# Hybrid Systems Differential Dynamic Programming for Whole-Body Motion Planning of Legged Robots

arXiv: https://arxiv.org/abs/2006.08102 · HTML: https://mlsanity.com/paper/2006.08102/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

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

- [PIP-Loco: A Proprioceptive Infinite Horizon Planning Framework for Quadrupedal Robot Locomotion](https://mlsanity.com/paper/2409.09441/) (2024)
- [PaaS: Planning as a Service for reactive driving in CARLA Leaderboard](https://mlsanity.com/paper/2304.08252/) (2023)
- [Data-Driven Motion Planning for Uncertain Nonlinear Systems](https://mlsanity.com/paper/2508.00154/) (2025)
- [Language-Guided Terrain-Adaptive Neural MPC for Autonomous Traversal of Articulated Tracked Robots](https://mlsanity.com/paper/2609.13083/) (2026)

## Abstract (arXiv)

This paper presents a Differential Dynamic Programming (DDP) framework for trajectory optimization (TO) of hybrid systems with state-based switching. The proposed Hybrid Systems DDP (HS-DDP) approach is considered for application to whole-body motion planning with legged robots. Specifically, HS-DDP incorporates three algorithmic advances: an impact-aware DDP step addressing the impact event in legged locomotion, an Augmented Lagrangian (AL) method dealing with the switching constraint, and a Switching Time Optimization (STO) algorithm that optimizes switching times by leveraging the structure of DDP. Further, a Relaxed Barrier (ReB) method is used to manage inequality constraints and is integrated into HS-DDP for locomotion planning. The performance of the developed algorithms is benchmarked on a simulation model of the MIT Mini Cheetah executing a bounding gait. We demonstrate the effectiveness of AL and ReB for handling switching constraints, friction constraints, and torque limits. By comparing to previous solutions, we show that the STO algorithm achieves 2.3 times more reduction of total switching times, demonstrating the efficiency of our method.