Density of the reachable states can help understand the risk of safety-critical systems, especially in situations when worst-case reachability is too conservative. Recent work provides a data-driven approach to compute the density distribution of autonomous systems' forward reachable states online. In this paper, we study the use of such approach in combination with model predictive control for verifiable safe path planning under uncertainties. We first use the learned density distribution to compute the risk of collision online. If such risk exceeds the acceptable threshold, our method will plan for a new path around the previous trajectory, with the risk of collision below the threshold. Our method is well-suited to handle systems with uncertainties and complicated dynamics as our data-driven approach does not need an analytical form of the systems' dynamics and can estimate forward state density with an arbitrary initial distribution of uncertainties. We design two challenging scenarios (autonomous driving and hovercraft control) for safe motion planning in environments with obstacles under system uncertainties. We first show that our density estimation approach can reach a similar accuracy as the Monte-Carlo-based method while using only 0.01X training samples. By leveraging the estimated risk, our algorithm achieves the highest success rate in goal reaching when enforcing the safety rate above 0.99.
Efficient Probabilistic Planning with Maximum-Coverage Distributionally Robust Backward Reachable Trees
Laboratory for Information and Decision Systems, Massachusetts Institute of Technology（信息与决策系统实验室，麻省理工学院）；Draper, Cambridge MA 02139（Draper，剑桥MA 02139）
An Overtaking Trajectory Planning Framework Based on Spatio-temporal Topology and Reachable Set Analysis Ensuring Time Efficiency
State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, 310027, China（工业控制技术国家重点实验室，浙江大学，杭州，310027，中国）；Shanghai STEP Electric Corporation, Shanghai, 201802, China（上海STEP电力有限公司，上海，201802，中国）
Mechanical Engineering, University of Michigan（密歇根大学机械工程学院）；Robotics Institute, University of Michigan（密歇根大学机器人研究所）；Mechanical and Industrial Engineering, Louisiana State University（路易斯安那州立大学机械与工业工程学院）；Naval Architecture and Marine Engineering, University of Michigan（密歇根大学船舶与海洋工程学院）；Ford Motor Company（福特汽车公司）；Office of Naval Research（美国海军研究办公室）
For robotic arms to operate in arbitrary environments, especially near people, it is critical to certify the safety of their motion planning algorithms. However, there is often a trade-off between safety and real-time performance; one can either carefully design safe plans, or rapidly generate potentially-unsafe plans. This work presents a receding-horizon, real-time trajectory planner with safety guarantees, called ARMTD (Autonomous Reachability-based Manipulator Trajectory Design). The method first computes (offline) a reachable set of parameterized trajectories for each joint of an arm. Eac…
RTD-RAX: Fast, Safe Trajectory Planning for Systems under Unknown Disturbances
Georgia Institute of Technology（佐治亚理工学院）；School of Electrical and Computer Engineering（电子与计算机工程学院）；School of Mechanical Engineering（机械工程学院）；School of Civil and Environmental Engineering（土木与环境工程学院）
The kinematic approximation of Dubin's Vehicle has been largely exploited in the formulation of various motion planning methods. In the majority of these methods, planning and control phases are decoupled, and the burden of rejecting disturbances is left to the controller. An alternative to this approach is the use of a feedback motion plan, where for each state there is a specific pre-computed action that will be executed. This planning approach provides the ability to verify all trajectories off-line. The verification can be performed using backward reachability, which provides the set of co…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
In multirotor systems, guaranteeing safety while considering unknown disturbances is essential for robust trajectory planning. The Forward reachable set (FRS), the set of feasible states subject to bounded disturbances, can be utilized to identify robust and collision-free trajectories by checking the intersections with obstacles. However, in many cases, the FRS is not calculated in real time and is too conservative to be used in actual applications. In this paper, we address these issues by introducing a nonlinear disturbance observer (NDOB) and an adaptive controller to the multirotor system…
Katholieke Universiteit Leuven（鲁汶天主教大学）；University of Melbourne（墨尔本大学）
We propose a safety-guaranteed planning and control framework for unmanned surface vessels (USVs), using Gaussian processes (GPs) to learn uncertainties. The uncertainties encountered by USVs, including external disturbances and model mismatches, are potentially state-dependent, time-varying, and hard to capture with constant models. GP is a powerful learning-based tool that can be integrated with a model-based planning and control framework, which employs a Hamilton-Jacobi differential game formulation. Such a combination yields less conservative trajectories and safety-guaranteeing control s…
This work introduces PokeRRT, a novel motion planning algorithm that demonstrates poking as an effective non-prehensile manipulation skill to enable fast manipulation of objects and increase the size of a robot's reachable workspace. Our qualitative and quantitative results demonstrate the advantages of poking over pushing and grasping in planning object trajectories through uncluttered and cluttered environments.
