INTELLIGENT OPTIMAL CONTROL OF ROBOT MANIPULATORS

This paper studies the optimal control problem for planar underactuated robot manipulators with two revolute joints and brakes at the unactuated joints in the presence of gravity. The presence of a brake at an unactuated joint gives rise to two operating modes for that joint: free and braked. As a consequence, there exist two operating modes for a robot manipulator with one unactuated joint and four operating modes for a manipulator with two unactuated joints. Since these systems can change dynamics, they can be regarded as switched dynamical systems. The optimal control problem for these systems is solved using the so-called embedding approach. The main advantages of this technique are that assumptions about the number of switches are not necessary, integer or binary variables do not have to be introduced to model switching decisions between modes, and the optimal switching times between modes are not unknowns of the optimal control problem. As a consequence, the resulting problem is a classical continuous optimal control problem. In this way, a general method for the solution of optimal control problems for switched dynamical systems is obtained. It is shown in this paper that it can deal with nonintegrable differential constraints.

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Discrete optimal control for robot manipulators

COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering ◽

10.1108/compel-10-2012-0204 ◽

2013 ◽

Vol 33 (1/2) ◽

pp. 423-444 ◽

Cited By ~ 4

Author(s):

Mohammad Mehdi Fateh ◽

Maryam Baluchzadeh

Keyword(s):

Optimal Control ◽

Control Strategy ◽

Optimal Algorithm ◽

Robot Manipulators ◽

Torque Control ◽

Linear Quadratic ◽

Voltage Control Strategy ◽

Content Type ◽

Discrete Optimal Control ◽

Electrically Driven Robot

Purpose – Applying discrete linear optimal control to robot manipulators faces two challenging problems, namely nonlinearity and uncertainty. This paper aims to overcome nonlinearity and uncertainty to design the discrete optimal control for electrically driven robot manipulators. Design/methodology/approach – Two novel discrete optimal control approaches are presented. In the first approach, a control-oriented model is applied for the discrete linear quadratic control while modeling error is estimated and compensated by a robust time-delay controller. Instead of the torque control strategy, the voltage control strategy is used for obtaining an optimal control that is free from the manipulator dynamics. In the second approach, a discrete optimal controller is designed by using a particle swarm optimization algorithm. Findings – The first controller can overcome uncertainties, guarantee stability and provide a good tracking performance by using an online optimal algorithm whereas the second controller is an off-line optimal algorithm. The first control approach is verified by stability analysis. A comparison through simulations on a three-link electrically driven robot manipulator shows superiority of the first approach over the second approach. Another comparison shows that the first approach is superior to a bounded torque control approach in the presence of uncertainties. Originality/value – The originality of this paper is to present two novel optimal control approaches for tracking control of electrically driven robot manipulators with considering the actuator dynamics. The novelty is that the proposed control approaches are free from the robot's model by using the voltage control strategy. The first approach is a novel discrete linear quadratic control design supported by a time-delay uncertainty compensator. The second approach is an off-line optimal design by using the particle swarm optimization.

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