Trajectory Planning of a Constrained Flexible Manipulator

Many of today’s flexible robots are required to perform tasks that can be considered as constrained motions. A robot is considered to be in constrained maneuvering when its end-effector contacts and/or interacts with the environment as the robot moves. These applications include grinding, deburring, cutting, polishing, and the list continues. For the last two decades many researchers have investigated the constrained motion problem through different techniques such as hybrid position/force control (Raibert, M. & Craig, J., 1981 and Shutter et al., 1996), force control (Su, et al., 1990) , nonlinear modified CorlessLeitman controller (Hu, F. & Ulsoy, G., 1994), two-time scale force position control (Rocco, P. & Book, W., 1996), multi-variable controller (Shi, et al., 1990), parallel force and position control (Siciliano & Villani, L.,2000) , and multi-time-scale fuzzy logic controller (Lin, J., 2003). Luca et al. (Luca, D. & Giovanni, G., 2001) introduced rest-to-rest motion of a twolink robot with a flexible forearm. The basic idea is to design a set of two outputs with respect to which the system has no zero dynamics. Ata and Habib have investigated the open loop performance of a constrained flexible manipulator in contact with a rotary surface (Ata, A. & Habib, J., 2004) and arbitrary shaped fixed surfaces (Ata, A. & Habib, J., 2004). The effect of the contact force on the required joint torques has been simulated for different contact surfaces. Despite the voluminous research done, the study of dynamics and control of the constrained motion of the flexible manipulators remains open for further investigations. The present study aims at investigating the dynamic performance of a constrained rigid/flexible manipulator. The Cartesian path of the end-effector is to be converted into joint trajectories at intermediate points (knots). The trajectory segments between knots are then interpolated by cubic-splines to ensure the smoothness of the trajectory for each joint. To avoid separation between the end-effector and the constraint surface and to minimize the contact surface as well, these knots are chosen at the contact surface itself. Simulation results have been carried out for three contact surfaces.