Geometry-Informed Contact Optimization and Model Predictive Control for Efficient Contact-Rich Manipulation

Contact-rich manipulation remains a paramount challenge in robotics due to the hybrid dynamics and non-smooth nature of making and breaking contacts. In this paper, we present a geometry-informed contact (GIC) optimization approach for contact-rich manipulation that encodes the friction-cone geometry and object geometry directly within an energy-consistent contact model. At each contact, an anisotropic Riemannian metric shapes the contact energy so that the resulting contact force is geometrically consistent with the friction cone, while a geometry-aware modulation biases contacts toward mechanically robust regions. This yields smooth, complementarity-free contact dynamics, consequently enabling an efficient contact-implicit model predictive control (MPC) formulation for contact-rich manipulation. The proposed GIC and MPC formulation is evaluated on several dexterous manipulation tasks with diverse contact numbers, initial configurations, and task dimensionality in both simulation and real-world experiments, achieving higher success rates and lower pose errors with less computation time.1