Continuous Trajectory Optimization via B-splines for Multi-jointed Robotic Systems

TL;DR

This paper presents a novel B-spline based trajectory optimization method for multi-jointed robots that guarantees continuous constraint satisfaction and effectively handles static and dynamic obstacles.

Contribution

It introduces a B-spline framework with rigorous operations for continuous trajectory optimization, ensuring constraints are satisfied at all times and incorporating obstacle avoidance.

Findings

Effective collision avoidance with static obstacles using signed distance fields.

Successful dynamic obstacle avoidance via time-varying separating hyperplanes.

Validated on simulations and a 6-link FANUC robot with moving obstacles.

Abstract

Continuous formulations of trajectory planning problems have two main benefits. First, constraints are guaranteed to be satisfied at all times. Secondly, dynamic obstacles can be naturally considered with time. This paper introduces a novel B-spline based trajectory optimization method for multi-jointed robots that provides a continuous trajectory with guaranteed continuous constraints satisfaction. At the core of this method, B-spline basic operations, like addition, multiplication, and derivative, are rigorously defined and applied for problem formulation. B-spline unique characteristics, such as the convex hull and smooth curves properties, are utilized to reformulate the original continuous optimization problem into a finite-dimensional problem. Collision avoidance with static obstacles is achieved using the signed distance field, while that with dynamic obstacles is accomplished via constructing time-varying separating hyperplanes. Simulation results on various robots validate the effectiveness of the algorithm. In addition, this paper provides experimental validations with a 6-link FANUC robot avoiding static and moving obstacles.