# Multitask-Based Trajectory Planning for Redundant Space Robotics Using Improved Genetic Algorithm
## 1 Introduction  
Space robotics are now increasingly employed in outer space for various tasks, such as the assembly and maintenance of the International Space Station (ISS) [1], and Lunar Base construction [2]. Examples of space robotics include the Japanese Experiment Module Remote Manipulator System (JEMRMS) of the Japan Aerospace Exploration Agency (JAXA) [3] and the Canadarm 2 of MacDonald Dettwiler and Associates Ltd. (MDA) [4], while examples of performing tasks include the Experimental Test Satellite VII (EST-VII) [5] and the Robot Technology Experiment [6]. The free-flying space robot (FFSR1) and the free-floating space robot (FFSR2) are two main types of space robotics. The base attitude of FFSR1 is controlled, contributing to establishing a good connection between the ground and the base spacecraft. This is because the attitude of the base spacecraft should be well-managed when sending signals to, or receiving signals from, the ground. The base spacecraft of FFSR2 is in free-floating mode, contributing to saving energy, which is part of the superiority of FFSR2 since energy is precious in outer-space environments. The trajectory planning for space robotics, aiming at generating the time histories of joints (or end effector) and contributing to the desired motion of robots, attracts extensive attention from both scientists and practitioners. The study of trajectory planning is essential for robots before physical manipulation and has been well developed. A primary trajectory-planning approach is based on the inverse kinematics of space robotics. Concepts such as the generalized Jacobian matrix [7], the enhanced disturbance map [8], the path independent workspace [9] and the reaction null-space [10] have been successively proposed for trajectory planning. The disadvantage of this approach is that it leads to kinematic singularity in some cases. Aiming at avoiding this kinematic singularity, an approach based on the direct kinematics of space robotics has been well-received. To begin with, mathematical functions such as the polynomial, trigonometric [11], or the Bezier function [12] are employed to depictthe joint trajectories. Then, according to predefined conditions, mathematical functions are depicted with a set of unknown coefficients. In the aforementioned mathematical functions, the polynomial function denotes the combination of constants and variables with limited addition and multiplication calculations, the trigonometric function is an elementary function with variables of angles, and the Bezier function contributes to the derivation of a smooth curve based on four random points. Next, the trajectory-planning problem is converted into a parameter-optimization problem, with the objective function of minimum maneuver time or maximum manipulability of the robotic system, or minimum attitude disturbance acting on the free-floating base spacecraft during the robotic maneuver. Finally, the unknown coefficients are optimized by the optimization algorithms, including the basic heuristic algorithms such as the particle-swarm optimization algorithm (PSO) [13] and genetic algorithm (GA) [14; 15], and the improved optimization algorithms such as hybrid PSO [16] and the constrained differential evolution algorithm (DE) [17]. In the aforementioned algorithms, the PSO is a random search algorithm based on group collaboration, more specifically, simulating the foraging behavior of a flock of birds. The DE, based on population, is a self-adaptive optimization algorithm with global search capability. To the authors' knowledge, the approaches mentioned above aim at solving the point-to-point trajectory-planning problem, meaning that the space robot executes one task in each travel. If the robot executes two or more tasks in each travel, it could save much energy. Maneuvering time would also be reduced, which is a significant advantage in an emergency. Therefore, it is meaningful to study the multitask-based trajectory-planning problem (MTTP) for space robotics.