# Global Contact-Rich Planning with Sparsity-Rich Semidefinite Relaxations

arXiv: https://arxiv.org/abs/2502.02829 · HTML: https://mlsanity.com/paper/2502.02829/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2025.

## Built on by (most cited first, 4 of 4)

- [Empirical Analysis of Sim-and-Real Cotraining of Diffusion Policies for Planar Pushing from Pixels](https://mlsanity.com/paper/2503.22634/) (2025)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [SIMPACT: Simulation-Enabled Action Planning using Vision-Language Models](https://mlsanity.com/paper/2512.05955/) (2025)
- [Tempered Sequential Monte Carlo for Trajectory and Policy Optimization with Differentiable Dynamics](https://mlsanity.com/paper/2604.21456/) (2026)

## Abstract (arXiv)

We show that contact-rich motion planning is also sparsity-rich when viewed as polynomial optimization (POP). We can exploit not only the correlative and term sparsity patterns that are general to all POPs, but also specialized sparsity patterns from the robot kinematic structure and the separability of contact modes. Such sparsity enables the design of high-order but sparse semidefinite programming (SDPs) relaxations--building upon Lasserre's moment and sums of squares hierarchy--that (i) can be solved in seconds by off-the-shelf SDP solvers, and (ii) compute near globally optimal solutions to the nonconvex contact-rich planning problems with small certified suboptimality. Through extensive experiments both in simulation (Push Bot, Push Box, Push Box with Obstacles, and Planar Hand) and real world (Push T), we demonstrate the power of using convex SDP relaxations to generate global contact-rich motion plans. As a contribution of independent interest, we release the Sparse Polynomial Optimization Toolbox (SPOT)--implemented in C++ with interfaces to both Python and Matlab--that automates sparsity exploitation for robotics and beyond.