REAL-TIME TRAJECTORY MODIFICATION BASED ON BEZIER SHAPE DEFORMATION

This paper presents a new technique for flexible path planning based on the deformation of a Bezier curve through a field of vectors. This new technique is called Bezier Shape Deformation (BSD). This deformation is computed with a constrained optimization method (Lagrange Multipliers Theorem). The main advantage of this method is how the solution is obtained. A linear system is solved to achieve the result. As a consequence, the deformed curve is computed in a few milliseconds where the linear system can be solved offline if the Bezier curve order is maintained constant during the movement of the robot. This method allows the use of these trajectories in dynamic environments where the computational cost is critical. This technique can be combined with any collision avoidance algorithm that produces a field of vectors. In particular, it is appropriate for artificial potential field methods. At the end of the paper, the presented methodology is combined with an artificial potential fields algorithm recently proposed, the Potential Field Projection method (PFP). This method is based on the combination of the classical Potential Fields method and the multi-rate Kalman filter estimation and takes into account the uncertainties on locations, the future trajectory of the robot and the obstacles and the multi-rate information supplied by sensors. As shown in the simulation results, flexible trajectories for collision avoidance are generated with smooth curves.