Physics

Control engineering

Euler angles

Nonlinear system

Quaternion

Mathematics

Agronomy

Biology

Politics

Linearization

Engineering

Model predictive control

Political science

Artificial intelligence

Controller (irrigation)

Control (management)

Hessian matrix

Geometry

Representation (politics)

Computer science

Quantum mechanics

Applied mathematics

Control theory (sociology)

Robot

IEEE Transactions on Robotics

This paper presents a novel Representation-Free Model Predictive Control (RF-MPC) framework for controlling various dynamic motions of a quadrupedal robot in three dimensional (3D) space. Our formulation directly represents the rotational dynamics using the rotation matrix, which liberates us from the issues associated with the use of Euler angles and quaternion as the orientation representations. With a variation-based linearization scheme and a carefully constructed cost function, the MPC control law is transcribed to the standard Quadratic Program (QP) form. The MPC controller can operate at real-time rates of 250 Hz on a quadruped robot. Experimental results including periodic quadrupedal gaits and a controlled backflip validate that our control strategy could stabilize dynamic motions that involve singularity in 3D maneuvers.

Representation-Free Model Predictive Control for Dynamic Motions in Quadrupeds