Collision Free and Energitaclly Optimized Motion Planning of Manipulators in Partially-Known Environment Using Modified D* Life Algorithm

Abstract

Robotics is a relatively young field of studies in modern technology and it has tremendously grown during the past fifty years. Manipulators are categorized as a group of robots designed to accomplish the manipulation tasks without direct contact by a human. Generating an optimized algorithm to transform high-level motion tasks to low-level description that are understandable by the robots, including manipulators, has been one of the most interesting problems in this field. Motion planning in robotics, is referred to the process of breaking down a desired movement task into discrete motions in order to satisfy some specific criteria and optimize some certain variables during the motion from the start point to the goal point. Although various types of problems in robot motion planning have been investigated; trajectory planning for the manipulators in partially-known environment with respect to the amount of energy consumption has not been fully addressed. This aspect of motion planning can be of great importance in optimizing the path planner algorithms while satisfying their collision free attribute. This study attempts to develop a comprehensive mathematical model for robot-actuator system dynamics to include the energy consumption level as a variable in the cost function of the path planner algorithm. For this purpose, the manipulator’s general equation of motion is derived using the Lagrange equations. Same approach has been taken to develop the equation of motion of the robot’s actuators which are considered to be DC motors at each joint of the manipulator. The fourth order of Runge-Kutta algorithm is used to solve the coupled governing differential equations of the system. The output of the modeling phase of the study is fed to the graph search algorithm as an input. Graph search algorithm deals with the start-to-goal node problem in which the best path in a network of nodes is desired. D* Lite algorithm is one the most well-known algorithms in dealing efficiently with the partially-known environment motion planning problems. The advantages of D* Lite algorithm over the other famous algorithms such as A* are investigated, the best path generation procedure is thoroughly discussed, and the implementation of the algorithm is deliberated. A modification on D* Lite algorithm is proposed here to enhance the efficiency of the best path generation method and the alternative procedure is provided correspondingly. A MATLAB framework is designed to define the robot and its workspace and the manipulator equation of motion is developed using MATLAB classes to transform the user input values into the state space variables of the system. Several scenarios have been simulated using the developed framework to verify the path planner effectiveness in avoiding the pre-known and partially-known obstacles while minimizing the amount of consumed energy by the manipulator during its motion from the start node to the goal node.