Funnel planning and control for manipulators using neural Signed Configuration Distance Functions
TL;DR
This work proposes a novel funnel planning and control solution that uses a neural Signed Configuration Distance Function (nSCDF) to estimate collision-free balls and gradients in a computationally efficient way and observes improved motion performance and robustness properties when using the nSCDF for funnel control.
Abstract
Robust motion planning and control for manipulators is the problem of guaranteeing safe execution and collision-free motion under disturbances. The Kinodynamic Motion Planning via Funnel Control (KDF) is a recently proposed planner that comes with robustness guarantees and is particularly attractive for collision-free control as it guarantees closed-loop evolution inside a funnel, i.e., a collision-free region around a nominal trajectory. Despite its attractive theoretical properties, the current approach for computing funnels is computationally demanding, which limits its expressiveness and performance. We address its current limitations by proposing a novel funnel planning and control solution. Our key tool to enable this is a neural Signed Configuration Distance Function (nSCDF) which allows us to estimate collision-free balls and gradients in a computationally efficient way. We use the nSCDF in our planner to compute a nominal trajectory, where path length and clearance are balanced. To track the trajectory with collision-avoidance guarantees, we design a funnel controller that exploits the geometric information from the nSCDF. From numerical experiments, we observe that our planner produces nominal paths $2$ times faster, while at the same time obtaining $20 \%$ shorter path length and $5$ times the clearance. Finally, we also observe improved motion performance and robustness properties when using the nSCDF for funnel control.