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

Abstract

This paper presents a chance-constrained formulation for robust trajectory optimization during manipulation. In particular, we present a chance-constrained optimization for Stochastic Discrete-time Linear Complementarity Systems (SDLCS). To solve the optimization problem, we formulate Mixed-Integer Quadratic Programming with Chance Constraints (MIQPCC). In our formulation, we explicitly consider joint chance constraints for complementarity as well as states to capture the stochastic evolution of dynamics. We evaluate robustness of our optimized trajectories in simulation on several systems. The proposed approach outperforms some recent approaches for robust trajectory optimization for SDLCS.

Robust Pivoting: Exploiting Frictional Stability Using Bilevel Optimization

“…We would also like to consider other uncertainties such as coefficient of friction, kinematics uncertainty, etc. However, these uncertainties lead to stochastic complementarity system, which requires the discussion in e.g., [2], [25]. Also, solving our proposed optimization can be intractable once we consider a nonlinear coupling term as described in Remark 1.…”

Tactile Tool Manipulation

“…where θO,k represent the reference trajectory computed offline using (5). We observed that slipping between the tool and object kept happening if the controller tracks the tool state as well.…”

“…4), the origin of pivoting, p A , changes over the trajectory. Thus, we cannot directly apply (5) for the non-convex objects. Hence, we solve (5) hierarchically for them where we solve (5) with the first contact origin and then we solve (5) with the next contact origin and so far and so forth.…”

Covariance Steering for Uncertain Contact-rich Systems

“…Using stochastic complementarity constraints for planning robust manipulation is not so well understood in literature. Some of the recent work could be found in [15], [1]. However, the problem with these approaches is that the uncertainty needs to be very small otherwise the optimization might be infeasible.…”

“…Complementarity constraints offer an efficient way of modeling contact systems. However, uncertainty in contact systems could lead to stochastic complementarity systems [1]. Even though complementarity systems are well studied, stochastic complementarity systems are not well understood.…”