Global Sampling-Based Trajectory Optimization for Contact-Rich Manipulation via KernelSOS

2026-04-29

AI Summary

This work addresses the challenge of local optima in trajectory optimization for high-dimensional, long-horizon dexterous manipulation tasks involving hybrid contact dynamics. To this end, the authors propose Global-MPPI, a novel framework that, for the first time, integrates Kernel Sum-of-Squares (KernelSOS) optimization with a log-sum-exp-based progressive nonconvex smoothing strategy into sampling-based trajectory optimization. The approach leverages KernelSOS to identify globally promising regions, employs progressive smoothing to handle nonsmooth contact dynamics, and refines solutions locally using Model Predictive Path Integral (MPPI) control. Evaluated on tasks such as PushT and in-hand dexterous manipulation, Global-MPPI demonstrates significantly faster convergence and higher solution quality compared to baseline methods, achieving efficient global exploration and robust optimization.

Abstract

Contact-rich manipulation is challenging due to its high dimensionality, the requirement for long time horizons, and the presence of hybrid contact dynamics. Sampling-based methods have become a popular approach for this class of problems, but without explicit mechanisms for global exploration, they are susceptible to converging to poor local minima. In this paper, we introduce Global-MPPI, a unified trajectory optimization framework that integrates global exploration and local refinement. At the global level, we leverage kernel sum-of-squares optimization to identify globally promising regions of the solution space. To enable reliable performance for the non-smooth landscapes inherent to contact-rich manipulation, we introduce a graduated non-convexity strategy based on log-sum-exp smoothing, which transitions the optimization landscape from a smoothed surrogate to the original non-smooth objective. Finally, we employ the model-predictive path integral method to locally refine the solution. We evaluate Global-MPPI on high-dimensional, long-horizon contact-rich tasks, including the PushT task and dexterous in-hand manipulation. Experimental results demonstrate that our approach robustly uncovers high-quality solutions, achieving faster convergence and lower final costs compared to existing baseline methods.

Problem

• contact-rich manipulation
• trajectory optimization
• global exploration
• local minima
• non-smooth dynamics

Innovation

• Global-MPPI
• kernel sum-of-squares optimization
• graduated non-convexity
• log-sum-exp smoothing
• contact-rich manipulation