# High-speed control and navigation for quadrupedal robots on complex and discrete terrain

arXiv: https://arxiv.org/abs/2506.02835 · HTML: https://mlsanity.com/paper/2506.02835/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2025.

## Built on by (most cited first, 19 of 19)

- [Hiking in the Wild: A Scalable Perceptive Parkour Framework for Humanoids](https://mlsanity.com/paper/2601.07718/) (2026)
- [Closing the Reality Gap: Zero-Shot Sim-to-Real Deployment for Dexterous Force-Based Grasping and Manipulation](https://mlsanity.com/paper/2601.02778/) (2026)
- [Flip Stunts on Bicycle Robots using Iterative Motion Imitation](https://mlsanity.com/paper/2603.27944/) (2026)
- [PUMA: Perception-driven Unified Foothold Prior for Mobility Augmented Quadruped Parkour](https://mlsanity.com/paper/2601.15995/) (2026)
- [Training and Simulation of Quadrupedal Robot in Adaptive Stair Climbing and Descending for Indoor Firefighting: An End-to-End Reinforcement Learning Approach](https://mlsanity.com/paper/2602.03087/) (2026)
- [LineRides: Line-Guided Reinforcement Learning for Bicycle Robot Stunts](https://mlsanity.com/paper/2605.05110/) (2026)
- [EFGCL: Learning Dynamic Motion through Spotting-Inspired External Force Guided Curriculum Learning](https://mlsanity.com/paper/2605.10063/) (2026)
- [Agile perceptive multi-skill locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2607.13579/) (2026)
- [Trajectory-Level Automatic Curriculum Learning for Legged Locomotion on Unstructured Terrain](https://mlsanity.com/paper/2608.16164/) (2026)
- [Dynamic Adaptive Legged Locomotion Policy via Decoupling Reaction Force Control and Gait Control](https://mlsanity.com/paper/2509.13737/) (2025)
- [GeCCo -- a Generalist Contact-Conditioned Policy for Loco-Manipulation Skills on Legged Robots](https://mlsanity.com/paper/2509.17582/) (2025)
- [Learning Quadrupedal Locomotion for a Heavy Hydraulic Robot Using an Actuator Model](https://mlsanity.com/paper/2601.11143/) (2026)
- [Co-jump: Cooperative Jumping with Quadrupedal Robots via Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2602.10514/) (2026)
- [Learning Task-Invariant Properties via Dreamer: Enabling Efficient Policy Transfer for Quadruped Robots](https://mlsanity.com/paper/2604.02911/) (2026)
- [Learning Dynamic Pick-and-Place for a Legged Manipulator](https://mlsanity.com/paper/2605.15713/) (2026)
- [Learning Perceptive Platform Adaptive Locomotion Controllers for Quadrupedal Robots](https://mlsanity.com/paper/2606.25179/) (2026)
- [WARL: Wrench-Augmented Reinforcement Learning for Task-Agnostic Learning in Legged Robots](https://mlsanity.com/paper/2607.24036/) (2026)
- [Bicycle Acrobatics with Reinforcement Learning](https://mlsanity.com/paper/2608.00880/) (2026)
- [PolyMorph: Learning Locomotion Policy for Cross-Embodiment Adaptation](https://mlsanity.com/paper/2610.19615/) (2026)

## Abstract (arXiv)

High-speed legged navigation in discrete and geometrically complex environments is a challenging task because of the high-degree-of-freedom dynamics and long-horizon, nonconvex nature of the optimization problem. In this work, we propose a hierarchical navigation pipeline for legged robots that can traverse such environments at high speed. The proposed pipeline consists of a planner and tracker module. The planner module finds physically feasible foothold plans by sampling-based optimization with fast sequential filtering using heuristics and a neural network. Subsequently, rollouts are performed in a physics simulation to identify the best foothold plan regarding the engineered cost function and to confirm its physical consistency. This hierarchical planning module is computationally efficient and physically accurate at the same time. The tracker aims to accurately step on the target footholds from the planning module. During the training stage, the foothold target distribution is given by a generative model that is trained competitively with the tracker. This process ensures that the tracker is trained in an environment with the desired difficulty. The resulting tracker can overcome terrains that are more difficult than what the previous methods could manage. We demonstrated our approach using Raibo, our in-house dynamic quadruped robot. The results were dynamic and agile motions: Raibo is capable of running on vertical walls, jumping a 1.3-meter gap, running over stepping stones at 4 meters per second, and autonomously navigating on terrains full of 30deg ramps, stairs, and boxes of various sizes.