We consider the problem of risk-sensitive motion planning in the presence of randomly moving obstacles. To this end, we adopt a model predictive control (MPC) scheme and pose the obstacle avoidance constraint in the MPC problem as a distributionally robust constraint with a KL divergence ambiguity set. This constraint is the dual representation of the Entropic Value-at-Risk (EVaR). Building upon this viewpoint, we propose an algorithm to follow waypoints and discuss its feasibility and completion in finite time. We compare the policies obtained using EVaR with those obtained using another common coherent risk measure, Conditional Value-at-Risk (CVaR), via numerical experiments for a 2D system. We also implement the waypoint following algorithm on a 3D quadcopter simulation.
In this paper, we address the trajectory planning problem in uncertain nonconvex static and dynamic environments that contain obstacles with probabilistic location, size, and geometry. To address this problem, we provide a risk bounded trajectory planning method that looks for continuous-time trajectories with guaranteed bounded risk over the planning time horizon. Risk is defined as the probability of collision with uncertain obstacles. Existing approaches to address risk bounded trajectory planning problems either are limited to Gaussian uncertainties and convex obstacles or rely on sampling…
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 genera…
We investigate the problem of risk averse robot path planning using the deep reinforcement learning and distributionally robust optimization perspectives. Our problem formulation involves modelling the robot as a stochastic linear dynamical system, assuming that a collection of process noise samples is available. We cast the risk averse motion planning problem as a Markov decision process and propose a continuous reward function design that explicitly takes into account the risk of collision with obstacles while encouraging the robot's motion towards the goal. We learn the risk-averse robot co…
Nanyang Technological University（南洋理工大学）；Civil Aviation University of China（中国民航大学）；Air Traffic Management Research Institute（空中交通管理研究院）
Various applications of advanced air mobility (AAM) in urban environments facilitate our daily life and public services. As one of the key issues of realizing these applications autonomously, path planning problem has been studied with main objectives on minimizing travel distance, flight time and energy cost. However, AAM operations in metropolitan areas bring safety and society issues. Because most of AAM aircraft are unmanned aerial vehicles (UAVs) and they may fail to operate resulting in fatality risk, property damage risk and societal impacts (noise and privacy) to the public. To quantit…
Understanding the probabilistic traffic environment is a vital challenge for the motion planning of autonomous vehicles. To make feasible control decisions, forecasting future trajectories of adjacent cars is essential for intelligent vehicles to assess potential conflicts and react to reduce the risk. This paper first introduces a Bayesian Long Short-term Memory (BLSTM) model to learn human drivers' behaviors and habits from their historical trajectory data. The model predicts the probability distribution of surrounding vehicles' positions, which are used to estimate dynamic conflict risks. N…
Seoul National University（首尔国立大学）；Automation and Systems Research Institute（自动化与系统研究所）
This paper proposes a novel safety specification tool, called the distributionally robust risk map (DR-risk map), for a mobile robot operating in a learning-enabled environment. Given the robot's position, the map aims to reliably assess the conditional value-at-risk (CVaR) of collision with obstacles whose movements are inferred by Gaussian process regression (GPR). Unfortunately, the inferred distribution is subject to errors, making it difficult to accurately evaluate the CVaR of collision. To overcome this challenge, this tool measures the risk under the worst-case distribution in a so-cal…
University of Tokyo（东京大学）；California Institute of Technology（加州理工学院）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）
Although ground robotic autonomy has gained widespread usage in structured and controlled environments, autonomy in unknown and off-road terrain remains a difficult problem. Extreme, off-road, and unstructured environments such as undeveloped wilderness, caves, and rubble pose unique and challenging problems for autonomous navigation. To tackle these problems we propose an approach for assessing traversability and planning a safe, feasible, and fast trajectory in real-time. Our approach, which we name STEP (Stochastic Traversability Evaluation and Planning), relies on: 1) rapid uncertainty-awa…
City-Wide Low-Altitude Urban Air Mobility: A Scalable Global Path Planning Approach via Risk-Aware Multi-Scale Cell Decomposition
School of Mechanical and Aerospace Engineering, Nanyang Technological University（南洋理工大学机械与航空航天工程学院）；School of Aeronautics and Astronautics, Purdue University（普渡大学航空航天学院）
California Institute of Technology（加州理工学院）；NASA Jet Propulsion Laboratory（美国国家航空航天局喷气推进实验室）
We consider the problem of designing policies for partially observable Markov decision processes (POMDPs) with dynamic coherent risk objectives. Synthesizing risk-averse optimal policies for POMDPs requires infinite memory and thus undecidable. To overcome this difficulty, we propose a method based on bounded policy iteration for designing stochastic but finite state (memory) controllers, which takes advantage of standard convex optimization methods. Given a memory budget and optimality criterion, the proposed method modifies the stochastic finite state controller leading to sub-optimal soluti…
University of Connecticut（康涅狄格大学）；Naval Undersea Warfare Center（海军水下作战中心）
