The principal objective of the paper is to show the importance of the Hamiltonian in control theory. Instead of using the Lagrangian formulation of electromechanical or robotic systems, our work is focused on robot dynamics by its Hamiltonian. Using the iterative Newton–Euler, we generate the local Hamiltonians and the derivative of the moments at each joint of the robot manipulator. Thus, we can apply decentralized controllers at each joint. We compare and discuss the efficiency of the controllers. We show that the performance of the sliding modes controller is more robust than that of the PD or Bang–Bang controllers.

This paper presents a collision-free motion planning method of two articulated robot arms in a three dimensional common work space. Each link of a robot arm is modeled by a cylinder ended by two hemispheres, and the remaining wrist and hand is modeled by a sphere. To describe the danger of collision between two modeled objects, minimum distance functions, which are defined by the Euclidean norm, are used. These minimum distance functions are used to describe the constraints that guarantee no collision between two robot arms. The collision-free motion planning problem is formulated as a pointwise constrained nonlinear minimization problem, and solved by a conjugate gradient method with barrier functions. To improve the minimization process, a simple grid technique is incorporated. Finally, a simulation study is presented to show the significance of the proposed method.

The optimum control of an industrial robot can be achieved by splitting the problem into two tasks: off-line programming of an optimum path, followed by an on-line path tracking.

The aim of this paper is to address the numerical solution of the optimum path planning problem. Because of its mixed nature, it can be expressed either in terms of Cartesian coordinates or at joint level.

Whatever the approach adopted, the optimum path planning problem can be formulated as the problem of minimizing the overall time (taken as objective function) subject to behavior and side constraints arising from physical limitations and deviation error bounds. The paper proposes a very general optimization algorithm to solve this problem, which is based on the concept of mixed approximation.

A numerical application is presented which demonstrates the computational efficiency of the proposed algorithm.

The problem of finding an allowable object trajectory for a cooperating two-robot system is investigated. The purpose is to move an object from one point to another by firmly grasping it at two different points using two robotic hands. The major difficulty is caused by the fact that, unless the robots have true six degrees of freedom, the trajectories the object can follow are severely limited and, in general, are difficult to find. The method proposed in the paper is based on reformulating the problem as a nonlinear optimization problem with equality constraints in terms of the joint variables. The optimization problem is then solved numerically on a computer. The solution automatically gives the corresponding joint variable trajectories as well, thus eliminating the need for solving the inverse kinematic problem. The method has been successfully applied to a real experimental system.

This paper presents a hybrid approach to optimize the counterweight balancing of a robot arm. A new technique that combines an artificial intelligence technique called the genetic algorithm (GA) and the weighted min-max multiobjective optimization method is proposed. These techniques are included in a system developed by the authors, called MOSES, which is intended to be used as a tool for engineering design optimization. The results presented here show how the new proposed technique can get better trade-off solutions and a more accurate Pareto front for this highly non-convex problem using an ad-hoc floating point representation and traditional genetic operators. Finally, a methodology to compute the ideal vector using a genetic algorithm is presented. It is shown how with a very simple dynamic approach to adjust the parameters of the GA, it is possible to obtain better results than those previously reported in the literature for this problem.