Simultaneous Decoupling of Inertia and Input via Coordinate Change: Investigation of the 2-DOF Case and Learning Based Solution

Abstract

Fully actuated robots may be controlled using well-understood techniques, such as computed torque control, which override natural system dynamics. For underactuated robots these dynamics cannot be fully cancelled out, and must instead be leveraged, complicating the control problem. We present a classification of underactuated robotic systems based on the degree to which their dynamics can be decoupled. Finding coordinates that decouple the system dynamics simplifies control for two classes of robots, which we identify as partially- and fully decouplable robotic systems. In these decoupling coordinates, the Euler-Lagrange system representation has a block-diagonal inertia matrix and decoupled input matrix. After delving into the fundamentals of this proposed classification, this work implements an autoencoder as a first ML-based framework to learn these decoupling coordinates for the 2 degrees of freedom (DOF) case. Furthermore, we demonstrate how such representations simplify control. Input decoupling allows for collocated control using a straightforward PD + gravity compensation controller. Inertial decoupling enables non-collocated control through feedback linearization within a small set of states. To demonstrate the theory, decoupling coordinates are learned for a 2-DOF toy system. Performance of the learned coordinate transform is analysed, and controllers on learned and analytic decoupling coordinates are compared.