neural networks not only capture the nonlinearities of the system but also provably preserve linearity in a certain region of the state space and thus can be tuned to resemble a linear quadratic regulator that is known to be stable for the real system. We have tested our new method by transferring simulated policies for a swing-up inverted pendulum to real systems and demonstrated its efficacy.

A mobility mechanism for robots to be used in tight spaces shared with people requires it to have a small footprint, to move omnidirectionally, as well as to be highly maneuverable. However, currently there exist few such mobility mechanisms that satisfy all these conditions well. Here we introduce Omnidirectional Balancing Unicycle Robot (OmBURo), a novel unicycle robot with active omnidirectional wheel. The effect is that the unicycle robot can drive in both longitudinal and lateral directions simultaneously. Thus, it can dynamically balance itself based on the principle of dual-axis wheeled inverted pendulum. This letter discloses the early development of this novel unicycle robot involving the overall design, modeling, and control, as well as presents some preliminary results including station keeping and path following. With its very compact structure and agile mobility, it might be the ideal locomotion mechanism for robots to be used in human environments in the future., Comment: ICRA 2020 Accepted