Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control

TL;DR

T tackles the problem of enabling highly dynamic quadruped locomotion with aerial phases. The authors combine Model Predictive Control (MPC) to plan ground-reaction forces with a high-bandwidth Whole-Body Impulse Control (WBIC) that executes full-body dynamics, using MPC forces as targets rather than CoM trajectories. Key contributions include a convex MPC formulation with a gait scheduler and footstep planner, a null-space-based WBIC with a small QP for torque computation, and hardware validation on the Mini-Cheetah achieving speeds up to 3.7 m/s across multiple gaits and terrains. This approach improves robustness and versatility, enabling smooth high-speed locomotion with flight phases and easy adaptation to new gaits or tasks.

Abstract

Dynamic legged locomotion is a challenging topic because of the lack of established control schemes which can handle aerial phases, short stance times, and high-speed leg swings. In this paper, we propose a controller combining whole-body control (WBC) and model predictive control (MPC). In our framework, MPC finds an optimal reaction force profile over a longer time horizon with a simple model, and WBC computes joint torque, position, and velocity commands based on the reaction forces computed from MPC. Unlike existing WBCs, which attempt to track commanded body trajectories, our controller is focused more on the reaction force command, which allows it to accomplish high speed dynamic locomotion with aerial phases. The newly devised WBC is integrated with MPC and tested on the Mini-Cheetah quadruped robot. To demonstrate the robustness and versatility, the controller is tested on six different gaits in a number of different environments, including outdoors and on a treadmill, reaching a top speed of 3.7 m/s.

Figures (5)

• Figure 1: Control Architecture. The proposed control architecture consists of two parts: Model predictive control and whole-body control. The reaction forces computed by MPC are modified by WBC to incorporate body stabilization and swing leg control. The final commands found in WBC are sent to the robot to perform dynamic locomotion.
• Figure 2: Overall Control Framework. Using the user commanded gait type, speed, and direction from the RC-controller, the MPC computes desired reaction forces and foot/body position commands. From these, WBC computes joint torque, position, and velocity commands that are delivered to the each joint-level controller. Each component's update frequency is represented by the color of its box.
• Figure 3: Configuration of Mini-Cheetah. Mini-cheetah uses 12 proprioceptive actuators to control 4 limbs. The numbering of joints starts from right front abduction/adduction joint and progresses to hip and knee flexion/extension joints.
• Figure 4: Running Experiment. Mini-Cheetah trots at $3.7m\per s$. (b) The observed maximum speed is $4 \ m\per s$ but the robot quickly lost its balance after reaching this speed. The highest stable speed reached was is $3.7\ m\per s$. (c) and (d) show the joint velocity, torque, and power. We only include data from three joints (abduction, hip, and knee) from the front left leg, but the other legs are similar. From the observed maximum velocity, torque, and power, we can see that our controller utilizes maximum hardware capacity of Mini-Cheetah. (d) and (e) show how the trajectory and reaction forces tracking work together to accomplish dynamic running. The robot's height goes up and down around the constant height command while making jumps and landing, which is accomplished by following the vertical reaction force command ($f_z$). (e) Reaction forces computed by MPC update only 4 times during a stance period, but WBIC computes the forces every $2\ ms$ and makes a modification from the force commands to control body posture and swing feet.
• Figure 5: Demonstration of Various Gaits. Our controller can demonstrate various dynamic running by switching the gait types. (b) The commanded vertical reaction forces are presented. (c) The commanded velocity and direction are presented with the measured velocity and yaw angle. The results show that the actual system follows the given commands well.