Mediating Between Contact Feasibility and Robustness of Trajectory Optimization Through Chance Complementarity Constraints

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.

Chance-Constrained Optimization in Contact-Rich Systems for Robust Manipulation

“…Our treatment of SDLCS leads to stochastic evolution of system states x k , while we treat λ k+1 as deterministic. The assumption of determinacy in λ k+1 is similar to several previous works [12], [13], [14], [23]. The authors in [13] use ERM to solve TO of SDLCS and use the following cost function:…”

“…This paper has the following contributions: 1) We present a novel formulation for chance-constrained optimization of SDLCS. 2) We compare our proposed approach with several previously proposed techniques and demonstrate that our method outperforms the recent techniques in [13], [14]. The proposed algorithm is demonstrated on several manipulation systems with linear dynamics.…”

“…There has been some recent work on robust TO in SNCS [13], [14], [17]. In [13], the authors have utilized the formulation of ERM for robust TO.…”

“…However, such a formulation does not consider the stochastic state evolution of the system during optimization. A chance-constrained formulation for SNCS is presented in [14]. This method augments the ERMaugmented objective in [13] with additional chance constraints on satisfying the complementarity constraints.…”

“…A major shortcoming of such an approach is that it fails to capture the stochastic evolution of system dynamics due to the † Yuki Shirai is with the Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA, USA 90095 yukishirai4869@g.ucla.edu ‡ Devesh K. Jha, Arvind U. Raghunathan and Diego Romeres are with Mitsubishi Electric Research Laboratories (MERL), Cambridge, MA, USA 02139 {jha,raghunathan,romeres}@merl.com stochastic complementarity constraint. In [14], the authors augment the formulation in [13] with chance constraints. However, this formulation has certain fundamental shortcomings which prevent constraint satisfaction guarantees.…”