A Real-Time Approach for Chance-Constrained Motion Planning with Dynamic Obstacles
University of Luxembourg（卢森堡大学）；Interdisciplinary Centre for Security, Reliability and Trust（安全、可靠性与信任跨学科中心）；ispace Europe（ispace欧洲公司）
Manuel Castillo-Lopez, Philippe Ludivig, Seyed Amin Sajadi-Alamdari, Jose Luis Sanchez-Lopez, Miguel A. Olivares-Mendez, Holger Voos
备注：
This paper has been accepted for publication in the IEEE Robotics and Automation Letters. Please cite the paper as: M. Castillo-Lopez, P. Ludivig, S. A. Sajadi-Alamdari, J. L. Sanchez-Lopez, M. A. Olivares-Mendez, H. Voos, "A Real-Time Approach for Chance-Constrained Motion Planning with Dynamic Obstacles", IEEE Robotics and Automation Letters (RA-L), 2020
发表信息：
IEEE Robotics and Automation Letters ( Volume: 5 , Issue: 2 , April 2020 ) Page(s): 3620 - 3625
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an obstacle's space: a polyhedron, such as a cuboid, or a nonlinear differentiable surface, such as an ellipsoid. The former approach relies on disjunctive programming, which has a relatively high computational cost that grows exponentially with the number of obstacles. The latter approach needs to be linearized locally to find a tractable evaluation of the chance constraints, which dramatically reduces the remaining free space and leads to over-conservative trajectories or even unfeasibility. In this work, we present a hybrid approach that eludes the pitfalls of both strategies while maintaining the original safety guarantees. The key idea consists in obtaining a safe differentiable approximation for the disjunctive chance constraints bounding the obstacles. The resulting nonlinear optimization problem is free of chance constraint linearization and disjunctive programming, and therefore, it can be efficiently solved to meet fast real-time requirements with multiple obstacles. We validate our approach through mathematical proof, simulation and real experiments with an aerial robot using nonlinear model predictive control to avoid pedestrians.
This comment presents the results of using chance-constrained model predictive control (MPC) to solve a one-horizon benchmark collision avoidance problem.
This paper introduces Chance Constrained Gaussian Process-Motion Planning (CCGP-MP), a motion planning algorithm for robotic systems under motion and state estimate uncertainties. The paper's key idea is to capture the variations in the distance-to-collision measurements caused by the uncertainty in state estimation techniques using a Gaussian Process (GP) model. We formulate the planning problem as a chance constraint problem and propose a deterministic constraint that uses the modeled distance function to verify the chance-constraints. We apply Simplicial Homology Global Optimization (SHGO) …
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…
IBM Watson Research Center（IBM沃森研究中心）；Laboratoire d’Analyse et d’Architecture des Systèmes (LAAS), Institute of Mathematics, University of Toulouse（图卢兹大学数学研究所系统分析与架构实验室）；Robotics at Google（谷歌机器人部门）
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of semidefinite programs that yield increasingly refined lower bounds converging monotonically to the optimal path length. For computational tractability, our global moment optimization approach motivates an iterative motion planner that outperforms competing sampling-based and nonlinear optimization baselines. Our method natively handles continuous time constraints …
Inner Mongolia University of Technology（内蒙古工业大学）；Yanshan University（燕山大学）
This article introduces a multimodal motion planning (MMP) algorithm that combines three-dimensional (3-D) path planning and a DWA obstacle avoidance algorithm. The algorithms aim to plan the path and motion of obstacle-overcoming robots in complex unstructured scenes. A novel A-star algorithm is proposed to combine the characteristics of unstructured scenes and a strategy to switch it into a greedy best-first strategy algorithm. Meanwhile, the algorithm of path planning is integrated with the DWA algorithm so that the robot can perform local dynamic obstacle avoidance during the movement alon…
Agent behavior is arguably the greatest source of uncertainty in trajectory planning for autonomous vehicles. This problem has motivated significant amounts of work in the behavior prediction community on learning rich distributions of the future states and actions of agents. However, most current works on chance-constrained trajectory planning under agent or obstacle uncertainty either assume Gaussian uncertainty or linear constraints, which is limiting, or requires sampling, which can be computationally intractable to encode in an optimization problem. In this paper, we extend the state-of-t…
