Task scheduling and motion planning for an industrial manipulator Paraskevi Th. Zacharia a,n , Elias K. Xidias b , Nikos A. Aspragathos a a Department of Mechanical & Aeronautical Engineering, University of Patras, Rion 26500, Greece b Department of Product and Systems Design Engineering, University of the Aegean, Syros 84100, Greece article info Article history: Received 4 October 2012 Received in revised form 23 April 2013 Accepted 24 May 2013 Available online 15 June 2013 Keywords: Industrial manipulators Motion planning Task scheduling Bump-Surface Genetic Algorithm abstract In many robotic industrial applications, a manipulator should move among obstacles and reach a set of task-points in order to perform a pre-defined task. It is quite important as well as very complicated to determine the time-optimum sequence of the task-points visited by the end-effector's tip only once assuring that the manipulator's motion through the successive task-points is collision-free. This paper introduces a method for simultaneously planning collision-free motion and scheduling time-optimal route along a set of given task-points. This method is based on the projection of the workspace and the robot on the B-Surface to formulate an objective function for the minimization of the cycle time in visiting multiple task-points and taken into account the multiple solutions of the inverse kinematics and the obstacle avoidance. A modified GA with special encoding to encounter the multi- plicity of the robot inverse kinematics and the required intermediate configurations is used for the searching of the optimal solution on the B-Surface. The simulation results show the efficiency and the effectiveness of the proposed approach to determine a suboptimal tour for multi-goal motion planning in complex environments cluttered with obstacles. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction In manufacturing, high productivity demands the completion of robot tasks in the minimum possible time. On the other hand, today's production lines usually incorporate robots that interact with a wide range of equipment and fixtures. Thus, considerable attention has been paid to applications, where the manipulator's tip is assigned to reach a sequence of task-points only once in the minimum total cycle time, while operating in an environment cluttered with obstacles. It is very important to solve this problem for many robotic applications in manufacturing, such as pin assembly, insertion of electronic components, multiple drilling, spot welding and inspection tasks. Programming these capital intensive installations can be made off-line in powerful robot simulation systems for reducing the setup cost. Therefore software tools integrated in the simulators for determining the minimum cycle time sequence of given task-points could provide consider- able support to the programmer, reduce the programming and setup time as well as the production time and cost. The present work introduces a new method for solving the multi-goal motion-planning problem for an industrial manipulator operating in a 3D environment cluttered with static obstacles and serving a set of task-points with point-to-point motion. The above combined problem (motion planning problem and task scheduling problem) is formulated over the Bump-Surface [1] concept into an optimization problem, where the optimum sequence of the task- points should be determined towards cycle time minimization and simultaneously a collision-free motion of the manipulator between the obstacles should be obtained. Using the Bump-Surface (B-Surface) concept the 3D manipula- tor's workspace is represented by a 3D surface embedded in ℜ 4 , which captures both the free-space and the forbidden areas of the manipulator's workspace. A global optimization problem is then formulated considering simultaneously the task-scheduling and the collision-free motion planning of the manipulator among the obstacles. The optimization problem is solved using a Genetic Algorithm (GA) with a special encoding that considers the multi- plicity of the Inverse Kinematics that introduced in [2]. In this work, this encoding is extended to incorporate the intermediate configurations necessary for optimal collision-free motion. 1.1. State-of-the-art The problem of optimal multi-goal motion planning for an industrial manipulator operating in 3D environments cluttered with obstacles can be considered as the coupling of the task scheduling problem and the motion planning problem between successive task-points. Since each end-effector pose can be Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/rcim Robotics and Computer-Integrated Manufacturing 0736-5845/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.rcim.2013.05.002 n Corresponding author. Tel.: +30 2610 969491. E-mail address: zacharia@mech.upatras.gr (P.Th. Zacharia). Robotics and Computer-Integrated Manufacturing 29 (2013) 449–462