Algorithm for Planning the Trajectory of Manipulators in a Multidimensional Joint Space

The paper presents an algorithm for planning the trajectory of manipulators taking into account obstacles. The problem of forming a hypersurface of constraints on the robot’s motion is stated. The formation is performed both in the space of output (end-effector) and in the space of generalized (joint) coordinates of the robot. Constraints in the space of end-effector coordinates are introduced to exclude interference of robot links with external objects, while constraints in the space of joint coordinates are associated with the ranges of permissible values of the joint coordinates, justified by the design features of the robot’s drive elements. Using the recursion principle made it possible to form a hypersurface of constraints in spaces of different dimensions, which justifies the applicability of the algorithms for robots with different numbers of drives. The algorithm consists in planning the trajectory and its subsequent correction in case of detecting an obstacle on the robot’s path.