# Motion Planning for Quadrupedal Locomotion: Coupled Planning, Terrain Mapping and Whole-Body Control

arXiv: https://arxiv.org/abs/2003.05481 · HTML: https://mlsanity.com/paper/2003.05481/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2020.

## Built on by (most cited first, 11 of 11)

- [DTC: Deep Tracking Control](https://mlsanity.com/paper/2309.15462/) (2023)
- [BeamDojo: Learning Agile Humanoid Locomotion on Sparse Footholds](https://mlsanity.com/paper/2502.10363/) (2025)
- [RL + Model-based Control: Using On-demand Optimal Control to Learn Versatile Legged Locomotion](https://mlsanity.com/paper/2305.17842/) (2023)
- [GLiDE: Generalizable Quadrupedal Locomotion in Diverse Environments with a Centroidal Model](https://mlsanity.com/paper/2104.09771/) (2021)
- [Morphological Symmetries in Robotics](https://mlsanity.com/paper/2402.15552/) (2024)
- [Hiking in the Wild: A Scalable Perceptive Parkour Framework for Humanoids](https://mlsanity.com/paper/2601.07718/) (2026)
- [Agile Maneuvers in Legged Robots: a Predictive Control Approach](https://mlsanity.com/paper/2203.07554/) (2022)
- [Autonomous Navigation for Quadrupedal Robots with Optimized Jumping through Constrained Obstacles](https://mlsanity.com/paper/2107.00773/) (2021)
- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)
- [TRANS: Terrain-aware Reinforcement Learning for Agile Navigation of Quadruped Robots under Social Interactions](https://mlsanity.com/paper/2602.12724/) (2026)
- [Mind Your Steps: A General Learning Framework for Accurate Humanoid Foothold Tracking](https://mlsanity.com/paper/2606.08253/) (2026)

## Abstract (arXiv)

Planning whole-body motions while taking into account the terrain conditions is a challenging problem for legged robots since the terrain model might produce many local minima. Our coupled planning method uses stochastic and derivatives-free search to plan both foothold locations and horizontal motions due to the local minima produced by the terrain model. It jointly optimizes body motion, step duration and foothold selection, and it models the terrain as a cost-map. Due to the novel attitude planning method, the horizontal motion plans can be applied to various terrain conditions. The attitude planner ensures the robot stability by imposing limits to the angular acceleration. Our whole-body controller tracks compliantly trunk motions while avoiding slippage, as well as kinematic and torque limits. Despite the use of a simplified model, which is restricted to flat terrain, our approach shows remarkable capability to deal with a wide range of non-coplanar terrains. The results are validated by experimental trials and comparative evaluations in a series of terrains of progressively increasing complexity.