A Fast Online Omnidirectional Quadrupedal Jumping Framework Via Virtual-Model Control and Minimum Jerk Trajectory Generation

TL;DR

A new framework to enable fast, omnidirectional jumping capabilities for quadruped robots is introduced, utilizing minimum jerk technology and efficiently generates jump trajectories that exploit its analytical solutions, ensuring numerical stability and dynamic compatibility with minimal computational resources.

Abstract

Exploring the limits of quadruped robot agility, particularly in the context of rapid and real-time planning and execution of omnidirectional jump trajectories, presents significant challenges due to the complex dynamics involved, especially when considering significant impulse contacts. This paper introduces a new framework to enable fast, omnidirectional jumping capabilities for quadruped robots. Utilizing minimum jerk technology, the proposed framework efficiently generates jump trajectories that exploit its analytical solutions, ensuring numerical stability and dynamic compatibility with minimal computational resources. The virtual model control is employed to formulate a Quadratic Programming (QP) optimization problem to accurately track the Center of Mass (CoM) trajectories during the jump phase. The whole-body control strategies facilitate precise and compliant landing motion. Moreover, the different jumping phase is triggered by time-schedule. The framework's efficacy is demonstrated through its implementation on an enhanced version of the open-source Mini Cheetah robot. Omnidirectional jumps-including forward, backward, and other directional-were successfully executed, showcasing the robot's capability to perform rapid and consecutive jumps with an average trajectory generation and tracking solution time of merely 50 microseconds.

Figures (5)

• Figure 1: Various jumping motion experiments to validate the proposed omnidirectional jumping framework. (a) Front-left jumping consecutively. (b) Single rear-right jumping. (c) Single rear jumping. (d) Single front jumping. The yellow line shows the trajectory of CoM, and the red dashed line represents the trajectory of the selected foot. The red dots indicate the foot's contact with the ground, and the orange dots indicate the foot in the flight phase.
• Figure 2: A model of a single rigid body (SRB) utilized in the framework for VMC. The blue arrow represents the CoM to the plantar position vector, while the red arrow represents the Ground Reaction Forces (GRFs).
• Figure 3: The Jumping phase, Flight phase, and Landing phase consist of the omnidirectional jumping motion.
• Figure 4: The overview of the fast online omnidirectional quadrupedal jumping framework, made of 3 primary components.
• Figure 5: Mini-Cheetah deployed with the omnidirectional jumping framework performs two jumping motions. Data charts in Fig. (a) and Fig. (b) are data records of the rear-right leg in front-left jumping and rear-right jumping, respectively. The blue line represents the start of the jumping phase, the dark red line indicates the start of the flight phase, the green line is the beginning of the landing phase, and the red dot lines represent the upper and lower bound of the torque limit with an absolute value of 24 Nm.