In this paper, we develop a new algorithm, called T$^{\star}$-Lite, that enables fast time-risk optimal motion planning for variable-speed autonomous vehicles. The T$^{\star}$-Lite algorithm is a significantly faster version of the previously developed T$^{\star}$ algorithm. T$^{\star}$-Lite uses the novel time-risk cost function of T$^{\star}$; however, instead of a grid-based approach, it uses an asymptotically optimal sampling-based motion planner. Furthermore, it utilizes the recently developed Generalized Multi-speed Dubins Motion-model (GMDM) for sample-to-sample kinodynamic motion plann…
RiskMap: A Unified Driving Context Representation for Autonomous Motion Planning in Urban Driving Environment
The Hong Kong University of Science and Technology（香港科技大学）；Division of Emerging Interdisciplinary Areas（新兴跨学科领域）；Robotics and Autonomous Systems Thrust（机器人与自主系统方向）；Department of Electronic and Computer Engineering（电子与计算机工程系）
Texas A&M University（得克萨斯农工大学）；Department of Computer Science and Engineering, Texas A&M University（得克萨斯农工大学计算机科学与工程系）
This paper develops a path planner that minimizes risk (e.g. motion execution) while maximizing accumulated reward (e.g., quality of sensor viewpoint) motivated by visual assistance or tracking scenarios in unstructured or confined environments. In these scenarios, the robot should maintain the best viewpoint as it moves to the goal. However, in unstructured or confined environments, some paths may increase the risk of collision; therefore there is a tradeoff between risk and reward. Conventional state-dependent risk or probabilistic uncertainty modeling do not consider path-level risk or is d…
This paper proposes a formal robot motion risk reasoning framework and develops a risk-aware path planner that minimizes the proposed risk. While robots locomoting in unstructured or confined environments face a variety of risk, existing risk only focuses on collision with obstacles. Such risk is currently only addressed in ad hoc manners. Without a formal definition, ill-supported properties, e.g. additive or Markovian, are simply assumed. Relied on an incomplete and inaccurate representation of risk, risk-aware planners use ad hoc risk functions or chance constraints to minimize risk. The fo…
Enforcing safety in the presence of stochastic uncertainty is a challenging problem. Traditionally, researchers have proposed safety in the statistical mean as a safety measure in this case. However, ensuring safety in the statistical mean is only reasonable if system's safe behavior in the large number of runs is of interest, which precludes the use of mean safety in practical scenarios. In this paper, we propose a risk sensitive notion of safety called conditional-value-at-risk (CVaR) safety, which is concerned with safe performance in the worst case realizations. We introduce CVaR barrier f…
Overcoming the Fear of the Dark: Occlusion-Aware Model-Predictive Planning for Automated Vehicles Using Risk Fields
Netherlands Organisation for Applied Scientific Research（荷兰应用科学研究组织）；Eindhoven University of Technology（埃因霍温理工大学）；KTH Royal Institute of Technology（KTH皇家理工学院）；Scania CV AB（斯堪尼亚商用车有限公司）
KTH Royal Institute of Technology（瑞典皇家理工学院）；Digital Futures（数字未来研究院）；University of Oxford（牛津大学）；Oxford Robotics Institute（牛津机器人研究院）
Recent trends envisage robots being deployed in areas deemed dangerous to humans, such as buildings with gas and radiation leaks. In such situations, the model of the underlying hazardous process might be unknown to the agent a priori, giving rise to the problem of planning for safe behaviour in partially known environments. We employ Gaussian process regression to create a probabilistic model of the hazardous process from local noisy samples. The result of this regression is then used by a risk metric, such as the Conditional Value-at-Risk, to reason about the safety at a certain state. The o…
Multi-Risk-RRT: An Efficient Motion Planning Algorithm for Robotic Autonomous Luggage Trolley Collection at Airports
Southern University of Science and Technology（南方科技大学）；Jiaxing Research Institute, Southern University of Science and Technology（南方科技大学嘉兴研究院）；University of Pennsylvania（宾夕法尼亚大学）；Shanghai Jiao Tong University（上海交通大学）；Yanshan University（燕山大学）
We propose a two-phase risk-averse architecture for controlling stochastic nonlinear robotic systems. We present Risk-Averse Nonlinear Steering RRT* (RANS-RRT*) as an RRT* variant that incorporates nonlinear dynamics by solving a nonlinear program (NLP) and accounts for risk by approximating the state distribution and performing a distributionally robust (DR) collision check to promote safe planning. The generated plan is used as a reference for a low-level tracking controller. We demonstrate three controllers: finite horizon linear quadratic regulator (LQR) with linearized dynamics around the…
The Chinese University of Hong Kong（香港中文大学）；Georgia Institute of Technology（佐治亚理工学院）；Southern University of Science and Technology（南方科技大学）；Shenzhen Research Institute of The Chinese University of Hong Kong（香港中文大学深圳研究院）
Balancing the trade-off between safety and efficiency is of significant importance for path planning under uncertainty. Many risk-aware path planners have been developed to explicitly limit the probability of collision to an acceptable bound in uncertain environments. However, convex obstacles or Gaussian uncertainties are usually assumed to make the problem tractable in the existing method. These assumptions limit the generalization and application of path planners in real-world implementations. In this article, we propose to apply deep learning methods to the sampling-based planner, developi…
Active Next-Best-View Optimization for Risk-Averse Path Planning
Department of Mechanical Engineering and Mechanics, Lehigh University（机械工程与力学系，莱维大学）；Department of Computer and Information Science, University of Pennsylvania（计算机与信息科学系，宾夕法尼亚大学）
