Jumping Control for a Quadrupedal Wheeled-Legged Robot via NMPC and DE Optimization

TL;DR

A mini-sized wheeled-legged robot for agile motion is developed and a novel motion control framework that integrates the Nonlinear Model Predictive Control (NMPC) for locomotion and the Differential Evolution based trajectory optimization for jumping in quadrupedal wheeled-legged robots is presented.

Abstract

Quadrupedal wheeled-legged robots combine the advantages of legged and wheeled locomotion to achieve superior mobility, but executing dynamic jumps remains a significant challenge due to the additional degrees of freedom introduced by wheeled legs. This paper develops a mini-sized wheeled-legged robot for agile motion and presents a novel motion control framework that integrates the Nonlinear Model Predictive Control (NMPC) for locomotion and the Differential Evolution (DE) based trajectory optimization for jumping in quadrupedal wheeled-legged robots. The proposed controller utilizes wheel motion and locomotion to enhance jumping performance, achieving versatile maneuvers such as vertical jumping, forward jumping, and backflips. Extensive simulations and real-world experiments validate the effectiveness of the framework, demonstrating a forward jump over a 0.12 m obstacle and a vertical jump reaching 0.5 m.

Figures (12)

• Figure 1: The jumping motion on our quadrupedal wheeled-legged robot: (a) The robot jumping over a 0.12 m obstacle; (b) The robot achieves a vertical jump with a maximum height of 0.5 m.
• Figure 2: The hardware design of our mini-size quadrupedal wheeled-legged robot (unit: mm).
• Figure 3: Overview of the control framework. The locomotion of our wheeled-legged robot is implemented by Nonlinear Model Predictive Control (NMPC), which generates the required forward velocity before the jump. The Differential Evolution (DE) algorithm is activated only during the take-off phase to solve the jumping trajectory optimization problem. The $d$ subscript indicates the desired value. The term $x_{c, \textnormal{roll}}$ represents the displacement of the Center of Mass (CoM) in the $x$-direction before the flight phase. The desired jumping state in the $x$-$z$ plane, denoted as $[x_c, z_c, \theta_c]$, corresponds to the desired jumping distance, height, and base rotation angle, respectively.
• Figure 4: The model of centroidal dynamic on our robot. $f_{ee1, x}$, $f_{ee1, y}$, $f_{ee1, z}$ indicates the GRF $\bm f_{ee1}$ in the $x$, $y$ ,$z$ direction w.r.t Body Frame.
• Figure 5: The foot's constraints when the wheel contacts the ground. It includes the velocity constraints of the wheel in the three directions ($\bm t$, $\bm n$, $\bm b$) and the friction cone constraints of foot force $\bm f_{eei}$. $\omega_i$ denotes the rotation speed of the wheel.