B-spline parameterized optimal motion trajectories for robotic systems with guaranteed constraint satisfaction

When optimizing the performance of constrained robotic system, the motion trajectory plays a crucial role. In this research the motion planning problem for systems that admit a polynomial description of the system dynamics through differential flatness is tackled by parameterizing the system’s so-called flat output as a polynomial spline. Using basic properties of B-splines, sufficient conditions on the spline coefficients are derived ensuring satisfaction of the operating constraints over the entire time horizon. Furthermore, an intuitive relaxation is proposed to tackle conservatism and a supporting software package is released. Finally, to illustrate the overall approach and potential, a numerical benchmark of a flexible link manipulator is discussed.