Dynamic Hybrid Locomotion and Jumping
for Wheeled-Legged Quadrupeds
Hybrid wheeled-legged quadrupeds have the potential to navigate challenging terrain with agility and speed and over long distances. However, obstacles can impede their progress by requiring the robots to either slow down to step over obstacles or modify their path to circumvent the obstacles. We propose a motion optimization framework for quadruped robots that incorporates non-steerable wheels and dynamic jumps, enabling them to perform hybrid wheeled-legged locomotion while overcoming obstacles without slowing down. Our approach involves a model predictive controller that uses a time-varying rigid body dynamics model of the robot, including legs and wheels, to track dynamic motions such as jumping. We also introduce a method for driving with minimal leg swings to reduce energy consumption by sparing the effort involved in lifting the wheels. Our method was tested successfully on the wheeled Mini Cheetah and the Unitree AlienGo robots.

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Overall Framework
Fig 1
Top: Hybrid locomotion control framework. The measured joint positions q̂ and velocities ˆ q̇, along with IMU data, are fed into the state estimator module to compute the robot state vector x̂, which includes position, orientation, velocity, and angular velocity of the robot [1]. The control then utilizes this information to generate joint positions q, velocities q̇, and torque commands τ . Bottom: our hybrid quadruped robot uses directly-driven wheels to drive quickly on regular terrain, restores a trapped leg by making a step, and executes a driving-jumping motion to overcome obstacles or gaps in the terrain.

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Control framework diagram.
Fig 2
The body state vector x̂ is estimated using the state estimator. The subscript i represents the leg number. The driving assistant (Section III-C) dynamically defines the parameter set P that is utilized by the trajectory and footstep planner, that generate reference trajectories, including state, contact, and foot trajectories (X ref , S ref , and P ref ) for the prediction horizon, and state commands (x cmd and p i cmd ) at the current control time. The MPC employs the aforementioned reference trajectories to compute optimal reaction forces f i for all contact points which are used in the WBC along with state and foot commands, to generate commands for the joints’ position, velocity, and torque (q k , q̇ k , and τ k ), i as well as refined reaction forces f̂ . Finally, the wheel controller uses the commanded foot velocities and the refined reaction forces to calculate the rotational speed and torque for the wheels ( q̇ w and τ w ).
Email : hosseini@ais.uni-bonn.de
Email : m.hosseini@outlook.com
Location : 53115, Bonn, Germany