Krzysztof Jankowski

An approach to discrete inverse dynamics control of flexible-joint robots

An inverse-dynamics-based method for discrete-time control of flexible-joint robots is presented. The main drawbacks of continuous-time analysis are its computational burden and the necessity for very high sampling frequencies. These inconveniences can be avoided by the use of numerical methods conceived for the solution of systems of differential-algebraic equations. Such an approach naturally leads to a predictive control scheme. As a consequence, in the control process a basic dynamic model of the flexible-joint robot can be used, which is much less complex than in the classical inverse dynamics solution. At the same time, the simplified inverse dynamics approach discussed here accepts low sampling frequencies. Control algorithms are presented and their properties are discussed. Successful experiments on computer control of a two-link manipulator with one flexible joint are described. >

Dynamics of controlled mechanical systems with material and program constraints— I. Theory

Abstract The general problem of control of constrained mechanical systems is considered using the concepts and methods of analytical mechanics. The mechanical actions of “material” and “program” constraints are considered separately, due to different ways of their realization. The procedures for obtaining a reduced set of controlled system equations of motion as well as the equations of motion with multipliers are developed in Part I of the paper. The methods of solution, with special attention focussed on singular cases, are presented in Part II. Illustrative examples and a discussion are presented in Part III.

Inverse dynamics task control of flexible joint robots—I: Continuous-time approach

Abstract This paper focuses on the problem of application of inverse dynamics control methods to robots with flexible joints. In Part I of the paper, there are answers presented to a number of questions related to the analytical formulation of nonlinear decoupling control laws. After discussion, the dynamic model of a robot with flexible joints and electrochemical actuators is chosen. The application of the extended computed torque technique together with the methods from the theory of differential-algebraic equations (DAE) to the developed fifth-order robot model gives a number of decoupled linear subsystems, which take robot task space commands as inputs. Due to drawbacks of the continuous-time inverse dynamics, discussed in the paper, a new control strategy in discrete-time is developed in Part II of the paper. The proposed control method is computationally efficient and admits low sampling frequencies. The results of extensive numerical experiments confirm the advantages of the designed control algorithm.

Discrete-Time Inverse Dynamics Control of Flexible Joint Robots

This paper focuses on the problem of the application of inverse dynamics control methods to robots with flexible joints and electromechanical actuators. Due to drawbacks of the continuous-time inverse dynamics, discussed in the paper, a new control strategy in discrete-time is presented. The proposed control algorithm is based on numerical methods conceived for the solution of index-three systems of differential- algebraic equations. The method is computationally efficient and admits low sampling frequencies. The results of numerical experiments confirm the advantages of the designed control algorithm

Inverse dynamics task control of flexible joint robots—II: Discrete-time approach

Abstract Due to drawbacks of the continuous-time inverse dynamics for robots with flexible joints, discussed in the paper, a new discrete-time approach to the problem is presented. After discussion, a numerical approach for the solution of the index three systems of differential-algebraic equations is adopted to solve the inverse dynamics problem. The satisfactory results show that the method can be used to off-line determination of nominal control inputs and joint trajectories. Next, a discrete-time control method is developed and a realistic control scheme is analysed. The implications of the results for the control of robots are discussed. The proposed control method is computationally efficient and admits low sampling frequencies. The results of extensive numerical experiments confirm the advantages of the designed control algorithm.

Dynamics of controlled mechanical systems with material and program constraints— II. Methods of solution

Abstract The methods of solution of mathematical models of constrained mechanical systems developed in Part I are presented. A great deal of attention is paid to singular cases which may appear in modelling of systems with program constraints. The case when the applied forces are nonlinear functions of control variables and the case of the control by constraints are considered. An approach to the evaluation of the solvability of the system equations of motion is proposed.

Dynamics of controlled mechanical systems with material and program constraints. III: Illustrative examples

Abstract The general theory and algorithms for solving the constrained system equations of motion presented in Part I and Part II are implemented for selected problems of mechanics. The detailed derivation of the mathematical model of a driven disk with three variants of program motion is presented. In the second example the condition of generalized precession of a rigid body is treated as the program constraint, which is performed by a control system. A comprehensive discussion ends the paper.