We propose a method to efficiently compute the forward stochastic reach (FSR) set and its probability measure for nonlinear systems with an affine disturbance input, that is stochastic and bounded. This method is applicable to systems with an a priori known controller, or to uncontrolled systems, and often arises in problems in obstacle avoidance in mobile robotics. When used as a constraint in finite horizon controller synthesis, the FSR set, and its probability measure facilitates probabilistic collision avoidance, in contrast to methods which presume the obstacles act in a worst-case fashion and generate hard constraints that cannot be violated. We tailor our approach to accommodate rigid body constraints, and show convexity is assured so long as the rigid body shape of each obstacle is also convex. We extend methods for multi-obstacle avoidance through mixed integer linear programming (with linear robot and obstacle dynamics) to accommodate chance constraints that represent the FSR set probability measure. We demonstrate our method on a rigid-body obstacle avoidance scenario, in which a receding horizon controller is designed to avoid several stochastically moving obstacles while reaching the desired goal. Our approach can provide solutions when approaches that presume a worst-case action from the obstacle fail.
This paper presents an algorithm for local motion planning in environments populated by moving elliptical obstacles whose velocity, shape and size are fully known but may change with time. We base the algorithm on a collision avoidance vector field (CAVF) that aims to steer an agent to a desired final state whose motion is described by a double integrator kinematic model. In addition to handling multiple obstacles, the method is applicable in bounded environments for more realistic applications (e.g., motion planning inside a building). We also incorporate a method to deal with agents whose co…
Obstacle avoidance via B-spline parameterizations of flat trajectories
Politehnica University of Bucharest（布加勒斯特理工大学）；Univ. Grenoble Alpes, Laboratory of Conception and Integration of Systems (LCIS EA 3747)（格勒诺布尔阿尔卑斯大学，系统设计与集成实验室）
This article considers collision avoidance (COLAV) for both static and moving obstacles using the branching-course model predictive control (BC-MPC) algorithm, which is designed for use by autonomous surface vehicles (ASVs). The BC-MPC algorithm originally only considered COLAV of moving obstacles, so in order to make the algorithm also be able to avoid static obstacles, we introduce an extra term in the objective function based on an occupancy grid. In addition, other improvements are made to the algorithm resulting in trajectories with less wobbling. The modified algorithm is verified throug…
In this letter we study variational obstacle avoidance problems on complete Riemannian manifolds. The problem consists of minimizing an energy functional depending on the velocity, covariant acceleration and a repulsive potential function used to avoid a static obstacle on the manifold, among a set of admissible curves. We derive the dynamical equations for extrema of the variational problem, in particular on compact connected Lie groups and Riemannian symmetric spaces. Numerical examples are presented to illustrate the proposed method.
In this paper we study a path planning problem from a variational approach to collision and obstacle avoidance for multi-agent systems evolving on a Riemannian manifold. The problem consists of finding non-intersecting trajectories between the agent and prescribed obstacles on the workspace, among a set of admissible curves, to reach a specified configuration, based on minimizing an energy functional that depends on the velocity, covariant acceleration and an artificial potential function used to prevent collision with the obstacles and among the agents. We apply the results to examples of a p…
In this work, we combine {Model Predictive Control} (MPC) and Control Barrier Function (CBF) design {methods} to create a hierarchical control law for simultaneous lane-keeping (LK) and obstacle avoidance (OA): at the low level, MPC performs LK via trajectory tracking during nominal operation; and at the high level, different CBF-based safety filters that ensure both LK and OA are designed and compared across some practical scenarios. In particular, we show that Exponential Safety (ESf) and Prescribed-Time Safety (PTSf) filters, which override the MPC control when necessary, result in feasible…
Control barrier functions (CBFs) recently introduced a systematic way to guarantee the system's safety through set invariance. Together with a nominal control method, it establishes a safety-critical control mechanism. The resulting safety constraints can be enforced as hard constraints in quadratic programming (QP) optimization, which rectifies the nominal control law based on the set of safe inputs. In this work, we introduce a multiple CBFs scheme which enforces several safety constraints with high relative degrees. This control structure is essential in many challenging robotic application…
