Optimum Trajectory Planning for Redundant and Hyper-redundant Manipulators through Inverse Dynamics

نویسندگان

  • Kagan K. Ayten
  • M. Necip Sahinkaya
  • P. Iravani
چکیده

This paper presents a method to develop minimum energy trajectories for redundant/hyper-redundant manipulators with pre-defined kinematic and dynamic constraints. The optimal trajectory planning uses fifth order B-spline functions to represent the Cartesian coordinates of the end-effector and angles of the redundant links. The actuator torques are considered for the formulation of the cost function. Calculation of the cost function is carried out by using an inverse dynamic analysis. The system constraints are handled within the cost function to avoid running the inverse dynamics when the constratints are not satisfied. A novel virtual link concept is introduced to replace all the redundant links to eliminate physicaly impossible configurations before running the inverse dynamic model. The process is applicable to hyper redundant manipulators with large number of links. The proposed scheme is verified with computer simulations based on a 5-link planar redundant manipulator. INTRODUCTION A manipulator may have more control inputs than required in order to control a desired motion. This is called redundancy, where more degrees-of-freedom are needed than necessary in a working space [1]. Redundancy offers high degree of manipu∗Address all correspondence to this author. lability during the implementation of the motion of the end effectors, and beneficial for specific task such as avoiding collision with obstacles, avoiding singularities, optimization of some cost function. Usually, inverse kinematic solution of non-redundant manipulators offer minimal numerical complexity. When a manipulator has redundancy, it has the capability of moving the joints in infinite ways for the same specified end effector motion. Therefore, despite their important features, inverse kinematic solutions and control of redundant/hyper-redundant manipulators become more and more complicated and trajectory planning problem also become increasingly difficult with each added redundant degreeof-freedom [2]. Most of the work that has been done for redundant/hyperredundant manipulators so far focused on finding a smooth path consisting of points close enough to each other in order to avoid infinite number of kinematic solution [3,4]. In some applications, the redundancy can also be used to satisfy other performance criterion such as avoiding collision with obstacles [1, 5–8], avoiding singularities where the manipulator lose some degrees-offreedom [9]. Most of the research on redundant/hyper-redundant manipulators concentrate on effective path following algorithms to avoid obstacles for large number of links. The trajectory planning problem for redundant/hyperredundant manipulators is also considered to be an optimization 1 Copyright c ⃝ 2011 by ASME Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference

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تاریخ انتشار 2011