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The paper presents a control oriented dynamic formulation for constrained robotic systems. We refer to this formulation as control oriented since it can be directly applied to design a model-based tracking control strategy. It enables one to obtain dynamic models for systems subjected to material constraints and non-material referred to as program constraints. The dynamic model for a constrained robot, where equations of program constraints specify tasks and motion requirements, is used as a program motion planner for a controller design. The formulation provides a theoretical framework, which is a basis for the study of robot performance of constrained tasks. Examples of developments of control oriented dynamic models are presented, and their applications for control are demonstrated and discussed.

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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.Index Terms-Adaptive programmed motion tracking, nonholonomic systems, repetitive programmed motion tracking.

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.

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