Real-time Bézier Trajectory Deformation for Potential Fields planning methods

This article presents a new technique for obtaining a flexible trajectory based on the deformation of a Be??zier curve through a field of vectors. This new technique is called Be??zier Trajectory Deformation (BTD). The trajectory deformation is computed with a constrained optimization method (Lagrange Multipliers Theorem). A linear system is solved to achieve the result. As a consequence, the deformed trajectory is computed in a few milliseconds. In addition, the linear system can be solved offline if the Be??zier curve order is maintained constant during the movement of the robot, which is the common case. This technique can be combined with any collision avoidance algorithm that produces a field of vectors. In particular, it has been developed for artificial potential field methods. BTD is combined with a recently proposed PF method, the Potential Field Projection method (PFP). The resulting technique is tested in dynamic environment showing its real-time performance and its efficacy for obstacle avoidance.