# Efficient Multi-Contact Pattern Generation with Sequential Convex Approximations of the Centroidal Dynamics

arXiv: https://arxiv.org/abs/2010.01215 · HTML: https://mlsanity.com/paper/2010.01215/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Model-free Reinforcement Learning for Robust Locomotion using Demonstrations from Trajectory Optimization](https://mlsanity.com/paper/2107.06629/) (2021)
- [A Unified and General Humanoid Whole-Body Controller for Versatile Locomotion](https://mlsanity.com/paper/2502.03206/) (2025)
- [Agile Maneuvers in Legged Robots: a Predictive Control Approach](https://mlsanity.com/paper/2203.07554/) (2022)
- [Hierarchical Contact-Rich Trajectory Optimization for Multi-Modal Manipulation using Tight Convex Relaxations](https://mlsanity.com/paper/2503.07963/) (2025)
- [ECO: Energy-Constrained Optimization with Reinforcement Learning for Humanoid Walking](https://mlsanity.com/paper/2602.06445/) (2026)
- [Optimal Gait Control for a Tendon-driven Soft Quadruped Robot by Model-based Reinforcement Learning](https://mlsanity.com/paper/2406.07069/) (2024)
- [Ask1: Development and Reinforcement Learning-Based Control of a Custom Quadruped Robot](https://mlsanity.com/paper/2412.08019/) (2024)
- [CMR: Contractive Mapping Embeddings for Robust Humanoid Locomotion on Unstructured Terrains](https://mlsanity.com/paper/2602.03511/) (2026)

## Abstract (arXiv)

This paper investigates the problem of efficient computation of physically consistent multi-contact behaviors. Recent work showed that under mild assumptions, the problem could be decomposed into simpler kinematic and centroidal dynamic optimization problems. Based on this approach, we propose a general convex relaxation of the centroidal dynamics leading to two computationally efficient algorithms based on iterative resolutions of second order cone programs. They optimize centroidal trajectories, contact forces and, importantly, the timing of the motions. We include the approach in a kino-dynamic optimization method to generate full-body movements. Finally, the approach is embedded in a mixed-integer solver to further find dynamically consistent contact sequences. Extensive numerical experiments demonstrate the computational efficiency of the approach, suggesting that it could be used in a fast receding horizon control loop. Executions of the planned motions on simulated humanoids and quadrupeds and on a real quadruped robot further show the quality of the optimized motions.