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

TL;DR

The FLIQC (Fast LInear Quadratic Complementarity based) motion 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.

Abstract

This paper is about generating motion plans for high degree-of-freedom systems that account for 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 constraints. However, introducing obstacles in this setting transforms the formulation into a non-convex problem (oftentimes with ill-posed bilinear constraints), which is non-trivial in a real-time setting. To this end, we present the FLIQC (Fast LInear Quadratic Complementarity based) motion planner. Our planner employs a novel motion model that captures the entire rigid robot as well as the obstacle geometry and ensures non-penetration 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 reactive motion plans at 1 kHz for modern collaborative robots with constant minimal parameters.

Figures (5)

• Figure 1: Top left inset depicts the reactive behavior of our planner with an interactive obstacle. The main illustration highlights a scenario where the purple dynamic obstacle approaches the robot's wrist as it is moving towards a goal. As soon as the robot link (green spheres denote the tracked surface) enters the obstacle sphere of influence ($\epsilon_i$), it experiences a compensating velocity $\boldsymbol{v}_{c_i}$ (magnified portion) that slides it along the surface, until it escapes. $\psi_i$ represents the robot link surface to the obstacle surface distance.
• Figure 2: Evolution of obstacle avoidance using FLIQC for a planar $2$R robot. The cyan color represents the starting and goal configurations of the robot.
• Figure 3: Interactive marker scenario with hardware-in-the-loop: The robot reacts in real-time to the marker nudge from left to right at the elbow.
• Figure 4: Data recorded from hardware experiments with static obstacles. (a) the critical moments marked with vertical dashed lines that an obstacle is attempting to violate the safety distance. This triggers the reaction of robot, which can be observed from the robot states as visualized in (b).
• Figure 5: Data recorded from hardware experiments with dynamic obstacles. (a) the critical moments marked with vertical dashed lines that an obstacle is attempting to violate the safety distance. This triggers the reaction of robot, which can be observed from the robot states as visualized in (b).