engleski

Optimal Robot Control with Unspecified Initial and Final Conditions

This paper presents the derivation of the numerical algorithm for optimal control of nonlinear multivariable systems with control and state vectors constraints and with unspecified initial and final conditions. The initial and final conditions depend on the parameter vector which represents a type of coordinate transformation. It is presented a detailed derivation of the algorithm for the calculation of the parameter vector, while the algorithm for time optimal control is described briefly. The algorithm derivation is based on the backpropagation-through-time algorithm, i.e. the chain rule for ordered derivations, and it is not based on Lagrange multiplier techniques and the calculus of variations. The derived algorithm is used for the solution of the minimum-time control of the robot with two degrees of freedom and with control vector constraint. The problem discussed in this paper is the determination of the control and parameter vector for the transition of the robot state from the initial to the final one in minimum time.

Optimal Control; Robot Control; Minimum-time control; Backpropagation Through Time Algorithm; Nonlinear Systems

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