Optimum Velocity Profile of Multiple Bernstein-Bézier Curves Subject to Constraints for Mobile Robots

Abstract

This article deals with trajectory planning that is suitable for nonholonomic differentially driven wheeled mobile robots. The path is approximated with a spline that consists of multiple Bernstein-Bézier curves that are merged together in a way that continuous curvature of the spline is achieved. The article presents the approach for optimization of velocity profile of Bernstein-Bézier spline subject to velocity and acceleration constraints. For the purpose of optimization, velocity and turning points are introduced. Based on these singularity points, local segments are defined where local velocity profiles are optimized independently of each other. From the locally optimum velocity profiles, the global optimum velocity profile is determined. Since each local velocity profile can be evaluated independently, the algorithm is suitable for concurrent implementation and modification of one part of the curve does not require recalculation of all local velocity profiles. These properties enable efficient implementation of the optimization algorithm. The optimization algorithm is also suitable for the splines that consist of Bernstein-Bézier curves that have substantially different lengths. The proposed optimization approach was experimentally evaluated and validated in simulation environment and on real mobile robots.