TAILIEUCHUNG - An overview and the time optimal cruising trajectory planning
In this paper, a method which intends to provide the motion in every point of the path with possible maximum velocity is described. In fact, the path is divided to transient and cruising parts and the maximum velocities are required only for the latter. The given motion is called “Time-optimal cruising motion”. Using the parametric method of motion planning, the equations for determining the motions are given. | Journal of Computer Science and Cybernetics, , (2014), 291–312 DOI: REVIEW PAPER AN OVERVIEW AND THE TIME-OPTIMAL CRUISING TRAJECTORY PLANNING ´ ´ SOMLO JANOS Obuda University, Budapest Hungary; somlo@ Abstract. In the practical application of robots, the part processing time has a key role. The part processing time is an idea borrowed from manufacturing technology. Industrial robots usually are made to cover a very wide field of applications. So, their abilities, for example, in providing high speeds are outstanding. In most of the applications the very high speed applications are not used. The reasons are: technological (physical), organizational, etc., even psychological. Nevertheless, it is reasonable to know the robot’s abilities. In this paper, a method which intends to provide the motion in every point of the path with possible maximum velocity is described. In fact, the path is divided to transient and cruising parts and the maximum velocities are required only for the latter. The given motion is called “Time-optimal cruising motion”. Using the parametric method of motion planning, the equations for determining the motions are given. Not only the translation motions of tool-center points, but also the orientation motions of tools are discussed. The time-optimal cruising motion planning is also possible for free paths (PTP motions). A general approach to this problem is proposed too. Keywords. Robot motion planning, path planning, trajectory planning, parametric method, path length, time-optimal, cruising motions, translation of tool-center points, orientation changes of tools, PTP motions, free paths 1. INTRODUCTION Robot motions may be described by the Lagrange’s equation H (q) q + h (q, q) = τ ¨ ˙ (1) where H (q) is the inertia matrix of the robot, the quantity q is the vector of joint displacements: q = (q1 , q2 , ., qn )T The components of the joint displacement of the joint coordinates, h (q,
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