Smooth transition for collision avoidance of redundant robots: An on-line polynomial approach

The presence of cooperation between robots and machines in the industrial environment improved the solution for several manufacturing problems. With cooperation, new challenges emerged, and among these stands out the collision avoidance between such robots and machines. Collision avoidance can be dealt with in several ways, taking into account the computational effort to make a decision and the quality of the calculated trajectory for the robots, evaluated, for instance, by smooth profiles avoiding sudden variations in joints’ velocities or acceleration. In these circumstances, the involved robots need to be redundant since new movements are necessary for avoiding collisions. The strategies for collision avoidance are offline (i.e., based on pre-programming the task), or online (i.e., implemented while the robot performs the main task). In online collision avoidance strategies, numerical performance must ensure the time requirements of the main task performed by the robot; so, numerically efficient solutions are the most appropriate. This paper presents a proposal for the collision avoidance treatment from fixed obstacles for redundant robots, based on polynomial functions. The proposed solution allows achieving smooth trajectories according to criteria based on the continuity of derivatives in trajectory curve transitions. When the robot is out of the imminent collision, it is proposed to solve the inverse kinematics through the Adaptive Extended Jacobians. Throughout the text, the mathematical developments based on polynomials are presented, and in the end, a case study graphically shows comparative results.