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.

Tracking control for underactuated non-minimum phase multibody systems

We consider tracking control for multibody systems which are modeled using holonomic and non-holonomic constraints. Furthermore, the systems may be underactuated and contain kinematic loops and are thus described by a set of differential-algebraic equations that cannot be reformulated as ordinary differential equations in general. We propose a control strategy which combines a feedforward controller based on the servo-constraints approach with a feedback controller based on a recent funnel control design. As an important tool for both approaches, we present a new procedure to derive the internal dynamics of a multibody system. Furthermore, we present a feasible set of coordinates for the internal dynamics avoiding the effort involved with the computation of the Byrnes–Isidori form. The control design is demonstrated by a simulation for a nonlinear non-minimum phase multi-input, multi-output robotic manipulator with kinematic loop.

Robust control design for home pension service mobile robots with passive and servo constraints

This paper presents a novel robust control design for a class of home pension service mobile robots (HPSMRs) with non-holonomic passive constraints, based on the Udwadia-Kalaba theory and Udwadia control. The approach has two portions: dynamics modeling and robust control design. The Udwadia-Kalaba theory is employed to deal with the non-holonomic passive constraints. The frame of the Udwadia control is employed to design the robust control to tracking the servo constraints. The designed approach is easy to implement because the analytical solution of the control force can explicitly be obtained even if the non-holonomic passive constraints exists. The uniform boundedness and uniform ultimate boundedness are demonstrated by the theoretical analysis. The effectiveness of the proposed approach is verified through the numerical simulation by a HPSMR.

Vibration Protection of Mechanical Systems Consisting of Solid And Deformable Bodies

In this paper active vibration protection of mechanical systems consisting of solid and deformable bodies is considered. To actively control the oscillations of dissipative mechanical systems, a constructive method is used to determine the structure of the reaction forces of servo constraints. As an example, we consider the system with a finite number of degrees of freedom. Numerical results for various harmonic are also given.

NEW CASE OF INTEGRABILITY IN DYNAMICS OF MULTI-DIMENSIONAL BODY

In this chapter the new results are systematized on study of the equations of motion of dynamically symmetrical four-dimensional (4D—) rigid body which residing in a certain nonconservative field of forces in case of special dynamical symmetry. Its type is unoriginal from dynamics of the real smaller-dimensional rigid bodies of interacting with a resisting medium on the laws of a jet flow, under which the nonconservative tracing force acts onto the body and forces both the value of velocity of a certain typical point of the rigid body and the certain phase variable to remain as constant in all time, that means the presence in system nonintegrable servo-constraints.