Dynamic optimization for the trajectory planning of robot manipulators in the presence of obstacles

Abstract

This paper presents an approach to the solution of moving a robot manipulator with minimum cost along a specified geometric path in the presence of obstacles. The main idea is to express obstacle avoidance in terms of the distances between potentially colliding parts. The optimal traveling time and the minimum mechanical energy of the actuators are considered together to build a multiobjective function. A simple numerical example involving a Cartesian manipulator arm with two-degree-of-freedom is described

A Projected Gradient Augmented Lagrangian Approach to Multi-Objective Trajectory Planning of Redundant Robots

“…The forward kinematics problem deals with the determination of the EE motion from a given motion of the joints [12]. At the velocity level, it is expressed in a vector form as:…”

“…is the m-dimensional position vector of the EE and J is the mxn robot's Jacobian [12]. Although this study is applicable to a general n-degrees-of-freedom (DOF) serial manipulator with m-DOF at the Cartesian EE level, it is implemented on a two dimensional positioning with three revolute joints robot.…”

“…The robot dynamic model is developed using a Lagrangian formalism, which includes actuators model. This model allows closed-form expression of joint rates and accelerations characterizing the motion resulting from joint torques [12,13]. It can be expressed in continuous-time as:…”

Optimal motion planning of redundant planar serial robots using a synergy-based approach of convex optimization, disjunctive programming and receding horizon

“…The problem of controlling hyper-redundant serial manipulators has been addressed by many researchers. 3,4 Various methods have been proposed in the literature in order to solve motion planning problems of robotic mechanical systems. 3,4 Early methods include geometric approaches performing in the configuration space (C-space), the dimension of which is equal to the number of DOFs of the robot.…”

“…3,4 Various methods have been proposed in the literature in order to solve motion planning problems of robotic mechanical systems. 3,4 Early methods include geometric approaches performing in the configuration space (C-space), the dimension of which is equal to the number of DOFs of the robot. Methods operating in the C-space, such as visibility graphs, 5 cell decomposition 6 and particle swarm optimization, 7,8 have the advantage of reducing the configuration of the robot to a single point.…”