Development of Task-Space Nonholonomic Motion Planning Algorithm Based on Lie-Algebraic Method

In this paper, a Lie-algebraic nonholonomic motion planning technique, originally designed to work in a configuration space, was extended to plan a motion within a task-space resulting from an output function considered. In both planning spaces, a generalized Campbell–Baker–Hausdorff–Dynkin formula was utilized to transform a motion planning into an inverse kinematic task known for serial manipulators. A complete, general-purpose Lie-algebraic algorithm is provided for a local motion planning of nonholonomic systems with or without output functions. Similarities and differences in motion planning within configuration and task spaces were highlighted. It appears that motion planning in a task-space can simplify a planning task and also gives an opportunity to optimize a motion of nonholonomic systems. Unfortunately, in this planning there is no way to avoid working in a configuration space. The auxiliary objective of the paper is to verify, through simulations, an impact of initial parameters on the efficiency of the planning algorithm, and to provide some hints on how to set the parameters correctly.

Nonholonomic motion planning for minimizing base disturbances of space manipulators based on multi-swarm PSO

SUMMARYBecause space manipulators must satisfy the law of conservation of momentum, any motion of a manipulator within a space-manipulator system disturbs the position and attitude of its free-floating base. In this study, the authors have designed a multi-swarm particle swarm optimization (PSO) algorithm to address the motion planning problem and so minimize base disturbances for 6-DOF space manipulators. First, the equation of kinematics for space manipulators in the form of a generalized Jacobian matrix (GJM) is introduced. Second, sinusoidal and polynomial functions are used to parameterize joint motion, and a quaternion representation is used to represent the attitude of the base. Moreover, by transforming the planning problem into an optimization problem, the objective function is analyzed and the proposed algorithm explained in detail. Finally, numerical simulation results are used to verify the validity of the proposed algorithm.