Constrained Online Motion Generation from Unfiltered User Commands

In manually operated robotic applications, where operators use a joystick as input device, it is more intuitive to command the velocity rather than the position. Existing algorithms, however, that admit following an arbitrary desired velocity in order to generate smooth trajectories, do not take into account the dynamic limits of velocity and position. In this paper a method is introduced for the smooth online path-parameter generation from unfiltered operator input that respects bounds on position, velocity, acceleration, and jerk. It builds upon a time discrete second-order smoothing filter. \(\mathcal {C}^3\) continuous trajectories are computed that achieve a motion between defined start and terminal positions in minimal time. A geometric path description based on B-spline interpolation connecting multiple points in task space is presented. The velocity signal deduced from this description is used as a time scaling parameter. Specific parametrization of the B-spline curve allows for generating motions where the tangential velocity is nearly proportional to the joystick modulation.