On the Synthesis of Reactive Collision-Free Whole-Body Robot Motions: A Complementarity-Based Approach

This paper is about generating motion plans for high degree-of-freedom systems that account for both static and dynamic collisions along the entire body. A particular class of mathematical programs with complementarity constraints become useful in this regard. Optimization-based planners can tackle confined space trajectory planning while being cognizant of robot and (mostly static) obstacle constraints. However, handling moving obstacles is non-trivial in a real-time setting. To this end, we present the FLIQC (Fast LInear Quadratic Complementarity based) motion planner. Our reactive planner employs a novel motion model that captures the entire rigid robot as well as the obstacle geometry and ensures nonpenetration between the surfaces due to the imposed constraint. We perform thorough comparative studies with the state-of-the-art, which demonstrate improved performance. Extensive simulation and hardware experiments validate our claim of generating continuous and real-time motion plans at 1 kHz for modern collaborative robots with constant minimal parameters.