# Differential Dynamic Programming for Multi-Phase Rigid Contact Dynamics

## TL;DR

This paper introduces a novel application of Differential Dynamic Programming (DDP) for generating whole-body locomotion trajectories in multi-phase rigid contact scenarios, improving efficiency and impact reduction by leveraging angular momentum.

## Contribution

It presents an original DDP formulation that incorporates contact constraints via KKT conditions, enabling more efficient and realistic robot motions compared to traditional inverse kinematics methods.

## Key findings

- Successful large steps walking on HRP-2 robot
- Reduced forces and impacts in generated motions
- Effective attitude control without external forces

## Abstract

A common strategy today to generate efficient locomotion movements is to split the problem into two consecutive steps: the first one generates the contact sequence together with the centroidal trajectory, while the second one computes the whole-body trajectory that follows the centroidal pattern. Yet the second step is generally handled by a simple program such as an inverse kinematics solver. In contrast, we propose to compute the whole-body trajectory by using a local optimal control solver, namely Differential Dynamic Programming (DDP). Our method produces more efficient motions, with lower forces and smaller impacts, by exploiting the Angular Momentum (AM). With this aim, we propose an original DDP formulation exploiting the Karush-Kuhn-Tucker constraint of the rigid contact model. We experimentally show the importance of this approach by executing large steps walking on the real HRP-2 robot, and by solving the problem of attitude control under the absence of external forces.