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Autonomous robots that are capable of operating safely in the presence of imperfect model knowledge or external disturbances are vital in safety-critical applications. In this paper, we present a planner-agnostic framework to design and certify safe tubes around desired trajectories that the robot is always guaranteed to remain inside of. By leveraging recent results in contraction analysis and $\mathcal{L}_1$-adaptive control we synthesize an architecture that induces safe tubes for nonlinear systems with state and time-varying uncertainties. We demonstrate with a few illustrative examples ho…
This paper presents a new trajectory planning method for multiple quadrotors in obstacle-dense environments. We suggest a relative safe flight corridor (RSFC) to model safe region between a pair of agents, and it is used to generate linear constraints for inter-collision avoidance by utilizing the convex hull property of relative Bernstein polynomial. Our approach employs a graph-based multi-agent pathfinding algorithm to generate an initial trajectory, which is used to construct a safe flight corridor (SFC) and RSFC. We express the trajectory as a piecewise Bernstein polynomial and formulate …
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
Consider a robot operating in an uncertain environment with stochastic, dynamic obstacles. Despite the clear benefits for trajectory optimization, it is often hard to keep track of each obstacle at every time step due to sensing and hardware limitations. We introduce the Safely motion planner, a receding-horizon control framework, that simultaneously synthesizes both a trajectory for the robot to follow as well as a sensor selection strategy that prescribes trajectory-relevant obstacles to measure at each time step while respecting the sensing constraints of the robot. We perform the motion pl…
This paper develops and compares two motion planning algorithms for a tethered UAV with and without the possibility of the tether contacting the confined and cluttered environment. Tethered aerial vehicles have been studied due to their advantages such as power duration, stability, and safety. However, the disadvantages brought in by the extra tether have not been well investigated by the robotic locomotion community, especially when the tethered agent is locomoting in a non-free space occupied with obstacles. In this work, we propose two motion planning frameworks that (1) reduce the reachabl…
We present the design of a motion planning algorithm that ensures safety for an autonomous vehicle. In particular, we consider a multimodal distribution over uncertainties; for example, the uncertain predictions of future trajectories of surrounding vehicles reflect discrete decisions, such as turning or going straight at intersections. We develop a computationally efficient, scenario-based approach that solves the motion planning problem with high confidence given a quantifiable number of samples from the multimodal distribution. Our approach is based on two preprocessing steps, which 1) sepa…
Peking University（北京大学）；College of Engineering, Peking University（北京大学工学院）
This paper addresses the online motion planning problem of mobile robots under complex high-level tasks. The robot motion is modeled as an uncertain Markov Decision Process (MDP) due to limited initial knowledge, while the task is specified as Linear Temporal Logic (LTL) formulas. The proposed framework enables the robot to explore and update the system model in a Bayesian way, while simultaneously optimizing the asymptotic costs of satisfying the complex temporal task. Theoretical guarantees are provided for the synthesized outgoing policy and safety policy. More importantly, instead of greed…
Maximal Controlled Invariant-MPC: Enhancing Feasibility and Reducing Conservatism through Terminal CBF Constraint in Safety-Critical Control
Graduate Student, Daniel Guggenheim School of Aerospace Engineering（丹尼尔·古吉恩航空航天工程学院研究生）；Assistant Professor, Director, Aerospace Robotics Lab, Daniel Guggenheim School of Aerospace Engineering（丹尼尔·古吉恩航空航天工程学院助理教授、主任、航空航天机器人实验室）
Otto von Guericke University（奥托·冯·格里克大学）；German Aerospace Center (DLR)（德国航空航天中心（DLR））；Technical University of Darmstadt（达姆施塔特工业大学）