Tsinghua University（清华大学）；Shanghai Qizhi Institute（上海期智研究院）；University of California, Berkeley（加州大学伯克利分校）；University of Tokyo（东京大学）
Motion planning under uncertainty is of significant importance for safety-critical systems such as autonomous vehicles. Such systems have to satisfy necessary constraints (e.g., collision avoidance) with potential uncertainties coming from either disturbed system dynamics or noisy sensor measurements. However, existing motion planning methods cannot efficiently find the robust optimal solutions under general nonlinear and non-convex settings. In this paper, we formulate such problem as chance-constrained Gaussian belief space planning and propose the constrained iterative Linear Quadratic Gaus…
University of California San Diego（加州大学圣地亚哥分校）；San Diego State University（圣地亚哥州立大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Safety is a critical concern for the success of urban air mobility, especially in dynamic and uncertain environments. This paper proposes a path planning algorithm based on RRT in conjunction with chance constraints in the presence of uncertain obstacles. The chance-constrained formulation for Gaussian distributed obstacles is developed by converting the probabilistic constraints to deterministic constraints in terms of distribution parameters. The probabilistic feasible region at every time step can be established through the simulation of the system state and the evaluation of convex constra…
We consider the problem of autonomous navigation using limited information from a remote sensor network. Because the remote sensors are power and bandwidth limited, we use event-triggered (ET) estimation to manage communication costs. We introduce a fast and efficient sampling-based planner which computes motion plans coupled with ET communication strategies that minimize communication costs, while satisfying constraints on the probability of reaching the goal region and the point-wise probability of collision. We derive a novel method for offline propagation of the expected state distribution…
This article presents a multi-robot trajectory planning method which not only guarantees optimization feasibility and but also resolves deadlocks in obstacle-dense environments. The method is proposed via formulating a recursive optimization problem, where a novel safe corridor is generated online to ensure obstacle avoidance in trajectory planning. A dynamic-priority mechanism is combined with the right-hand rule to handle potential deadlocks that are much harder to resolve due to static obstacles. Comparisons with other state-of-the-art results are conducted to validate the improved safety a…
This paper presents a minimum displacement motion planning problem wherein obstacles are displaced by a minimum amount to find a feasible path. We define a metric for robot-obstacle intersection that measures the extent of the intersection and use this to penalize robot-obstacle overlaps. Employing the actual robot dynamics, the planner first finds a path through the obstacles that minimizes the robot-obstacle intersections. The metric is then used to iteratively displace the obstacles to achieve a feasible path. Several examples are provided that successfully demonstrates the proposed problem…
If we give a robot the task of moving an object from its current position to another location in an unknown environment, the robot must explore the map, identify all types of obstacles, and then determine the best route to complete the task. We proposed a mathematical model to find an optimal path planning that avoids collisions with all static and moving obstacles and has the minimum completion time and the minimum distance traveled. In this model, the bounding box around obstacles and robots is not considered, so the robot can move very close to the obstacles without colliding with them. We …
This study investigates the exact geometry of the configuration space in three-dimensional rotational motion planning. A parameterization of configuration space obstacles is derived for a given triangulated or ball-approximated scene with an object rotating around a given point. The results obtained are an important step towards a complete description of the rich structure of a configuration space in three-dimensional rotational motion planning.