Formation control with the flocking approach is an efficient method that can reach the formation without determining the agent's position. This paper focuses on reaching the circular formation around the leader or target with a specific geometric pattern for the second-order multi-agent system. This means that the polygon formation is formed with arbitrary initial conditions. To create the circular formation, two potential function terms have been used for agent-agent and leader-agent interaction. In our approach, if some faults occur during the circular formation and some agents fail, the reg…
This paper introduces control barrier functions for discrete-time systems, which can be shown to be necessary and sufficient for controlled invariance of a given set. Moreover, we propose nonlinear discrete-time control barrier functions for partially control affine systems that lead to controlled invariance conditions that are affine in the control input, leading to a tractable formulation that enables us to handle the safety optimal control problem for a broader range of applications with more complicated safety conditions than existing approaches. In addition, we develop mixed-integer formu…
We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Lagrangian and obtain the reduced optimality conditions from a reduced variational principle via symmetry reduction techniques in both settings, continuous-time, and discrete-time. We apply the results to a collision and obstacle avoidance problem for mult…
This paper introduces a class of time-varying controllers for Euler-Lagrange systems such that the convergence occurs at an arbitrary finite time, independently of initial conditions, and free of chattering. The proposed controller is based on a mapping technique and is designed in two steps: First, a conventional (obstacle avoidance) asymptotically stable controller is specified for the nominal system; then, by a simple substitution, a prescribed-time (obstacle avoidance) controller is achievable for the perturbed system. It is proved that the proposed scheme is uniformly prescribed-time stab…
Hanoi University of Industry（河内工业大学）；University of Economics - Technology for Industries（经济与技术工业大学）
In recent years, the mobile robot has been considerable attention to researchers for its application in various environments. For a mobile robot navigating its way from starting point to a goal point while traversing through deterrents, needs to recognize the obstacles and generate new trajectories to reach the destination. This paper presents an obstacle avoidance method for mobile robots using an open-source in robot operation system (ROS) combining with the dynamic window approach (DWA) algorithm. The experiment is carried out using a mobile robot in which the navigation data is based on da…
This paper studies the reduction by symmetry of a variational obstacle avoidance problem. We derive the reduced necessary conditions in the case of Lie groups endowed with a left-invariant metric, and for its corresponding Riemannian homogeneous spaces by considering an alternative variational problem written in terms of a connection on the horizontal bundle of the Lie group. A number of special cases where the obstacle avoidance potential can be computed explicitly are studied in detail, and these ideas are applied to the obstacle avoidance task for a rigid body evolving on SO$(3)$ and for th…
In this paper, we investigate the obstacle avoidance and navigation problem in the robotic control area. For solving such a problem, we propose revised Deep Deterministic Policy Gradient (DDPG) and Proximal Policy Optimization algorithms with an improved reward shaping technique. We compare the performances between the original DDPG and PPO with the revised version of both on simulations with a real mobile robot and demonstrate that the proposed algorithms achieve better results.
University of Quebec in Outaouais（乌塔韦魁北克大学）；University of Groningen（格罗宁根大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）
In this paper we present a hybrid feedback approach to solve the navigation problem of a point mass in the n-dimensional space containing an arbitrary number of ellipsoidal shape obstacles. The proposed hybrid control algorithm guarantees both global asymptotic stabilization to a reference and avoidance of the obstacles. The intuitive idea of the proposed hybrid feedback is to switch between two modes of control: stabilization and avoidance. The geometric construction of the flow and jump sets of the proposed hybrid controller, exploiting hysteresis regions, guarantees Zeno-free switching betw…
We study variational obstacle avoidance problems on complete Riemannian manifolds and apply the results to the construction of piecewise smooth curves interpolating a set of knot points in systems with impulse effects. We derive the dynamical equations for extrema in the variational problem, and show the existence of minimizers by using lower-continuity arguments for weak convergence on an infinite-dimensional Hilbert manifold. We then provide conditions under which it is possible to ensure that the extrema will safely avoid a given obstacle within some desired tolerance.