Planning and control for autonomous vehicles usually are hierarchical separated. However, increasing performance demands and operating in highly dynamic environments requires an frequent re-evaluation of the planning and tight integration of control and planning to guarantee safety. We propose an integrated hierarchical predictive control and planning approach to tackle this challenge. Planner and controller are based on the repeated solution of moving horizon optimal control problems. The planner can choose different low-layer controller modes for increased flexibility and performance instead…
Robust motion planning entails computing a global motion plan that is safe under all possible uncertainty realizations, be it in the system dynamics, the robot's initial position, or with respect to external disturbances. Current approaches for robust motion planning either lack theoretical guarantees, or make restrictive assumptions on the system dynamics and uncertainty distributions. In this paper, we address these limitations by proposing the robust rapidly-exploring random-tree (Robust-RRT) algorithm, which integrates forward reachability analysis directly into sampling-based control traj…
People with lower-limb loss, the majority of which use passive prostheses, exhibit a high incidence of falls each year. Powered lower-limb prostheses have the potential to reduce fall rates by actively helping the user recover from a stumble, but the unpredictability of the human response makes it difficult to design controllers that ensure a successful recovery. This paper presents a method called TRIP-RTD (Trip Recovery in Prostheses via Reachability-based Trajectory Design) for online trajectory planning in a knee prosthesis during and after a stumble that can accommodate a set of possible …
Manipal Institute of Technology（马尼帕尔理工学院）；Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）
Motion Planning under uncertainty is critical for safe self-driving. In this paper, we propose a unified obstacle avoidance framework that deals with 1) uncertainty in ego-vehicle motion; and 2) prediction uncertainty of dynamic obstacles from environment. A two-stage traffic participant trajectory predictor comprising short-term and long-term prediction is used in the planning layer to generate safe but not over-conservative trajectories for the ego vehicle. The prediction module cooperates well with existing planning approaches. Our work showcases its effectiveness in a Frenet frame planner.…
This paper reports on developing an integrated framework for safety-aware informative motion planning suitable for legged robots. The information-gathering planner takes a dense stochastic map of the environment into account, while safety constraints are enforced via Control Barrier Functions (CBFs). The planner is based on the Incrementally-exploring Information Gathering (IIG) algorithm and allows closed-loop kinodynamic node expansion using a Model Predictive Control (MPC) formalism. Robotic exploration and information gathering problems are inherently path-dependent problems. That is, the …
Autonomous vehicles need to plan at the task level to compute a sequence of symbolic actions, such as merging left and turning right, to fulfill people's service requests, where efficiency is the main concern. At the same time, the vehicles must compute continuous trajectories to perform actions at the motion level, where safety is the most important. Task-motion planning in autonomous driving faces the problem of maximizing task-level efficiency while ensuring motion-level safety. To this end, we develop algorithm Task-Motion Planning for Urban Driving (TMPUD) that, for the first time, enable…
Uber ATG（Uber 先进技术集团）；University of Toronto（多伦多大学）
In this paper we propose a novel end-to-end learnable network that performs joint perception, prediction and motion planning for self-driving vehicles and produces interpretable intermediate representations. Unlike existing neural motion planners, our motion planning costs are consistent with our perception and prediction estimates. This is achieved by a novel differentiable semantic occupancy representation that is explicitly used as cost by the motion planning process. Our network is learned end-to-end from human demonstrations. The experiments in a large-scale manual-driving dataset and clo…
We present a method to solve planning problems involving sequential decision making in unpredictable environments while accomplishing a high level task specification expressed using the formalism of linear temporal logic. Our method improves the state of the art by introducing a pruning step that preserves correctness while significantly reducing the time needed to compute an optimal policy. Our theoretical contribution is coupled with simulations substantiating the value of the proposed method.
