یک رویکرد تکاملی برای حل مسئله سینماتیک معکوس چندمدلی روبات های صنعتی

The inverse kinematics solution of an industrial robot may provide multiple robot configurations that all achieve the required goal position of the manipulator. In the absence of obstacles, multiplicity resolution can be achieved by selecting the robot configuration closest to the current robot configuration in the joint space. An evolutionary approach based on a real-coded genetic algorithm is used to obtain the solution of the multimodal inverse kinematics problem of industrial robots. All the multiple configurations obtained by this approach can be displayed using a 3D modeler developed in MATLAB for the purpose of visualization. The multiple configurations are then compared on the basis of their closeness in joint space to the current robot configuration. Simulation experiments are carried out on a SCARA robot and a PUMA robot to illustrate the efficacy of the approach.

The kinematics equations of an industrial robot are non-linear and transcendental in nature. Their inverse kinematics solution provides the joint angles that are required to attain a particular position of the robot wrist in the robot workspace. The inverse kinematics solution may provide multiple robot configurations that all achieve the required goal position of the manipulator. In the absence of obstacles, the robot configuration closest to the current robot configuration in the joint space may be selected. This process of obtaining a unique solution can be referred to as a ‘multiplicity resolution’. Paul [1] proposed the use of homogeneous transformation matrices to obtain the inverse kinematics solution. The solution is obtained in a sequential manner, isolating each joint variable by pre-multiplication by a number of homogeneous transforms in each equation. Geometric intuition is suggested at certain points of the solution for certain manipulators. Multiple solutions for an elbow manipulator corresponding to ‘elbow up’ and ‘elbow down’ configurations are obtained trigonometrically. The issue of multiplicity resolution is also not addressed by the author.

An evolutionary approach based on a real-coded GA has been used to evaluate the multiple inverse kinematics solutions of industrial robots. Simulation experiments were carried out on a SCARA robot and a PUMA robot. An acceptable distribution of population members around the multiple inverse kinematics solutions is obtained with the use of a niching strategy for the binary tournament selection operator and mating restriction. The approach is straightforward and does not require the user to specify arm configuration indicators. It evaluates the multiple robot configurations correctly even when some of the configurations are not possible due to the limits on the joint variables. Further, it evaluates the joint variables within the joint variable limits correctly in all instances for a particular link coordinate frame assignment scheme. In the geometric approach certain joint variable values may seemingly lie outside the actual joint variable limits and have to re-interpreted considering the fact that a joint variable value +β and −(2π − β) are equivalent. All the available multiple configurations can be displayed using a 3D modeler developed in MATLAB for the purpose of visualization. The total joint displacement associated with these multiple robot configurations can be used for multiplicity resolution of the robotic manipulator. The evolutionary approach is therefore appropriate for obtaining the multiple inverse kinematics solutions of a robotic manipulator and subsequently achieving a multiplicity resolution.