Dynamically Consistent Online Adaptation of Fast Motions for Robotic Manipulators

The planning and execution of real-world robotic tasks largely depends on the ability to generate feasible motions online in response to changing environment conditions or goals. A spline deformation method is able to modify a given trajectory so that it matches the new boundary conditions, e.g., on positions, velocities, accelerations, etc. At the same time, the deformed motion preserves velocity, acceleration, jerk, or higher derivatives of motion profile of the precalculated trajectory. The deformed motion possessing such properties can be expressed by translation of original trajectory and spline interpolation. This spline decomposition considerably reduces the computational complexity and allows real-time execution. Formal feasibility guarantees are provided for the deformed trajectory and for the resulting torques. These guarantees are based on the special properties of Bernstein polynomials used for the deformation and on the structure of the chosen computed-torque control scheme. The approach is experimentally evaluated in a number of planar volleyball experiments using 3 degree-of-freedom robots and human participants.