Gradient Algorithm For Systems Research Articles

Minimum-Time Control of a Two-Link Robot Arm

Minimum time paths for a two-link robot arm are determined so that the tip moves a specified distance, starting from rest and ending at rest. Two torquers are used, one at the shoulder and one at the elbow, each having bounded torque. The optimal locations of the two end points in the robot coordinate system are determined as part of the solution. The paths are found to be “bang-bang” in both controls. For distances that are small compared to the reach of the arm, the minimum time paths are asymmetric, changing to symmetric paths when the distance is just slightly less than the maximum reach of the arm. A new gradient algorithm for systems with multiple bounded controls was developed to solve the problem.

Minimum-time control of a two-link robot arm

Minimum time paths for a two-link robot arm are determined so that the tip moves a specified distance, starting from rest and ending at rest. Two torquers are used, one at the shoulder and one at the elbow, each having bounded torque. The optimal locations of the two end points in the robot coordinate system are determined as part of the solution. The paths are found to be “bang-bang” in both controls. For distances that are small compared to the reach of the arm, the minimum time paths are asymmetric, changing to symmetric paths when the distance is just slightly less than the maximum reach of the arm. A new gradient algorithm for systems with multiple bounded controls was developed to solve the problem.

Optimal control of systems with state-dependent time delay†

Necessary conditions for optimal control of systems containing a time delay that is a function of the state of the system and of time are derived by utilizing calculus of variations. The time delay may be in the state vector and in the control vector. The state vector and the control vector can be constrained by inequality constraints. A transformation to eliminate state variable inequality constraints by increasing the dimensions of state space, developed by Jacobson for an undelayed system, is extended to a system with time delays. Necessary conditions to obtain an optimal delay are shown, and an example of finding an optimal delay is included. A gradient algorithm for systems with state dependent time delays has been developed.