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.

中文翻译：

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使用混合整数规划对接触丰富的系统进行机会约束优化

不确定的接触丰富的系统的随机和鲁棒优化相对尚未被探索。本文提出了一种用于操作过程中稳健轨迹优化的机会约束公式。特别是，我们提出了随机离散时间线性互补系统（SDLCS）的机会约束优化。优化问题被表述为具有机会约束的混合整数二次规划 (MIQPCC)。在我们的公式中，我们明确考虑互补变量和状态的联合机会约束，以捕获动力学的随机演化。此外，我们还演示了如何使用我们提出的方法来设计具有平面推动系统互补约束的随机模型预测控制器（SMPC）。我们在多个系统上的模拟中评估了优化轨迹的稳健性。所提出的方法优于 SDLCS 鲁棒轨迹优化的一些最新方法。