# Towards Tight Convex Relaxations for Contact-Rich Manipulation

arXiv: https://arxiv.org/abs/2402.10312 · HTML: https://mlsanity.com/paper/2402.10312/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2024.

## Built on by (most cited first, 9 of 9)

- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [Physics-Driven Data Generation for Contact-Rich Manipulation via Trajectory Optimization](https://mlsanity.com/paper/2502.20382/) (2025)
- [Empirical Analysis of Sim-and-Real Cotraining of Diffusion Policies for Planar Pushing from Pixels](https://mlsanity.com/paper/2503.22634/) (2025)
- [Ambient Diffusion Policy: Imitation Learning from Suboptimal Data in Robotics](https://mlsanity.com/paper/2606.12365/) (2026)
- [Hierarchical Contact-Rich Trajectory Optimization for Multi-Modal Manipulation using Tight Convex Relaxations](https://mlsanity.com/paper/2503.07963/) (2025)
- [Search-Based Spatiotemporal and Multi-Robot Motion Planning on Graphs of Space-Time Convex Sets](https://mlsanity.com/paper/2607.00444/) (2026)
- [Approximately Optimal Global Planning for Contact-Rich SE(2) Manipulation on a Graph of Reachable Sets](https://mlsanity.com/paper/2601.10827/) (2026)
- [Global Convergence of Sampling-Based Nonconvex Optimization through Diffusion-Style Smoothing](https://mlsanity.com/paper/2605.16520/) (2026)
- [Unified Branch-and-Bound Search for the Steiner Traveling Salesman Problem on Graphs of Convex Sets](https://mlsanity.com/paper/2608.21319/) (2026)

## Abstract (arXiv)

We present a novel method for global motion planning of robotic systems that interact with the environment through contacts. Our method directly handles the hybrid nature of such tasks using tools from convex optimization. We formulate the motion-planning problem as a shortest-path problem in a graph of convex sets, where a path in the graph corresponds to a contact sequence and a convex set models the quasi-static dynamics within a fixed contact mode. For each contact mode, we use semidefinite programming to relax the nonconvex dynamics that results from the simultaneous optimization of the object's pose, contact locations, and contact forces. The result is a tight convex relaxation of the overall planning problem, that can be efficiently solved and quickly rounded to find a feasible contact-rich trajectory. As an initial application for evaluating our method, we apply it on the task of planar pushing. Exhaustive experiments show that our convex-optimization method generates plans that are consistently within a small percentage of the global optimum, without relying on an initial guess, and that our method succeeds in finding trajectories where a state-of-the-art baseline for contact-rich planning usually fails. We demonstrate the quality of these plans on a real robotic system.