In this paper, we address the problem of sampling-based motion planning under motion and measurement uncertainty with probabilistic guarantees. We generalize traditional sampling-based tree-based motion planning algorithms for deterministic systems and propose belief-$\mathcal{A}$, a framework that extends any kinodynamical tree-based planner to the belief space for linear (or linearizable) systems. We introduce appropriate sampling techniques and distance metrics for the belief space that preserve the probabilistic completeness and asymptotic optimality properties of the underlying planner. W…
Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control…
Many practical applications of robotics require systems that can operate safely despite uncertainty. In the context of motion planning, two types of uncertainty are particularly important when planning safe robot trajectories. The first is environmental uncertainty -- uncertainty in the locations of nearby obstacles, stemming from sensor noise or (in the case of obstacles' future locations) prediction error. The second class of uncertainty is uncertainty in the robots own state, typically caused by tracking or estimation error. To achieve high levels of safety, it is necessary for robots to co…
Collision-free mobile robot navigation is an important problem for many robotics applications, especially in cluttered environments. In such environments, obstacles can be static or dynamic. Dynamic obstacles can additionally be interactive, i.e. changing their behavior according to the behavior of other entities. The perception and prediction modules of robotic systems create probabilistic representations and predictions of such environments. In this paper, we propose a novel prediction representation for interactive behaviors of dynamic obstacles. Then, we propose a real-time trajectory plan…
This work investigates the use of Neural implicit representations, specifically Neural Radiance Fields (NeRF), for geometrical queries and motion planning. We show that by adding the capacity to infer occupancy in a radius to a pre-trained NeRF, we are effectively learning an approximation to a Euclidean Signed Distance Field (ESDF). Using backward differentiation of the augmented network, we obtain an obstacle gradient that is integrated into an obstacle avoidance policy based on the Riemannian Motion Policies (RMP) framework. Thus, our findings allow for very fast sampling-free obstacle avoi…
IIIT Hyderabad（印度海得拉巴国际信息技术学院）；University of Tartu（塔尔图大学）
We present CCO-VOXEL: the very first chance-constrained optimization (CCO) algorithm that can compute trajectory plans with probabilistic safety guarantees in real-time directly on the voxel-grid representation of the world. CCO-VOXEL maps the distribution over the distance to the closest obstacle to a distribution over collision-constraint violation and computes an optimal trajectory that minimizes the violation probability. Importantly, unlike existing works, we never assume the nature of the sensor uncertainty or the probability distribution of the resulting collision-constraint violations.…
Georgia Institute of Technology（佐治亚理工学院）；George W. Woodruff School of Mechanical Engineering（乔治·W·伍德拉夫机械工程学院）；Department of Electrical and Computer Engineering（电气与计算机工程系）
As robots move from the laboratory into the real world, motion planning will need to account for model uncertainty and risk. For robot motions involving intermittent contact, planning for uncertainty in contact is especially important, as failure to successfully make and maintain contact can be catastrophic. Here, we model uncertainty in terrain geometry and friction characteristics, and combine a risk-sensitive objective with chance constraints to provide a trade-off between robustness to uncertainty and constraint satisfaction with an arbitrarily high feasibility guarantee. We evaluate our a…
With the incremental development of robotic platforms to automate the manual processes, path planning has become a critical domain with or without the knowledge of the indoor and outdoor environment. The algorithms can be intelligent or pre-structured and should optimally reach the destination efficiently. The major challenge in this domain is to find a path which is free from static obstacles as well as dynamic obstacles. In this paper, a methodology is proposed with the implementation details of the robotic platform to cover the critical key points and to arrive at the original key point in …
We present a novel approach to perform probabilistic collision detection between a high-DOF robot and high-DOF obstacles in dynamic, uncertain environments. In dynamic environments with a high-DOF robot and moving obstacles, our approach efficiently computes accurate collision probability between the robot and obstacles with upper error bounds. Furthermore, we describe a prediction algorithm for future obstacle position and motion that accounts for both spatial and temporal uncertainties. We present a trajectory optimization algorithm for high-DOF robots in dynamic, uncertain environments base…
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；Hanoi University of Science and Technology（河内科技大学）
A new path planning method for Mobile Robots (MR) has been developed and implemented. On the one hand, based on the shortest path from the start point to the goal point, this path planner can choose the best moving directions of the MR, which helps to reach the target point as soon as possible. On the other hand, with an intelligent obstacle avoidance, our method can find the target point with the near-shortest path length while avoiding some infinite loop traps of several obstacles in unknown environments. The combination of two approaches helps the MR to reach the target point with a very re…