N-dimensional Convex Obstacle Avoidance using Hybrid Feedback Control (Extended version)
Department of Electrical and Computer Engineering, Lakehead University（电气与计算机工程系，拉科赫大学）；Department of Electrical and Computer Engineering, Western University（电气与计算机工程系，西部大学）
Trajectory Planning with Model Predictive Control for Obstacle Avoidance Considering Prediction Uncertainty
Institute of Electromobility, RPTU University Kaiserslautern-Landau（电磁移动研究所，科隆-兰道大学）；Institute of Wireless Communications and Navigation, RPTU University Kaiserslautern-Landau（无线通信与导航研究所，科隆-兰道大学）
Hybrid Feedback Control for Global Navigation with Locally Optimal Obstacle Avoidance in n-Dimensional Spaces
Department of Electrical Engineering, Lakehead University（电气工程系，拉科夫大学）；Department of Computer Science and Engineering, University of Quebec in Outaouais（计算机科学与工程系，魁北克大学瓦省分校）
This paper proposes a framework for 3D obstacle avoidance in the presence of partial observability of environment obstacles. The method focuses on the utility of the Artificial Potential Function (APF) controller in a practical setting where noisy and incomplete information about the proximity is inevitable. We propose a Particle Filter (PF) approach to estimate potential obstacle locations in an input depth image stream. The probable candidates are then used to generate an action that maneuvers the robot towards the negative gradient of potential at each time instant. Rigorous experimental va…
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…
In recent years, nonlinear model predictive control (NMPC) has been extensively used for solving automotive motion control and planning tasks. In order to formulate the NMPC problem, different coordinate systems can be used with different advantages. We propose and compare formulations for the NMPC related optimization problem, involving a Cartesian and a Frenet coordinate frame (CCF/ FCF) in a single nonlinear program (NLP). We specify costs and collision avoidance constraints in the more advantageous coordinate frame, derive appropriate formulations and compare different obstacle constraints…
Dynamic Bipedal MPC with Foot-level Obstacle Avoidance and Adjustable Step Timing
Mechanical Engineering Department at the FAMU-FSU College of Engineering（佛罗里达州立大学工程学院机械工程系）；FAMU-FSU College of Engineering（佛罗里达大学-萨拉姆斯学院工程学院）；Toyota Research Institute（丰田研究院）；Ford Motor Company（福特汽车公司）
Efficient Collision-Avoidance Constraints for Ellipsoidal Obstacles in Optimal Control: Application to Path-Following MPC and UAVs
Institute of Engineering and Computational Mechanics, University of Stuttgart（工程与计算力学研究所，斯图加特大学）；Chair of Systems Modeling and Simulation, Saarland University（系统建模与仿真教授团，萨尔兰大学）；Department of Mechanical Engineering, LUT University（机械工程系，卢霍斯大学）
University of Florida（佛罗里达大学）；Amazon Robotics（亚马逊机器人公司）；Tongdun Technology（同盾科技）
We propose a deep reinforcement learning (DRL) methodology for the tracking, obstacle avoidance, and formation control of nonholonomic robots. By separating vision-based control into a perception module and a controller module, we can train a DRL agent without sophisticated physics or 3D modeling. In addition, the modular framework averts daunting retrains of an image-to-action end-to-end neural network, and provides flexibility in transferring the controller to different robots. First, we train a convolutional neural network (CNN) to accurately localize in an indoor setting with dynamic foreg…
School of Aeronautic Science and Engineering, Beihang University（北京航空航天大学航空科学与工程学院）；Research Institute for Frontier Science, Beihang University（北京航空航天大学前沿科学研究院）；School of Electronic and Information Engineering, Beihang University（北京航空航天大学电子信息工程学院）
