The topic of optimal motion planning for multi-arm robotic manipulators was addressed in several research directions. In regard to the first direction, it was assumed that both arms would have all the necessary degrees-of-freedom (dof) to carry out the task at hand individually. We addressed the problem of optimal trajectory generation for coordinating the motion of two arms which cooperate to perform contact operations, such as deburring. The first arm, which is equipped with a machining tool, operates on a workpiece held and maneuvered continually by a second arm. The two arms move simultaneously relative to each other so that the tool maintains contact with the workpiece as it moves along its prescribed trajectory at a constant speed, while providing the necessary contact force to the workpiece.
The original tool trajectory, normally assigned to a single arm is thus resolved into a pair of conjugate trajectories for the two arms. This resolution process is not unique. The optimization problem was formulated by parameterization of one of the arm’s trajectories in task space using an nth order polynomial. For a chosen polynomial, the second arm’s trajectory was resolved using standard matrix algebra via the utilization of both arms’ kinematic models and the desired tool path on the object. The objective was maximizing the (constant) tool speed along the desired path, thus minimizing motion time. The variables were the 6(n+1) coefficients of the polynomials, where 6 of the coefficients defined the initial configurations of both arms. The optimization was subject to all the kinematic and dynamic constraints of both arms, and a special relationship between the necessary contact force and tool speed along the path.
For the second research direction, it was assumed that two-arm robotic manipulators could be configured optimally through the use of modular components (i.e., actuators, links, etc.). Thus, each arm could individually have one-to-six dof, yielding up to six redundant dof for the overall two-arm manipulator.
This optimization problem was formulated along the lines of the first problem, however herein the common workspace of the two arms becomes restricted as the number of redundant dof is reduced. Thus, a new concept of iso-pose regions was introduced. These regions define the feasible search space for the resolution of the tool trajectory into two conjugate individual robot arm trajectories. The iso-pose regions can be spatial curves, surfaces or complex volumes based on the geometry of the two arms and the desired tool trajectory.
For the third research direction, a multi-robot assembly planning problem, which in essence is a Travelling Salesperson Problem (TSP) type optimization problem, was addressed. However, in this augmented TSP (TSP+), both the “salesperson” (a robot with a tool) as well as the “cities” (another robot with a workpiece) move. Namely, in addition to the sequencing of tasks, further planning is required to choose where the “salesperson” should rendezvous with each “city”. As an example area, the optimization of the electronic-component placement process was investigated. The use of a genetic algorithm was chosen as the search engine for the solution of the TSP+ optimization problem.
The simulation tools developed within the framework of this work were tested on five different component-placement system configurations. In the most generalized configuration, two individual placement robots meet component-delivery systems at optimal rendezvous locations for the pick-up of the components and subsequently meet the PCB (placed on a mobile XY-table) also at optimal rendezvous locations for the placement of the components. In addition to the solution of the component-placement sequencing problem and the rendezvous-point planning problem, the collision-avoidance issue was also addressed.