Saarland University（萨尔兰大学）；Ilmenau University of Technology（伊尔梅瑙工业大学）
We present a toolchain for solving path planning problems for concentric tube robots through obstacle fields. First, ellipsoidal sets representing the target area and obstacles are constructed from labelled point clouds. Then, the nonlinear and highly nonconvex optimal control problem is solved by introducing a homotopy on the obstacle positions where at one extreme of the parameter the obstacles are removed from the operating space, and at the other extreme they are located at their intended positions. We present a detailed example (with more than a thousand obstacles) from stereotactic neuro…
FZI Research Center for Information Technology（FZI信息技术研究中心）
We present a biologically inspired approach for path planning with dynamic obstacle avoidance. Path planning is performed in a condensed configuration space of a robot generated by self-organizing neural networks (SONN). The robot itself and static as well as dynamic obstacles are mapped from the Cartesian task space into the configuration space by precomputed kinematics. The condensed space represents a cognitive map of the environment, which is inspired by place cells and the concept of cognitive maps in mammalian brains. The generation of training data as well as the evaluation were perform…
Chance-constrained motion planning requires uncertainty in dynamics to be propagated into uncertainty in state. When nonlinear models are used, Gaussian assumptions on the state distribution do not necessarily apply since almost all random variables propagated through nonlinear dynamics results in non-Gaussian state distributions. To address this, recent works have developed moment-based approaches for enforcing chance-constraints on non-Gaussian state distributions. However, there still lacks fast and accurate moment propagation methods to determine the necessary statistical moments of these …
California Institute of Technology（加州理工学院）；Jet Propulsion Laboratory（喷气推进实验室）
We present gPC-SCP: Generalized Polynomial Chaos-based Sequential Convex Programming to compute a sub-optimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion planning for robotic systems under uncertainty. The gPC-SCP method involves two steps. The first step is to derive a surrogate problem of \emph{deterministic} nonlinear optimal control (DNOC) with convex constraints by using gPC expansion and the distributionally-robust convex subset of the chance constraints. The second step is to solve the DNOC problem us…
Automation and Control Institute (ACIN), TU Wien（维也纳工业大学自动化与控制研究所）；Center for Vision, Automation and Control, AIT Austrian Institute of Technology（奥地利技术研究所视觉、自动化与控制中心）；Department of Computer Science, University of Liverpool（利物浦大学计算机科学系）
This paper presents a two-step algorithm for online trajectory planning in indoor environments with unknown obstacles. In the first step, sampling-based path planning techniques such as the optimal Rapidly exploring Random Tree (RRT*) algorithm and the Line-of-Sight (LOS) algorithm are employed to generate a collision-free path consisting of multiple waypoints. Then, in the second step, constrained quadratic programming is utilized to compute a smooth trajectory that passes through all computed waypoints. The main contribution of this work is the development of a flexible trajectory planning f…
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；JSC Integrant（JSC Integrant公司）；Federal Research Center for Computer Science and Control RAS（俄罗斯科学院计算机科学与控制联邦研究中心）；AIRI
This paper addresses the kinodynamic motion planning for non-holonomic robots in dynamic environments with both static and dynamic obstacles -- a challenging problem that lacks a universal solution yet. One of the promising approaches to solve it is decomposing the problem into the smaller sub problems and combining the local solutions into the global one. The crux of any planning method for non-holonomic robots is the generation of motion primitives that generates solutions to local planning sub-problems. In this work we introduce a novel learnable steering function (policy), which takes into…
Technion - Israel Institute of Technology（以色列理工学院）
An important capability of autonomous Unmanned Aerial Vehicles (UAVs) is autonomous landing while avoiding collision with obstacles in the process. Such capability requires real-time local trajectory planning. Although trajectory-planning methods have been introduced for cases such as emergency landing, they have not been evaluated in real-life scenarios where only the surface of obstacles can be sensed and detected. We propose a novel optimization framework using a pre-planned global path and a priority map of the landing area. Several trajectory planning algorithms were implemented and evalu…
Autonomous Systems Lab. (ASL), ETH Zürich（苏黎世联邦理工学院自主系统实验室）；TU Delft（代尔夫特理工大学）
Target search with unmanned aerial vehicles (UAVs) is relevant problem to many scenarios, e.g., search and rescue (SaR). However, a key challenge is planning paths for maximal search efficiency given flight time constraints. To address this, we propose the Obstacle-aware Adaptive Informative Path Planning (OA-IPP) algorithm for target search in cluttered environments using UAVs. Our approach leverages a layered planning strategy using a Gaussian Process (GP)-based model of target occupancy to generate informative paths in continuous 3D space. Within this framework, we introduce an adaptive rep…
Obstacle clearance in state space is an important optimization objective in path planning because it can result in safe paths. This technical report presents admissible solution- and path-cost heuristics for this objective, which can be used to improve the performance of informed path planning algorithms.
