Due to nonholonomic dynamics, the motion planning of nonholonomic robots is always a difficult problem. This letter presents a Discrete States-based Trajectory Planning(DSTP) algorithm for autonomous nonholonomic robots. The proposed algorithm represents the trajectory as x and y positions, orientation angle, longitude velocity and acceleration, angular velocity, and time intervals. More variables make the expression of optimization and constraints simpler, reduce the error caused by too many approximations, and also handle the gear shifting situation. L-BFGS-B is used to deal with the optimization of many variables and box constraints, thus speeding up the problem solving. Various simulation experiments compared with prior works have validated that our algorithm has an order-of-magnitude efficiency advantage and can generate a smoother trajectory with a high speed and low control effort. Besides, real-world experiments are also conducted to verify the feasibility of our algorithm in real scenes. We will release our codes as ros packages.

翻译：由于非完整动力学特性，非完整机器人的运动规划始终是一个难题。本文提出了一种基于离散状态轨迹规划（DSTP）算法，适用于自主非完整机器人。该算法将轨迹表示为x、y坐标、方向角、纵向速度与加速度、角速度及时间间隔。更多变量使优化与约束表达更简洁，减少了因过度近似导致的误差，同时解决了换挡工况问题。采用L-BFGS-B算法处理多变量优化及箱型约束，从而加速问题求解。与先前工作的多种仿真实验验证表明，本算法具有数量级的效率优势，能够生成高速度、低控制代价且更平滑的轨迹。此外，还开展了真实场景实验以验证算法在实际环境中的可行性。我们将以ROS功能包形式发布相关代码。