# Sampling-Based Motion Planning for Free-Floating Space Robot without Inverse Kinematics
## 1 Introduction
The success of this optimization-based approach for robotic motion planning [11; 12; 13] inspired scholars to apply this idea to the motion planning of space robots. [PERSON], [PERSON] et al. [14] studied the motion planning problem of a space robot with task constraints in 2017, and the problem was constructed as a convex quadratic programming problem. Inspired by [PERSON] [PERSON] et al. [11], [PERSON], [PERSON] et al. [15] used convex optimization to develop a motion planning method for a space robot to capture a spin target. This method divides the process of capturing the spin target into the whole system transfer phase and the internal reconstruction phase. Therefore, the whole planning process is divided into two suboptimization problems. However, the aforementioned methods are not aimed at a space robot working in free-floating mode. Due to the advancement of nonlinear optimization technology and the promotion of various open-source optimization tools, regarding robotic motion planning problem as an optimal control problem is receiving more and more attention. However, this method can lead to local minimum results. The last type of method is specially developed for FFSRs and is called the approach based on direct kinematics (ABDK). Polynomials with unknown coefficients are first used to parameterize joint trajectories, and then the initial and final configurations of FFSRs are used to eliminate some unknown coefficients of polynomials. The remaining unknown parameters are finally regarded as parameters to be optimized. The objective function is set as a base attitude disturbance at the final time, and the motion planning problem is converted into a nonlinear optimization problem. The nonlinear optimization problem can be solved using particle swarm optimization [16], genetic algorithm [17], differential evolution algorithm [18], and other metaheuristic algorithms. Optimization-based approach for robotic motion planning (OPMP), such as CHOMP (covariant Hamiltonian optimization for motion planning) [12] and STOMP (stochastic trajectory optimization for motion planning) [13], also convert motion planning problems into nonlinear optimization problems, but they are different from ABDK. The trajectory is discretized into N-1 segments in OPMP, and then positions of N discrete points are selected as the variables to be optimized. Therefore, the trajectory shape is easy to be controlled by optimizing N discrete points, and the no-collisions constraint is also easily formulated. Finally, in OPMP, the optimization problem is solved using fast convergence optimization methods based on gradient or the Hessian matrix. In ABDK for FFSRs, the trajectory is parameterized, with only the initial and final configurations, so the trajectory shape cannot be controlled. Finally, ABDK for FFSRs does not consider obstacle avoidance, so the researchers who use this method do not consider whether the initial configuration and the target configuration are in the same connected domain. Sampling-based motion planners (SBMPs) can efficiently solve the motion planning problem for robots with high degrees-of-freedom (DOF), and local minima can also be avoided in SBMPs. Among existing SBMPs, rapidly exploring random trees (RRTs) are especially suitable for motion planning with differential constraints. Basic RRTs usually take the initial configuration and the goal configuration as input to construct a tree data structure. The initial configuration is selected as the root node, and the goal configuration is used as a heuristic. The tree is grown in the iterative process, and local planning is performed from one selected node of the tree in each iteration; we call this node a node to be extended. During the process of local planning, a guiding point is used to guide the growth of the tree. The guiding point can be a randomly selected configuration or the goal configuration. Goal configuration guiding growth ensures the rapid convergence of the algorithm, while random guiding growth prevents the algorithm from falling into a local minimum.