# Multitask-Based Trajectory Planning for Redundant Space Robotics Using Improved Genetic Algorithm
## 1 Introduction
As a matter of fact, the MTTP for industrial robotics has been widely studied for its high productivity and low cost [18; 19], and two categories of approaches were developed. For simplicity, the location of each task is usually considered to be a waypoint, which is also followed. One category of approaches aims at directly solving the MTTP. In [20], the MTTP is studied using the branch-and-bound method, where multiple inverse kinematic solutions of the robotic system are not considered. The branch-and-bound method aims at searching for solutions to solve optimization problems with constraints, where the feasible solution space is finite. In [21], the MTTP is transformed into a mixed-integer nonlinear programming problem, where a solver is developed to improve calculation speed. The approach developed in [21] works well with a relatively small number of waypoints. In [22], an improved genetic algorithm (IGA) was developed where each chromosome consists of two parts. The first part represents the waypoint sequence, while the second part represents the sequence of the joint configurations at the waypoints, which corresponds to the first part. In [23], each chromosome consists of three parts, the waypoint sequence, the sequence of joint configurations, and the robot placement. The technique of dividing each chromosome into several parts was also employed in [24; 25; 26]. A common point of IGAs in [22; 23; 24; 25; 26] is that the parameter denoting the joint angular velocity is predefined as a constant. The other category of approaches aims at dividing MTTP into several subproblems which are then solved successively. In [27; 28], MTTP is divided into two subproblems, the problem of the waypoint sequence, and the problem of joint trajectories. In [27], Tabu search was employed to optimize the waypoint sequence, after which joint trajectories were derived according to the inverse kinematics of industrial robotics. The Tabu search algorithm, a meta-heuristic algorithm, searches for the global optimal solution by constructing a Tabu table with the functions of cycling and memory. In [28], an improved lazy algorithm, according to the direct kinematics of industrial robotics, was developed to optimize the joint trajectories. Among MTTP documents for industrial robotics, manipulators are nonredundant, meaning that a point in the task space corresponds with finite points in the joint space. However, the redundant robot [29] provides the manipulator with high dexterity, contributing to the solution of problems such as obstacle avoidance, singularity avoidance, and joint limits. Unlike ground environments [30; 31], there is microgravity in outer-space environments. Moreover, for FFSR2, strong coupling between manipulator and free-floating base is usually generated during a maneuver. Therefore, the aforementioned approaches, which were developed to solve MTTP for nonredundant industrial robotics, cannot be directly employed to solve MTTP for redundant space robotics. In some cases, an urgent task should be performed in ISS, while the functional completeness of ISS should be guaranteed in advance. Component maintenance, assembly, and refueling of ISS should be finished successively, contributing to the functional completeness of ISS before performing the urgent task. Finishing a series of tasks successively also contributes to saving energy in outer space. Therefore, The MTTP for redundant space robotics is studied. In the MTTP, the location of each task is simplified as a task point, called waypoint. The position and attitude of each waypoint are predefined in the Cartesian space. First, the end effector is required to visit the waypoints with minimum time, thus the sequential order of visiting the waypoints should be optimized. Second, the joint configuration corresponding to each waypoint should be optimized, thus the feasible joint movements between adjacent waypoints can be guaranteed. Third, the joint movements should meet the predefined constraints.