AN ALGEBRAIC APPROACH TO COLLISION-AVOIDANCE TRAJECTORY PLANNING FOR DUAL-ROBOT SYSTEMS - FORMULATION AND OPTIMIZATION

Abstract

Collision-Avoidance is a key issue in planning trajectories for dual robots whose workspaces overlap. In this paper, we develop a new trajectory planning method by proposing a traffic control schemes. The traffic controller determines the next positions for each robot based on the motion priority and path direction subject to the collision-avoidance conditions and the robots' physical limits. The problem of determining the next positions is formulated and optimized. Algebraic expressions for collision avoidance between every-pair of links - one from the first robot and the other from the second robot - are derived in configuration space. These algebraic expressions are then used to solve the problem of determining "optimal" (in the sense of path direction and motion priority) robots' trajectories. A solution procedure is developed using a nonlinear programming (NLP) solver. The main advantage of our approach is that the two robots' trajectories can be determined simultaneously without requiring any a priori path information. Several numerical examples are presented to demonstrate the validity and effectiveness of the proposed approach.