Keio University（庆应义塾大学）；OMRON SINIC X Corporation（欧姆龙SINIC X公司）
Machine learning (ML) plays a crucial role in assessing traversability for autonomous rover operations on deformable terrains but suffers from inevitable prediction errors. Especially for heterogeneous terrains where the geological features vary from place to place, erroneous traversability prediction can become more apparent, increasing the risk of unrecoverable rover's wheel slip and immobilization. In this work, we propose a new path planning algorithm that explicitly accounts for such erroneous prediction. The key idea is the probabilistic fusion of distinctive ML models for terrain type c…
This paper introduces Probabilistic Chekov (p-Chekov), a chance-constrained motion planning system that can be applied to high degree-of-freedom (DOF) robots under motion uncertainty and imperfect state information. Given process and observation noise models, it can find feasible trajectories which satisfy a user-specified bound over the probability of collision. Leveraging our previous work in deterministic motion planning which integrated trajectory optimization into a sparse roadmap framework, p-Chekov shows superiority in its planning speed for high-dimensional tasks. P-Chekov incorporates…
We consider scenarios where a ground vehicle plans its path using data gathered by an aerial vehicle. In the aerial images, navigable areas of the scene may be occluded due to obstacles. Naively planning paths using aerial images may result in longer paths as a conservative planner may try to avoid regions that are occluded. We propose a modular, deep learning-based framework that allows the robot to predict the existence of navigable areas in the occluded regions. Specifically, we use image inpainting methods to fill in parts of the areas that are potentially occluded, which can then be seman…
Automated vehicles require the ability to cooperate with humans for smooth integration into today's traffic. While the concept of cooperation is well known, developing a robust and efficient cooperative trajectory planning method is still a challenge. One aspect of this challenge is the uncertainty surrounding the state of the environment due to limited sensor accuracy. This uncertainty can be represented by a Partially Observable Markov Decision Process. Our work addresses this problem by extending an existing cooperative trajectory planning approach based on Monte Carlo Tree Search for conti…
Massachusetts Institute of Technology（麻省理工学院）；Toyota Research Institute（丰田研究院）
Risk-bounded motion planning is an important yet difficult problem for safety-critical tasks. While existing mathematical programming methods offer theoretical guarantees in the context of constrained Markov decision processes, they either lack scalability in solving larger problems or produce conservative plans. Recent advances in deep reinforcement learning improve scalability by learning policy networks as function approximators. In this paper, we propose an extension of soft actor critic model to estimate the execution risk of a plan through a risk critic and produce risk-bounded policies …
Considering Perspectives for Automated Driving Ethics: Collective Risk in Vehicular Motion Planning
Eindhoven University of Technology（埃因霍温理工大学）；CARISSMA Institute of Safety in Future Mobility（未来移动安全研究所）；Technische Hochschule Ingolstadt（因戈尔施塔特技术大学）；TNO（荷兰代尔夫特理工大学）
NUS Graduate School for Integrative Sciences and Engineering（新加坡国立大学综合科学与工程研究生院）；National University of Singapore（新加坡国立大学）；The Hong Kong University of Science and Technology（香港科技大学）；University of California, Berkeley（加州大学伯克利分校）
In this paper, we present an innovative risk-bounded motion planning methodology for stochastic multi-agent systems. For this methodology, the disturbance, noise, and model uncertainty are considered; and a velocity obstacle method is utilized to formulate the collision-avoidance constraints in the velocity space. With the exploitation of geometric information of static obstacles and velocity obstacles, a distributed optimization problem with probabilistic chance constraints is formulated for the stochastic multi-agent system. Consequently, collision-free trajectories are generated under a pre…
Motion planning at urban intersections that accounts for the situation context, handles occlusions, and deals with measurement and prediction uncertainty is a major challenge on the way to urban automated driving. In this work, we address this challenge with a sampling-based optimization approach. For this, we formulate an optimal control problem that optimizes for low risk and high passenger comfort. The risk is calculated on the basis of the perception information and the respective uncertainty using a risk model. The risk model combines set-based methods and probabilistic approaches. Thus, …
The aim of this book is to introduce different robot path planning algorithms and suggest some of the most appropriate ones which are capable of running on a variety of robots and are resistant to disturbances. Being real-time, being autonomous, and the ability to identify high-risk areas and risk management are the other features that will be mentioned throughout these methods.
Autonomous agents such as self-driving cars or parcel robots need to recognize and avoid possible collisions with obstacles in order to move successfully in their environment. Humans, however, have learned to predict movements intuitively and to avoid obstacles in a forward-looking way. The task of collision avoidance can be divided into a global and a local level. Regarding the global level, we propose an approach called "Predictive Collision Management Path Planning" (PCMP). At the local level, solutions for collision avoidance are used that prevent an inevitable collision. Therefore, the ai…
