# An Optimal Motion Planning Framework for Quadruped Jumping

arXiv: https://arxiv.org/abs/2207.12002 · HTML: https://mlsanity.com/paper/2207.12002/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2022.

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

- [Robust and Versatile Bipedal Jumping Control through Reinforcement Learning](https://mlsanity.com/paper/2302.09450/) (2023)
- [Guided Reinforcement Learning for Omnidirectional 3D Jumping in Quadruped Robots](https://mlsanity.com/paper/2507.16481/) (2025)
- [Explosive Jumping with Rigid and Articulated Soft Quadrupeds via Example Guided Reinforcement Learning](https://mlsanity.com/paper/2503.16197/) (2025)
- [Co-jump: Cooperative Jumping with Quadrupedal Robots via Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2602.10514/) (2026)

## Abstract (arXiv)

This paper presents an optimal motion planning framework to generate versatile energy-optimal quadrupedal jumping motions automatically (e.g., flips, spin). The jumping motions via the centroidal dynamics are formulated as a 12-dimensional black-box optimization problem subject to the robot kino-dynamic constraints. Gradient-based approaches offer great success in addressing trajectory optimization (TO), yet, prior knowledge (e.g., reference motion, contact schedule) is required and results in sub-optimal solutions. The new proposed framework first employed a heuristics-based optimization method to avoid these problems. Moreover, a prioritization fitness function is created for heuristics-based algorithms in robot ground reaction force (GRF) planning, enhancing convergence and searching performance considerably. Since heuristics-based algorithms often require significant time, motions are planned offline and stored as a pre-motion library. A selector is designed to automatically choose motions with user-specified or perception information as input. The proposed framework has been successfully validated only with a simple continuously tracking PD controller in an open-source Mini-Cheetah by several challenging jumping motions, including jumping over a window-shaped obstacle with 30 cm height and left-flipping over a rectangle obstacle with 27 cm height.