# Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds

arXiv: https://arxiv.org/abs/1607.04537 · HTML: https://mlsanity.com/paper/1607.04537/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2016.

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

- [Learning Humanoid Standing-up Control across Diverse Postures](https://mlsanity.com/paper/2502.08378/) (2025)
- [Imitate and Repurpose: Learning Reusable Robot Movement Skills From Human and Animal Behaviors](https://mlsanity.com/paper/2203.17138/) (2022)
- [Autonomous Navigation for Quadrupedal Robots with Optimized Jumping through Constrained Obstacles](https://mlsanity.com/paper/2107.00773/) (2021)
- [Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications](https://mlsanity.com/paper/2607.00442/) (2026)
- [Robust Contact State Estimation in Humanoid Walking Gaits](https://mlsanity.com/paper/2208.00278/) (2022)
- [Towards Quadrupedal Jumping and Walking for Dynamic Locomotion using Reinforcement Learning](https://mlsanity.com/paper/2510.24584/) (2025)
- [ADP: Adversarial Dynamics Priors for Physically Grounded Humanoid Locomotion](https://mlsanity.com/paper/2607.03454/) (2026)
- [Optimal Gait Control for a Tendon-driven Soft Quadruped Robot by Model-based Reinforcement Learning](https://mlsanity.com/paper/2406.07069/) (2024)

## Abstract (arXiv)

In this work we present a trajectory Optimization framework for whole-body motion planning through contacts. We demonstrate how the proposed approach can be applied to automatically discover different gaits and dynamic motions on a quadruped robot. In contrast to most previous methods, we do not pre-specify contact switches, timings, points or gait patterns, but they are a direct outcome of the optimization. Furthermore, we optimize over the entire dynamics of the robot, which enables the optimizer to fully leverage the capabilities of the robot. To illustrate the spectrum of achievable motions, here we show eight different tasks, which would require very different control structures when solved with state-of-the-art methods. Using our trajectory Optimization approach, we are solving each task with a simple, high level cost function and without any changes in the control structure. Furthermore, we fully integrated our approach with the robot's control and estimation framework such that optimization can be run online. By demonstrating a rough manipulation task with multiple dynamic contact switches, we exemplarily show how optimized trajectories and control inputs can be directly applied to hardware.