# Receding-Horizon Perceptive Trajectory Optimization for Dynamic Legged Locomotion with Learned Initialization

arXiv: https://arxiv.org/abs/2104.09078 · HTML: https://mlsanity.com/paper/2104.09078/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2021.

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

- [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)
- [VILENS: Visual, Inertial, Lidar, and Leg Odometry for All-Terrain Legged Robots](https://mlsanity.com/paper/2107.07243/) (2021)
- [Agile Maneuvers in Legged Robots: a Predictive Control Approach](https://mlsanity.com/paper/2203.07554/) (2022)
- [Gaitor: Learning a Unified Representation Across Gaits for Real-World Quadruped Locomotion](https://mlsanity.com/paper/2405.19452/) (2024)
- [Next Steps: Learning a Disentangled Gait Representation for Versatile Quadruped Locomotion](https://mlsanity.com/paper/2112.04809/) (2021)
- [VAE-Loco: Versatile Quadruped Locomotion by Learning a Disentangled Gait Representation](https://mlsanity.com/paper/2205.01179/) (2022)
- [Agile and versatile bipedal robot tracking control through reinforcement learning](https://mlsanity.com/paper/2404.08246/) (2024)
- [Mind Your Steps: A General Learning Framework for Accurate Humanoid Foothold Tracking](https://mlsanity.com/paper/2606.08253/) (2026)
- [Multi-Resolution Planar Region Extraction for Uneven Terrains](https://mlsanity.com/paper/2311.12562/) (2023)

## Abstract (arXiv)

To dynamically traverse challenging terrain, legged robots need to continually perceive and reason about upcoming features, adjust the locations and timings of future footfalls and leverage momentum strategically. We present a pipeline that enables flexibly-parametrized trajectories for perceptive and dynamic quadruped locomotion to be optimized in an online, receding-horizon manner. The initial guess passed to the optimizer affects the computation needed to achieve convergence and the quality of the solution. We consider two methods for generating good guesses. The first is a heuristic initializer which provides a simple guess and requires significant optimization but is nonetheless suitable for adaptation to upcoming terrain. We demonstrate experiments using the ANYmal C quadruped, with fully onboard sensing and computation, to cross obstacles at moderate speeds using this technique. Our second approach uses latent-mode trajectory regression (LMTR) to imitate expert data - while avoiding invalid interpolations between distinct behaviors - such that minimal optimization is needed. This enables high-speed motions that make more expansive use of the robot's capabilities. We demonstrate it on flat ground with the real robot and provide numerical trials that progress toward deployment on terrain. These results illustrate a paradigm for advancing beyond short-horizon dynamic reactions, toward the type of intuitive and adaptive locomotion planning exhibited by animals and humans.