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

Contact-rich manipulation tasks — like pushing objects or dexterous in-hand reorientation — are notoriously difficult for robots because they involve high-dimensional state spaces, long time horizons, and hybrid contact dynamics that create non-smooth cost landscapes. Traditional sampling-based planners often get stuck in poor local minima without explicit global search mechanisms. Now, a new paper by Zhongqi Wei and Frederike Dümbgen introduces Global-MPPI, a unified trajectory optimization framework that systematically integrates global exploration with local refinement.

The global layer uses kernel sum-of-squares (SOS) optimization to identify promising regions of the solution space, providing a meaningful starting point for subsequent local optimization. To handle the non-smooth nature of contact-rich costs, the authors introduce a graduated non-convexity strategy based on log-sum-exp smoothing, which gradually transitions from a smoothed surrogate to the original objective. The local refinement is executed via the model-predictive path integral (MPPI) method. Experiments on the PushT benchmark and dexterous in-hand manipulation tasks show Global-MPPI robustly uncovers high-quality solutions with faster convergence and lower final costs compared to existing baselines.