# Single Sequential Trajectory Optimization with Centroidal Dynamics and Whole-Body Kinematics for Vertical Jump of Humanoid Robot

## TL;DR

This paper introduces a new method for optimizing humanoid robot vertical jumps by combining centroidal dynamics and whole-body kinematics in a single optimization process.

## Contribution

The novel contribution is a single sequential trajectory optimization method that integrates centroidal dynamics and whole-body kinematics for efficient vertical jumping.

## Key findings

- The proposed method efficiently solves whole-body motion trajectories for vertical jumping.
- A real humanoid robot achieved a vertical jump of 0.5 m in height using the optimized method.

## Abstract

High vertical jumping motion, which enables a humanoid robot to leap over obstacles, is a direct reflection of its extreme motion capabilities. This article proposes a single sequential kino-dynamic trajectory optimization method to solve the whole-body motion trajectory for high vertical jumping motion. The trajectory optimization process is decomposed into two sequential optimization parts: optimization computation of centroidal dynamics and coherent whole-body kinematics. Both optimization problems converge on the common variables (the center of mass, momentum, and foot position) using cost functions while allowing for some tolerance in the consistency of the foot position. Additionally, complementarity conditions and a pre-defined contact sequence are implemented to constrain the contact force and foot position during the launching and flight phases. The whole-body trajectory, including the launching and flight phases, can be efficiently solved by a single sequential optimization, which is an efficient solution for the vertical jumping motion. Finally, the whole-body trajectory generated by the proposed optimized method is demonstrated on a real humanoid robot platform, and a vertical jumping motion of 0.5 m in height (foot lifting distance) is achieved.