Robot trajectory optimisation with dynamic constraints

Objects located within a robot arm workspace fragment this space, since a path obstructed by an object is non-viable. Point-to-point motion of a robot arm in such a fragmented workspace has to be carefully planned in order to avoid collision. The problem of planning the trajectory of the robot arm can be represented as a constrained optimisation problem from which an optimal time can be deduced.The solution of the optimisation problem for an optimal continuous trajectory is complex and costly. However, a motion strategy, whereby the robot arm path is formed of single linear segments, renders the optimisation problem solvable and produces a sub-optimal but practical trajectory.This paper describes a motion strategy that is based on the concept of defining via intermediate and control points which the robot arm has to pass by along its path, and takes into consideration the torque limitation of the different axis drives. Joint motion planning is based on a function of time approximated by a sequence of polynomials with boundary conditions that would result in continuous motion at the via points. Motion between each two points is divided into two transition zones and a constant speed zone in between. A result is obtained by selecting polynomial coefficients that would minimise, subject to the constraints of the robot dynamics, the time required to accelerate and decelerate the joint to the appropriate speeds at the boundary of these zones. The joint is allowed to move at the maximum speed for the remainder of the time.