The rapid development of unmanned aerial vehicles (UAV) puts forward a higher requirement for autonomous obstacle avoidance. Due to the limited payload and power supply, small UAVs such as quadrotors usually carry simple sensors and computation units, which makes traditional methods more challenging to implement. In this paper, a novel framework is demonstrated to control a quadrotor flying through crowded environments autonomously with monocular vision. The framework adopts a two-stage architecture, consisting of a sensing module and a decision module. The sensing module is based on an unsupe…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Tübingen（图宾根大学）；International Institute for Information Technology（国际信息技术研究所）
In this work, we consider the problem of decentralized multi-robot target tracking and obstacle avoidance in dynamic environments. Each robot executes a local motion planning algorithm which is based on model predictive control (MPC). The planner is designed as a quadratic program, subject to constraints on robot dynamics and obstacle avoidance. Repulsive potential field functions are employed to avoid obstacles. The novelty of our approach lies in embedding these non-linear potential field functions as constraints within a convex optimization framework. Our method convexifies non-convex const…
An Autonomous Road Vehicle (ARV) can navigate various types of road networks using inputs such as throttle (acceleration), braking (deceleration), and steering (change of lateral direction). In most ARV driving scenarios that involve normal vehicle traffic and encounters with vulnerable road users (VRUs), ARVs are not required to take evasive action. This paper presents a novel Emergency Obstacle Avoidance Maneuver (EOAM) methodology for ARVs traveling at higher speeds and lower road surface friction, involving time-critical maneuver determination and control. The proposed EOAM Framework offer…
As passenger vehicle technologies have advanced, so have their capabilities to avoid obstacles, especially with developments in tires, suspensions, steering, as well as safety technologies like ABS, ESC, and more recently, ADAS systems. However, environments around passenger vehicles have also become more complex, and dangerous. There have previously been studies that outline driver tendencies and performance capabilities when attempting to avoid obstacles while driving passenger vehicles. Now that autonomous vehicles are being developed with obstacle avoidance capabilities, it is important to…
Stream Function-Based Navigation for Complex Quadcopter Obstacle Avoidance
GIPSA-lab, Université Grenoble Alpes - CNRS（格拉诺布尔大学实验室，格拉诺布尔大学-国家科学研究中心）；Department of Mechanical Engineering, Dalhousie University（达勒豪西大学机械工程系）；Advanced Control and Mechatronics Laboratory, Department of Mechanical Engineering, Dalhousie University（达勒豪西大学先进控制与机电实验室，机械工程系）
Learning Barrier-Certified Polynomial Dynamical Systems for Obstacle Avoidance with Robots
Munich Institute of Robotics and Machine Intelligence (MIRMI)（慕尼黑机器人与机器智能研究所）；Technical University of Munich (TUM)（慕尼黑工业大学）；Omar Al-Mukhtar University (OMU)（奥马尔·阿尔-穆赫塔尔大学）；School of Computer Science, University of Nottingham（诺丁汉大学计算机学院）；Learning Algorithms and Systems Laboratory（学习算法与系统实验室）；EPFL（洛桑联邦理工学院）
Hamburg University of Technology（汉堡工业大学）；Institute of Mechanics and Ocean Engineering（力学与海洋工程研究所）
The goal of this thesis is to propose the combination of Control-Barrier-Functions (CBF) with Model-Predictive-Control (MPC) resulting in the novel Model-Predictive-Control-Barrier-Function (MPCBF). It can be shown, that the performance of the MPCBF surpasses the performance of the CBF due to the increased time horizon of the MPC. Moreover, the MPCBF was applied to a quadrotor, a system strongly in need of fast and predictive control. Using the MPCBF, the quadrotor was able to avoid obstacles, which the CBF failed to avoid due to the relative speed of the obstacle. The results of this work are…
Study of dynamical system based obstacle avoidance via manipulating orthogonal coordinates
Artificial Intelligence Research Center of National Innovation Institute of Defense Technology（国家创新技术研究院人工智能研究中心）；Tianjin Artificial Intelligence Innovation Center（天津人工智能创新中心）
