Time scaling of cooperative multirobot trajectories

Abstract

In this paper we develop an algorithm to modify the trajectories of multiple robots in cooperative manipulation. If a given trajectory results in joint torques which exceed the admissible torque range for one or more joints, the algorithm slows down or speeds up the trajectory so as to maintain all the torques within the admissible boundary. Our trajectory modification algorithm uses the concept of time scaling developed by Hollerbach[10] for single robots. A multiple robot system in cooperative manipulation has significantly different dynamics compared to single robot dynamics. As a result, time scaling algorithm for single robots is not usable with multi-robot system. The trajectory scaling schemes described in this paper requires the use of linear programming techniques and is designed to accommodate the internal force constraints and payload distribution strategies. As the multi-robot system is usually redundantly actuated, the actuator torques may be found from the quadratic minimization which has the effect of lowering energy consumption for the trajectory. A scheme for generating a robust multi-robot trajectories when the carried load mass and inertia matrix are unknown but vary within a certain range is also described in this paper. Several examples are given to show the effectiveness o f our multi-robot trajectory sealing scheme.

Motion Planning for Multiple Mobile Robots Using Time-Scaling

“…The scaled velocity can be generated by multiplying the original velocity function and the derivative of the time-scaling function (see (6)). It is only necessary to calculate the values of the new velocity in those real-time instants where parameters in the original velocity have changed and where the time-scaling function changes its nature.…”

“…The time-plane is the space spanned by the virtual and global time parameters. If a collision is possible between two units according to the path geometries (so that they intersect each other), the collision to be avoided can be converted into a so called static timeobstacle in the time-plane [5,6]. A mapping avoiding the static time-obstacles shall be used to define the time-scaling of the path of the current unit.…”

Intelligent systems:

“…The simplified case of the optimality is related to the requirement of cooperation. In [505] [415]) then for a two-arm manipulator system the solution of the problem is described in [506]. The need for exhaustive search can be avoided by using multiple heuristic rules, which check interference between different subsystems of the manipulator, and apply the collision-avoidance strategy of planning incrementally [507] [509].…”

Robot Control Using On-Line Modification of Reference Trajectories

“…However, this method assumes that the robot dynamics is perfectly known and robustness issues were not considered. It is noteworthy that this approach has been extended to the cases of multiple robots in cooperative tasks (Moon & Ahmad, 1991) and robot manipulators with elastic joints (De Luca & Farina, 2002). In order to tackle the drawback of the assumption that the robot model in exactly known, Dahl and Nielsen (1990) proposed a control algorithm that result in the tracking of a time-scaled trajectory obtained from a specified geometric path and a modified on-line velocity profile.…”