Mediating between Contact Feasibility and Robustness of Trajectory Optimization through Chance Complementarity Constraints

TL;DR

This paper introduces a method that balances robustness and feasibility in robot motion planning under contact uncertainty by combining chance constraints with a risk-sensitive objective, demonstrated through simple robotic examples.

Contribution

It presents a novel approach that mediates between contact feasibility and robustness using chance complementarity constraints, enhancing motion planning under uncertainty.

Findings

Chance constraints produce trajectories similar to strict complementarity constraints.

Robust objective allows trade-off between robustness and constraint satisfaction.

Approach improves reasoning about contact uncertainty in motion planning.

Abstract

As robots move from the laboratory into the real world, motion planning will need to account for model uncertainty and risk. For robot motions involving intermittent contact, planning for uncertainty in contact is especially important, as failure to successfully make and maintain contact can be catastrophic. Here, we model uncertainty in terrain geometry and friction characteristics, and combine a risk-sensitive objective with chance constraints to provide a trade-off between robustness to uncertainty and constraint satisfaction with an arbitrarily high feasibility guarantee. We evaluate our approach in two simple examples: a push-block system for benchmarking and a single-legged hopper. We demonstrate that chance constraints alone produce trajectories similar to those produced using strict complementarity constraints; however, when equipped with a robust objective, we show the chance constraints can mediate a trade-off between robustness to uncertainty and strict constraint satisfaction. Thus, our study may represent an important step towards reasoning about contact uncertainty in motion planning.