Elżbieta Jarzębowska

Advanced Programmed Motion Tracking Control of Nonholonomic Mechanical Systems

Trajectory tracking control of nonholonomic systems has been extended to tracking a desired motion. The desired motion is specified by equations of constraints, referred to as programmed, which may be differential equations of high order and may be nonholonomic. The strategy enables motion tracking control under the assumption that the system dynamics are accurately known. It is referred to as a model reference tracking control strategy for programmed motion. In this paper, adaptive and repetitive extensions of the strategy are proposed. Two selected advanced tracking control algorithms, i.e., the desired compensation adaptation law and the repetitive control law, which were originally dedicated to holonomic systems, are adapted to motion tracking control of nonholonomic systems. Simulation studies that illustrate programmed motion tracking control of systems with unknown parameters and the performance of repetitive motions are provided. A new performance measure to evaluate a programmed motion tracking performance is introduced.

On Derivation of Motion Equations for Systems with Non-Holonomic High-Order Program Constraints

The paper develops and discusses the generalization of modeling methods for systems with non-holonomic constraints. The classification of constraints has been revisited and a concept of program constraints introduced. High-order non-holonomic constraints (HONC), as presented in examples, are the generalization of the constraint concept and may, as a constraint class, include many of motion requirements that are put upon mechanical systems. Generalized program motion equations (GPME) that have been derived in the paper can be applied to systems with HONC. Concepts of virtual displacements and a generalized variational principle for high-order constraints are presented. Classical modeling methods for non-holonomic systems based on Lagrange equations with multipliers, Maggi, Appell–Gibbs, Boltzman–Hamel, Chaplygin and others are peculiar cases of GPME. The theory has been illustrated with examples of high-order constraints. Motion equations have been derived for a system subjected to a constraint that programmed a trajectory curvature profile. Efficiency, advantages and disadvantages of GPME have been discussed.

Robot motion planning in the presence of program constraints

Abstract The paper presents a method of a motion planning and tracking for constrained robots. Specifically, we are interested in program constraints, by which robot tasks can be defined. The program constraint is an input to a kind of a motion planning system, which has been based on a generalized motion equation method suitable for systems with bilateral constraints of arbitrary orders. For the program motion planned by the motion planner a closed-loop program motion tracking using a class of feedback controllers has been designed. Global tracking conditions were developed for the case of nonlinear dynamics using a modification of the computed torque method.

Tracking control design for underactuated constrained systems

An extension of a model-based tracking control strategy to underactuated systems is presented. Originally, it is designed for actuated systems that can perform tasks specified by equations of algebraic or differential constraints referred to as programmed, which may be nonintegrable. It is demonstrated that for both actuated and underactuated nonholonomically constrained systems one tracking control strategy can be designed. Systems we consider are nonholonomic because of constraints put on their motions as well as unactuated degrees of freedom. We detail an example, which illustrates the theory and demonstrates advantages of application of one tracking control strategy for actuated and underactuated constrained systems.

MODELING AND CONTROL DESIGN USING THE BOLTZMANN-HAMEL EQUATIONS: A ROLLER-RACER EXAMPLE

Abstract The paper presents a dynamic modeling and control design for a wheeled vehicle with idle wheels. An example we detail is a roller-racer. For this system, we cannot determine its global motion by just the shape variation, since it does not posses a sufficient number of nonholonomic constraint equations. Kinematics must be complemented with the system dynamics. Using the Boltzmann-Hamel equations we develop a control oriented dynamic model for the roller-racer. Based on this model we design a modified computed torque controller to track its desired motion. We demonstrate that the Boltzmann-Hamel equations offer a competitive tool to develop dynamic control models for constrained systems and they may facilitate a subsequent controller design.

Design of a tracking controller-observer system for a mobile robot

The paper presents a model-based tracking control strategy for a mobile robot based on a controller design that uses only position and orientation measurement. This model-based tracking strategy is the programmed motion tracking originally developed under the assumption that the foil state of a system is available for measurement. To meet practical requirements that not all state variables are accessible, we develop the programmed motion tracking for a mobile robot using only position and orientation measurement. Our approach exploits a structure of a control dynamics of the mobile robot.

Automated generation of reference dynamical models for constrained robotic systems in the presence of friction and damping effects

This paper details a new automated generation method of dynamic models of structures allowing presence of friction and damping in their models as well as subjected to position or kinematic constraints. The constraints may be material, which come from the system interaction with environment, or may be programmed. The novelty of the presented dynamics generation method is to include friction and damping into modeling and to require predefined constraint satisfaction as well. The latter requirement is critical, since when friction and damping are neglected, controllers may be inadequately designed, constraints may be violated, and overall system performance may be poor. The developed method is applied to a manipulator model, whose end‐effector performance is predefined by programmed constraints. Simulation results present manipulator constrained motion. The advantage of this method is that it serves both reference and control oriented dynamics derivation, and the final dynamics models are obtained in the reduced state form, ie, constraint reaction forces are eliminated. This is the fundamental difference between the presented approach and the Lagrange based approaches to constrained system modeling.

Model-based control of a third-order nonholonomic system

This paper addresses dynamics modelling and control of mechanical systems subjected to constraints due to the tasks they are to perform. The researched problem refers to the control of a manipulator end-effector motion subjected to a constraint on an acceleration change, that is, jerk. In the presented approach, the acceleration and jerk constraints are incorporated into a system constrained dynamics and then passed to its control dynamics using a unified approach, which is based on an advanced dynamics modelling method, that is, on the generalized programmed motion equations method. This enables one to derive motion equations for systems subjected to high-order constraints. The novelty of this approach consists of the formulation of a unified representation of constraints by differential equations, merging them into system constrained dynamics and then using nonlinear control theory techniques to design controllers for tracking motions along the pre-specified constraints.

Development of a Computational Based Reference Dynamics Model of a Flexible Link Manipulator

Development of a new derivation method of a reference dynamics model of a flexible link manipulator is presented in the paper. The model including flexibility can map dynamics and performance of lightweight and fast manipulators correctly and may serve their motion analysis and control design in the presence of kinematic or programmed constraints, which are assumed to be position or first order nonholonomic. The reference dynamics model is derived using the formalism of joint coordinates and homogeneous transformation matrices. This approach allows generating dynamics equations of a manipulator without formulating additional material constraint equations. The constraints present in the reference dynamics model are the programmed ones only. The flexibility of a link is modelled using the rigid finite element method. The main advantage of this method is its ability of application of the rigid-body approach to modeling dynamics of multi-body systems with flexible links. The novelty of the presented method relies on the combination of dynamics modeling of flexible system models with the programmed constraints satisfaction problem for them. The computational algorithm underlying the derivation method presented in the paper is based on Generalized Programmed Motion Equations (GPME) approach. The reference dynamics model derivation is demonstrated for a flexible link manipulator model.

Quaternion Based Dynamics for Servicing Satellite with Mission Protocol Description

The paper presents the dynamics of the servicing satellite. The model includes attitude and orbital dynamics of the satellite, with the goal to dock to the target satellite. The dynamics model is free of the singularities because of quaternion use. Orbital dynamics was defined in the internal reference frame with disturbances. To the satellite dynamic model the control system was proposed and the task was defined for the system was defined. Control algorithm was proposed based on Computed Torque control law. The new approach was to defined step by step procedure of the servicing mission of the telecommunication satellites.