Globally Optimal Inverse Kinematics Method for a Redundant Robot Manipulator with Linear and Nonlinear Constraints

Abstract

This paper presents a novel inverse kinematics global method for a redundant robot manipulator performing a tracking maneuver. The proposed method, based on the choice of appropriate initial joint trajectories that satisfy the kinematic constraints to be used as inputs for a multi-start optimization algorithm, allows for the optimization of different integral cost functions, such as kinetic energy and joint torques norm, and can provide solutions with a variety of constraints, both linear and nonlinear. Furthermore, it is suitable for multi-objective optimization, and it is able to find multiple optima with minimal input from the user, and to solve cyclic trajectories. Problems with a high number of parameters have been addressed providing a sequential version of the method based on successive stages of interpolation. The results of simulations with a three-Degrees-of-Freedom (DOF) redundant manipulator have been compared with a solution available in the literature based on the calculus of variations, thus leading to the validation of the method. Moreover, the effectiveness of the presented method has been shown when used to solve problems with constraints on joint displacement, velocity, torque, and power.

A Constrained Intelligent Nonlinear Control Method for Redundant Robotic Manipulators

“…Remark 2: In fact, there are infinite solutions for the problem (3). Hence, it is possible to shape possible solutions inside the expected regions [30].…”

“…Remark 4: At this time, values of the constraint components will be adjusted up by the Gaussian-type gain when the joint variables approach the upper limits or the lower limits. This is caused by the characteristics of the Gaussian function [30], [31] as the variable values approach their centers. Conversely, when the joints move away from the upper and lower limits, depending on the slope of the Gaussian function, the gain will decrease very quickly and push the influence of the constraint down very small.…”

“…where (0 < m < 1) and α are positive constants, and • i , • i−1 denote current and previous states of (•) . Remark 5: The advantage of this learning algorithm is that it could solve the problems of the normal gradient descent learning methods which are slow to converge and easy to get stuck at the local minimum that is difficult or impossible to reach the global minimum [2], [4], [30]. The Momentum approach could help convergence faster by creating momentum behaviors from the previous velocity, while the shortcoming of instability of Momentum methods would be handled by the Levenberg-Marquardt part due to its ability to damp and ensure all the joint velocities not too different.…”

PD-Impedance Combined Control Strategy for Capture Operations Using a 3-DOF Space Manipulator with a Compliant End-Effector

“…Furthermore, the desired trajectory of each joint can be obtained by integrating Equation (24). For redundant space manipulators, proper trajectory planning for joints can minimize base disturbance, kinetic energy, joint torques, and avoid singularities and physical joint limits [38,39]. This paper mainly studies the 3 DOF space manipulator, which has the minimum number of joints to meet the requirements of two-dimensional motion.…”

Improved Uncalibrated Visual Servo Strategy for Hyper-Redundant Manipulators in On-Orbit Automatic Assembly

“…Considering the complexity of on-orbit maintenance tasks and the need for flexibility, a redundant manipulator with more degrees of freedom is a reasonable choice [41,42]. Redundancy is often used in space manipulators; for example, to minimize the reactions transferred from the manipulator to the spacecraft [43] or to minimize the kinetic energy and joint torques [44]. Therefore, a hyper-redundant manipulator with nine degrees of freedom has been designed to implement on-orbit maintenance tasks for large space facilities.…”