Time-optimal Trajectory Generation Research Articles

Time-Optimal Trajectory Generation for Machine Tool Feed Drives and Implementation by Contouring Control

Time-optimal trajectory planning for mechanical systems has been widely studied thus far because of its effectiveness to reduce the time required for many industrial tasks. However, in general, because the time-optimal trajectory is generated based on ideal dynamics of controlled systems, it may be difficult to implement the obtained trajectory to actual systems with vibration mode that is neglected in the trajectory generation. In other words, high-speed motion based on the time-optimal trajectory may cause the vibration of the real system. Hence, in this paper, we propose to employ the contouring control developed by the authors, which enables to reduce controller gain magnitudes while contouring performance are maintained. First, this paper presents a method of generating the time-optimal trajectory for machine tool feed drives. The presented method considers viscous friction that is significant in high-speed motion of mechanical systems and has an advantage that the number of variables required for the optimization is reduced compared to the conventional method. Next, the contouring controller is applied to implement the time-optimal trajectory to an actual machine tool system. The effectiveness of the proposed method and the contouring controller is demonstrated by comparative experiments with the conventional method.

An efficient processor-based online generation of time-optimal trajectories

We present a novel method to online generation of time-optimal acceleration, velocity, and position trajectory values for servo-control systems using low-cost fixed-point processors with no on-chip multipliers. As in the case of many product designs, reducing system cost is a key constraint in our method. We address this constraint by optimizing required memory size, computational time, and introducing multiplication-free recursive algorithms most suitable for real-time implementation on low-cost microcontrollers. An efficient search algorithm is presented optimizing the trajectories with respect to total move time for any distance subject to physical constraints of the system. We also introduce a normalized set of first-order difference equations using only integer arithmetic and additions to compute the trajectory values. Complexity of the proposed method is compared with multiplication-based and lookup table methods using three popular microcontrollers with and without an on-chip hardware multiplier

Optimization of Trajectories for Industrial Robots Using Mathematica

In this paper a practical method for the generation of time-optimal trajectories for industrial robots is presented. It is assumed that an industrial robot is programmed through instructions at effector level. The parameters which may then be optimized are specified degrees of freedom affixed to the acquired frames. Optimization may then be obtained through an off-line programming aid. the optimized values being then transmitted directly to the control panel. The control schemes and the optimization Are emulated through Mathematica in order to test examples on an industrial robot.