Chance-constrained Optimization for Contact-Rich Systems Using Mixed Integer Programming

Stochastic and robust optimization of uncertain contact-rich systems is relatively unexplored. This paper presents a chance-constrained formulation for robust trajectory optimization during manipulation. In particular, we present chance-constrained optimization of Stochastic Discrete-time Linear Complementarity Systems (SDLCS). The optimization problem is formulated as a Mixed-Integer Quadratic Program with Chance Constraints (MIQPCC). In our formulation, we explicitly consider joint chance constraints for complementarity variables and states to capture the stochastic evolution of dynamics. Additionally, we demonstrate the use of our proposed approach for designing a Stochastic Model Predictive Controller (SMPC) with complementarity constraints for a planar pushing system. We evaluate the robustness of our optimized trajectories in simulation on several systems. The proposed approach outperforms some recent approaches for robust trajectory optimization for SDLCS.