# Integrating Trajectory Optimization and Reinforcement Learning for Quadrupedal Jumping with Terrain-Adaptive Landing

arXiv: https://arxiv.org/abs/2509.12776 · HTML: https://mlsanity.com/paper/2509.12776/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 19 of 19)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Expressive Whole-Body Control for Humanoid Robots](https://mlsanity.com/paper/2402.16796/) (2024)
- [Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior](https://mlsanity.com/paper/2212.03238/) (2022)
- [DreamWaQ: Learning Robust Quadrupedal Locomotion With Implicit Terrain Imagination via Deep Reinforcement Learning](https://mlsanity.com/paper/2301.10602/) (2023)
- [DTC: Deep Tracking Control](https://mlsanity.com/paper/2309.15462/) (2023)
- [Perceptive Locomotion through Nonlinear Model Predictive Control](https://mlsanity.com/paper/2208.08373/) (2022)
- [RL + Model-based Control: Using On-demand Optimal Control to Learn Versatile Legged Locomotion](https://mlsanity.com/paper/2305.17842/) (2023)
- [Curriculum-Based Reinforcement Learning for Quadrupedal Jumping: A Reference-free Design](https://mlsanity.com/paper/2401.16337/) (2024)
- [Cat-like Jumping and Landing of Legged Robots in Low-gravity Using Deep Reinforcement Learning](https://mlsanity.com/paper/2106.09357/) (2021)
- [Contact-timing and Trajectory Optimization for 3D Jumping on Quadruped Robots](https://mlsanity.com/paper/2110.06764/) (2021)
- [Continuous Jumping for Legged Robots on Stepping Stones via Trajectory Optimization and Model Predictive Control](https://mlsanity.com/paper/2204.01147/) (2022)
- [Rapid and Reliable Quadruped Motion Planning with Omnidirectional Jumping](https://mlsanity.com/paper/2111.13648/) (2021)
- [Quadruped-Frog: Rapid Online Optimization of Continuous Quadruped Jumping](https://mlsanity.com/paper/2403.06954/) (2024)
- [Reactive Landing Controller for Quadruped Robots](https://mlsanity.com/paper/2305.07748/) (2023)

## Built on by (most cited first, 1 of 1)

- [Dynamic Adaptive Legged Locomotion Policy via Decoupling Reaction Force Control and Gait Control](https://mlsanity.com/paper/2509.13737/) (2025)

## Abstract (arXiv)

Jumping constitutes an essential component of quadruped robots' locomotion capabilities, which includes dynamic take-off and adaptive landing. Existing quadrupedal jumping studies mainly focused on the stance and flight phase by assuming a flat landing ground, which is impractical in many real world cases. This work proposes a safe landing framework that achieves adaptive landing on rough terrains by combining Trajectory Optimization (TO) and Reinforcement Learning (RL) together. The RL agent learns to track the reference motion generated by TO in the environments with rough terrains. To enable the learning of compliant landing skills on challenging terrains, a reward relaxation strategy is synthesized to encourage exploration during landing recovery period. Extensive experiments validate the accurate tracking and safe landing skills benefiting from our proposed method in various scenarios.