让机器人自动规划最优路径，避开障碍还能保持平滑运动。
Reward-Based Collision-Free Algorithm for Trajectory Planning of Autonomous Robots
- 用遗传算法结合惩罚机制优化路径选择，兼顾奖励与约束。
- 通过曲率连续的螺旋线轨迹减少抖动，提升运动可行性。
- 适用于地面车、无人机和四足机器人，实测表现稳定高效。
本文提出一种新型自主机器人任务规划算法，从预定义点集中选择最优航点序列，在满足障碍物避让、状态、输入、导数、任务时长和距离约束的前提下最大化总奖励。该问题扩展自带奖赏的旅行商问题。采用定制遗传算法，通过适应度函数、交叉和变异演化候选解，并以惩罚法处理约束。利用微分平坦性与曳矢曲线有效惩罚不可行轨迹，同时通过欧拉螺旋方法实现曲率连续且曲率有界的轨迹，显著提升动态可行性并缓解最小加加速度与最小加加加速度参数化常见的振荡问题。针对离散变量长度的优化空间，交叉操作采用基于动态时间规整的方法，并结合扩展凸组合与投影策略。算法性能通过地面车辆、四旋翼无人机和四足机器人的仿真与实验验证，辅以基准测试与时间复杂度分析。
原文摘要 · Abstract (English)
This paper proposes a novel mission planning algorithm for autonomous robots that selects an optimal waypoint sequence from a predefined set to maximize total reward while satisfying obstacle avoidance, state, input, derivative, mission time, and distance constraints. The formulation extends the prize-collecting traveling salesman problem. A tailored genetic algorithm evolves candidate solutions using a fitness function, crossover, and mutation, with constraint enforcement via a penalty method. Differential flatness and clothoid curves are employed to penalize infeasible trajectories efficiently, while the Euler spiral method ensures curvature-continuous trajectories with bounded curvature, enhancing dynamic feasibility and mitigating oscillations typical of minimum-jerk and snap parameterizations. Due to the discrete variable length optimization space, crossover is performed using a dynamic time-warping-based method and extended convex combination with projection. The algorithm's performance is validated through simulations and experiments with a ground vehicle, quadrotor, and quadruped, supported by benchmarking and time-complexity analysis.
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