Trajectory Planning Based on Screw Theory with Consideration of the Optimal Berth Position for a Space Robot

摘要

Trajectory planning is a prerequisite for the tracking control of a free-floating space robot. There are usually multiple planning objectives, such as the pose of the end-effector and the base attitude. In efforts to achieve these goals, joint variables are often taken as exclusive operable parameters, while the berth position is neglected. This paper provides a novel trajectory planning strategy that considers the berth position by applying screw theory and an optimization method. First, kinematic equations at the position level are established on the basis of the product of exponential formula and the conservation of the linear momentum of the system. Then, generalized Jacobian matrices of the base and end-effector are derived separately. According to the differential relationship, an ordinary differential equation for the base attitude is established, and it is solved by the modified Euler method. With these sufficient and necessary preconditions, a parametric optimization strategy is proposed for two trajectory planning cases: zero attitude disturbance and attitude adjustment of the base. First, the berth position is transformed into the desired position of the end-effector, and its constraints are described. Joint variables are parameterized using a sinusoidal function combined with a five-order polynomial function. Then, objective functions are constructed. Finally, a genetic algorithm with a modified mutation operator is used to solve this optimization problem. The optimal berth position and optimized trajectory are obtained synchronously. The simulation of a planar dual-link space robot demonstrates that the proposed strategy is feasible, concise, and efficient.