Predictive Trajectory Tracking Algorithm of Underactuated Systems Based On the Calculus of Variations

The tracking control of underactuated systems is a challenging problem due to the structural differences compared to fully actuated systems. Contrarily to fully actuated systems, resolving the inverse kinematics problem of underactuated systems is not possible independently from the dynamic equations. Instead, the inverse dynamics must be addressed. It is common to extend the computed torque control (CTC) technique with servo constraints. Besides the CTC's clearness, the stability of the system cannot be always guaranteed. A novel predictive controller (PC) is presented in this paper. Our PC applies the variational principle to design the motion of the system in order to achieve a stable motion with the lowest possible tracking error. To demonstrate the applicability and the performance of the PC method, a numerical study is presented for a planar manipulator resulting in about 20% RMS error compared to the CTC method from the literature.

Stabilization of Energy Level Sets of Underactuated Mechanical Systems Exploiting Impulsive Braking

Recent investigations of underactuated systems have demonstrated the benefits of control inputs that are impulsive in nature. Here we consider the problem of stabilization of energy level sets of underactuated systems exploiting impulsive braking. We consider systems with one passive degree-of-freedom (DOF) and the energy level set is a manifold where the active coordinates are fixed and the mechanical energy equals some desired value. A control strategy comprised of continuous inputs and intermittent impulsive braking inputs is presented. The generality of the approach is shown through simulation of a three-DOF Tiptoebot; the feasibility of implementation of impulsive control using standard hardware is demonstrated using a rotary pendulum.

Dual Adaptive Neural Network Controller for Underactuated Systems

SUMMARY A new stable adaptive controller based on a neural network for underactuated systems is proposed in this paper. The control scheme has been developed for two underactuated systems as examples. The Furuta pendulum and the Inertia Wheel Pendulum (IWP) have been examined in this paper. The presented approach aims to address the control problem of the given system in swing up, stabilization, and disturbance rejection. To avoid oscillations, two adaptive neural networks (ANNs) are implemented. The first one is used to approximate the equivalent control online and the second one to minimize the oscillations.