Mechanical work reduction during manipulation tasks of a planar 3-DOF manipulator
Keywords:planar 3-DOF manipulator,, manipulation task, mechanical work reduction, maximum torque
The problem addressed in this paper concerns a planar 3-DOF manipulator operating in horizontal plane, that must move from an initial position characterized by angles theta1(0), theta2(0) and theta3(0) to a required final position characterized by angles theta1(TF), theta2(TF) and theta3(TF). The manipulator can follow any trajectory from the initial to the final position, the goal being to reduce as much as possible the overall mechanical work of this manipulation task in horizontal plane. The approach here is not an optimal theory one, so that to find the global minimum of the overall mechanical work function. Our proposal is just a simple engineering method to reduce the overall mechanical work, trying several possibilities of simple methods of trajectory generation: (1) variations of thetai parameters corresponding to constant accelerations a+i from t0 = 0 to t1/2 = TF /2, followed by constant decelerations a-i =-a+i from t1/2 = TF /2 to TF ; (2) variations/ evolutions of thetai parameters having the form of cosine functions; (3) evolutions of thetai parameters corresponding to straight line variations, but using smooth departures at t0 and smooth arrivals at TF , with limitations concerning the departure accelerations and arrival decelerations; (4) considering the evolutions of angles theta1(t), theta2(t) and theta3(t) between the initial time t0 = 0 and the final time TF , as linear segments between t0 = 0 and t1/2 = TF /2 on one hand, and as other linear segments between t1/2 = TF/2 and TF on the other hand. In this fourth case of trajectory, smooth departures, arrivals and transitions from one straight linear segment to another were also considered, thus limiting the maximum torques in the actuators. The results are interesting from an engineering point of view: a non-optimal minimization of the overall mechanical work is analyzed. From the point of view of protecting the actuators and thus increasing their lifetime, a second important criterion was also taken into account: the maximum torques were compared for the four possibilities of trajectories considered here. Further work will find the optimal solution of this manipulation problem, which will better evaluate the performance of the method proposed in this paper for mechanical work and maximum torque reduction.
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