# Contact-timing and Trajectory Optimization for 3D Jumping on Quadruped Robots

arXiv: https://arxiv.org/abs/2110.06764 · HTML: https://mlsanity.com/paper/2110.06764/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2021.

## Built on by (most cited first, 10 of 10)

- [Creating a Dynamic Quadrupedal Robotic Goalkeeper with Reinforcement Learning](https://mlsanity.com/paper/2210.04435/) (2022)
- [Curriculum-Based Reinforcement Learning for Quadrupedal Jumping: A Reference-free Design](https://mlsanity.com/paper/2401.16337/) (2024)
- [Simultaneous Contact-Rich Grasping and Locomotion via Distributed Optimization Enabling Free-Climbing for Multi-Limbed Robots](https://mlsanity.com/paper/2207.01418/) (2022)
- [Guided Reinforcement Learning for Omnidirectional 3D Jumping in Quadruped Robots](https://mlsanity.com/paper/2507.16481/) (2025)
- [Efficient Reinforcement Learning for Jumping Monopods](https://mlsanity.com/paper/2309.07038/) (2023)
- [Integrating Trajectory Optimization and Reinforcement Learning for Quadrupedal Jumping with Terrain-Adaptive Landing](https://mlsanity.com/paper/2509.12776/) (2025)
- [Towards Quadrupedal Jumping and Walking for Dynamic Locomotion using Reinforcement Learning](https://mlsanity.com/paper/2510.24584/) (2025)
- [Symbolic Learning of Interpretable Reduced-Order Models for Jumping Quadruped Robots](https://mlsanity.com/paper/2508.06538/) (2025)
- [GeCCo -- a Generalist Contact-Conditioned Policy for Loco-Manipulation Skills on Legged Robots](https://mlsanity.com/paper/2509.17582/) (2025)
- [Co-jump: Cooperative Jumping with Quadrupedal Robots via Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2602.10514/) (2026)

## Abstract (arXiv)

Performing highly agile acrobatic motions with a long flight phase requires perfect timing, high accuracy, and coordination of the full-body motion. To address these challenges, we present a novel approach on timings and trajectory optimization framework for legged robots performing aggressive 3D jumping. In our method, we firstly utilize an effective optimization framework using simplified rigid body dynamics to solve for contact timings and a reference trajectory of the robot body. The solution of this module is then used to formulate a full-body trajectory optimization based on the full nonlinear dynamics of the robot. This combination allows us to effectively optimize for contact timings while ensuring that the jumping trajectory can be effectively realized in the robot hardware. We first validate the efficiency of the proposed framework on the A1 robot model for various 3D jumping tasks such as double-backflips off the high altitude of 2m. Experimental validation was then successfully conducted for various aggressive 3D jumping motions such as diagonal jumps, barrel roll, and double barrel roll from a box of heights 0.4m and 0.9m, respectively.