International Institute of Information Technology Hyderabad（海得拉巴国际信息技术学院）
In this paper, an algorithm for Unmanned Aircraft Systems Traffic Management (UTM) for a finite number of unmanned aerial vehicles (UAVs) is proposed. This algorithm is developed by combining the Rapidly-Exploring Random Trees (RRT) and Velocity Obstacle (VO) algorithms and is referred to as the RRT-VO UTM algorithm. Here, the RRT algorithm works offline to generate obstacle-free waypoints in a given environment with known static obstacles. The VO algorithm, on the other hand, operates online to avoid collisions with other UAVS and known static obstacles. The boundary of the static obstacles a…
Thanks to the rapid evolvement of robotic technologies, robot mowing is emerging to liberate humans from the tedious and time-consuming landscape work. Traditionally, robot mowing is perceived as a "Coverage Path Planning" problem, with a simplification that converts non-convex obstacles into convex obstacles. Besides, the converted obstacles are commonly dilated by the robot's circumcircle for collision avoidance. However when applied to robot mowing, an obstacle in a lawn is usually non-convex, imagine a garden on the lawn, such that the mentioned obstacle processing methods would fill in so…
Safe UAV navigation is challenging due to the complex environment structures, dynamic obstacles, and uncertainties from measurement noises and unpredictable moving obstacle behaviors. Although plenty of recent works achieve safe navigation in complex static environments with sophisticated mapping algorithms, such as occupancy map and ESDF map, these methods cannot reliably handle dynamic environments due to the mapping limitation from moving obstacles. To address the limitation, this paper proposes a trajectory planning framework to achieve safe navigation considering complex static environmen…
Inria（法国国家信息与自动化研究所）；École normale supérieure（巴黎高等师范学院）；CNRS（法国国家科学研究中心）；PSL Research University（巴黎文理研究大学）；University Grenoble Alpes（格勒诺布尔大学）；Grenoble INP（格勒诺布尔理工学院）
Motion planning and obstacle avoidance is a key challenge in robotics applications. While previous work succeeds to provide excellent solutions for known environments, sensor-based motion planning in new and dynamic environments remains difficult. In this work we address sensor-based motion planning from a learning perspective. Motivated by recent advances in visual recognition, we argue the importance of learning appropriate representations for motion planning. We propose a new obstacle representation based on the PointNet architecture and train it jointly with policies for obstacle avoidance…
Chalmers University of Technology（查尔姆斯理工大学）；Lund University（隆德大学）
Motion planning methods like navigation functions and harmonic potential fields provide (almost) global convergence and are suitable for obstacle avoidance in dynamically changing environments due to their reactive nature. A common assumption in the control design is that the robot operates in a disjoint star world, i.e. all obstacles are strictly starshaped and mutually disjoint. However, in real-life scenarios obstacles may intersect due to expanded obstacle regions corresponding to robot radius or safety margins. To broaden the applicability of aforementioned reactive motion planning method…
Many path planning algorithms are based on sampling the state space. While this approach is very simple, it can become costly when the obstacles are unknown, since samples hitting these obstacles are wasted. The goal of this paper is to efficiently identify obstacles in a map and remove them from the sampling space. To this end, we propose a pre-processing algorithm for space exploration that enables more efficient sampling. We show that it can boost the performance of other space sampling methods and path planners. Our approach is based on the fact that a convex obstacle can be approximated p…
This paper presents a sequential Model Predictive Control (MPC) approach to reactive motion planning for bipedal robots in dynamic environments. The approach relies on a sequential polytopic decomposition of the free space, which provides an ordered collection of mutually intersecting obstacle free polytopes and waypoints. These are subsequently used to define a corresponding sequence of MPC programs that drive the system to a goal location avoiding static and moving obstacles. This way, the planner focuses on the free space in the vicinity of the robot, thus alleviating the need to consider a…
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…
This paper focuses on automatic guided vehicle (AGV) trajectory planning in the presence of moving obstacles with known but complicated trajectories. In order to achieve good solution precision, optimality and unification, the concerned task should be formulated as an optimal control problem, and then discretized into a nonlinear programming (NLP) problem, which is numerically optimized thereafter. Without a near-feasible or near-optimal initial guess, the NLP-solving process is usually slow. With the purpose of accelerating the NLP solution, a search-based rough planning stage is added to gen…
Graph-based Path Planning with Dynamic Obstacle Avoidance for Autonomous Parking
Honda Research Institute (HRI)（本田研究院）；GRASP Lab（GRASP实验室）；University of Pennsylvania（宾夕法尼亚大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of California at Riverside（加州大学河滨分校）
本文提出时间索引Hybrid A star算法，将动态障碍物预测融入在线规划框架，在垂直、斜向和平行泊车场景中实现高效安全的动态避障路径规划。