Cornell Tech（康奈尔理工学院）；University of Pennsylvania（宾夕法尼亚大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
In this paper, we introduce a new probabilistically safe local steering primitive for sampling-based motion planning in complex high-dimensional configuration spaces. Our local steering procedure is based on a new notion of a convex probabilistically safe corridor that is constructed around a configuration using tangent hyperplanes of confidence ellipsoids of Gaussian mixture models learned from prior collision history. Accordingly, we propose to expand a random motion planning graph towards a sample goal using its projection onto probabilistically safe corridors, which efficiently exploits th…
KTH Royal Institute of Technology（KTH皇家理工学院）；Yale University（耶鲁大学）；Örebro University（厄勒布鲁大学）
We address the problem of motion planning for a robotic manipulator with the task to place a grasped object in a cluttered environment. In this task, we need to locate a collision-free pose for the object that a) facilitates the stable placement of the object, b) is reachable by the robot manipulator and c) optimizes a user-given placement objective. Because of the placement objective, this problem is more challenging than classical motion planning where the target pose is defined from the start. To solve this task, we propose an anytime algorithm that integrates sampling-based motion planning…
Simon Fraser University（西蒙菲莎大学）；Princeton University（普林斯顿大学）；University of Melbourne（墨尔本大学）；California Institute of Technology（加州理工学院）
Real-time, guaranteed safe trajectory planning is vital for navigation in unknown environments. However, real-time navigation algorithms typically sacrifice robustness for computation speed. Alternatively, provably safe trajectory planning tends to be too computationally intensive for real-time replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that achieves both real-time replanning and guaranteed safety. In this framework, real-time computation is achieved by allowing any trajectory planner to use a simplified \textit{planning model} of the system. The plan is tracked by th…
Zhejiang University（浙江大学）；Huzhou Institute of Zhejiang University（浙江大学湖州研究院）；DJI（大疆创新）
Free-space-oriented roadmaps typically generate a series of convex geometric primitives, which constitute the safe region for motion planning. However, a static environment is assumed for this kind of roadmap. This assumption makes it unable to deal with dynamic obstacles and limits its applications. In this paper, we present a dynamic free-space roadmap, which provides feasible spaces and a navigation graph for safe quadrotor motion planning. Our roadmap is constructed by continuously seeding and extracting free regions in the environment. In order to adapt our map to environments with dynami…
Fast and safe navigation of dynamical systems through a priori unknown cluttered environments is vital to many applications of autonomous systems. However, trajectory planning for autonomous systems is computationally intensive, often requiring simplified dynamics that sacrifice safety and dynamic feasibility in order to plan efficiently. Conversely, safe trajectories can be computed using more sophisticated dynamic models, but this is typically too slow to be used for real-time planning. We propose a new algorithm FaSTrack: Fast and Safe Tracking for High Dimensional systems. A path or trajec…
Safe Reinforcement Learning with a Predictive Safety Filter for Motion Planning and Control: A Drifting Vehicle Example
State Key Laboratory of Industrial Control Technology, Zhejiang University（浙江大学工业控制技术国家重点实验室）；Professorship of Autonomous Vehicle Systems, Technical University of Munich（慕尼黑工业大学自主车辆系统教授职位）
SafeMove-RL: A Certifiable Reinforcement Learning Framework for Dynamic Motion Constraints in Trajectory Planning
Sino-German College of Intelligent Manufacturing, Shenzhen Technology University（深圳技术大学中德智能制造学院）；Faculty of Science and Technology, University of Macau（澳门大学科技学院）
