Discrete States-Based Trajectory Planning for Nonholonomic Robots

TL;DR

This paper introduces a Discrete States-based Trajectory Planning algorithm for nonholonomic robots that improves efficiency, smoothness, and real-world applicability by representing trajectories with multiple variables and optimizing with L-BFGS-B.

Contribution

The paper proposes a novel DSTP algorithm that simplifies trajectory optimization for nonholonomic robots and demonstrates significant efficiency and performance improvements over prior methods.

Findings

Order-of-magnitude faster than previous methods

Produces smoother trajectories with high speed and low control effort

Validated through both simulations and real-world experiments

Abstract

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.