多运动障碍物无碰撞运动规划算法的拓扑复杂性

非结构化环境下动态避障的局部路径规划

Local Path Planning with Dynamic Obstacle Avoidance in Unstructured Environments

针对无人地面车辆在动态障碍物密集非结构化环境中的局部路径规划问题，提出结合基于切线的路径规划与外推方法的决策算法，通过处理多项式轨迹动态障碍物，生成无碰撞路径，实现安全导航。

基于控制屏障函数的动态避障安全规划与控制

Safety-Critical Planning and Control for Dynamic Obstacle Avoidance Using Control Barrier Functions

本文提出一种结合MPC与离散时间高阶控制屏障函数的框架，通过网格映射生成凸多面体构建安全约束，无需已知障碍物边界方程，并集成路径规划保证全局最优性，在动态狭窄环境中实现独轮机器人的高效安全避障。

带移动障碍物的移动目标旅行商问题的两阶段双层搜索

Two-Phase Bilevel Search for the Moving-Target Traveling Salesman Problem with Moving Obstacles

针对带移动障碍物的移动目标旅行商问题，提出混合整数锥规划公式和两阶段双层搜索算法，显著优于基线方法。

A Generalization of Bellman's Equation with Application to Path Planning, Obstacle Avoidance and Invariant Set Estimation

The standard Dynamic Programming (DP) formulation can be used to solve Multi-Stage Optimization Problems (MSOP's) with additively separable objective functions. In this paper we consider a larger class of MSOP's with monotonically backward separable objective functions; additively separable functions being a special case of monotonically backward separable functions. We propose a necessary and sufficient condition, utilizing a generalization of Bellman's equation, for a solution of a MSOP, with a monotonically backward separable cost function, to be optimal. Moreover, we show that this propose…

Safety-Critical Control and Planning for Obstacle Avoidance between Polytopes with Control Barrier Functions

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…

Piecewise-Linear Motion Planning amidst Static, Moving, or Morphing Obstacles

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 …

Path Planning for Concentric Tube Robots: a Toolchain with Application to Stereotactic Neurosurgery

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…

路径规划中用于避障的组合析取约束

Combinatorial Disjunctive Constraints for Obstacle Avoidance in Path Planning

本文提出一种基于组合析取约束和独立分支方案的2D避障路径规划新方法，利用多项式时间算法构建理想公式，并开源Julia库，实验证明其比标准big-M技术更紧凑且具竞争力。

Shape and Trajectory Tracking of Moving Obstacles

This work presents new methods and algorithms for tracking the shape and trajectory of moving reflecting obstacles with broken rays, or rays reflecting at an obstacle. While in tomography the focus of the reconstruction method is to recover the velocity structure of the domain, the shape and trajectory reconstruction procedure directly finds the shape and trajectory of the obstacle. The physical signal carrier for this innovative method are ultrasonic beams. When the speed of sound is constant, the rays are straight line segments and the shape and trajectory of moving objects will be reconstru…

使用相干风险度量的风险规避滚动时域运动规划用于避障

Risk-Averse Receding Horizon Motion Planning for Obstacle Avoidance using Coherent Risk Measures

本文针对不确定动力学智能体在随机动态障碍物环境中的避障问题，提出基于相干风险度量的MPC方案，并设计航点跟随算法证明其递归可行性与有限时间任务完成保证。

A Real-Time Approach for Chance-Constrained Motion Planning with Dynamic Obstacles

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 co…