Convex optimization based planning and control methods for space-robotic systems
Creators: name: Misra, Gaurav
Publisher: name: No Publisher Supplied
Year: 2019

description: Space-robotic systems are arguably the most promising technologies available currently for on-orbit satellite operations including docking, berthing, and repair, which have been demonstrated in typically manned and semi-autonomous missions. Another important application of space-robotic systems is space debris mitigation. Space debris are uncooperative space objects (i.e. without any internal actuation) including defunct satellites and spent rocket stages, all of which pose tremendous risk to current operational space assets. Autonomous robotic capture, control, and stabilization of such objects are becoming critical. However, space-robotic operations in proximity of such uncooperative object is challenging with large uncertainties. As a result, optimality, robustness, and tractability constitute some of the desirable properties for any planning and control algorithm used for spacecraft guidance, control, and robotic operations.Through the development of fast interior point methods for solving convex optimization problems with globally optimality, convex programming methods have been proposed and experimentally validated for real-time guidance and control of space systems. However, most current developments have explored solving locally optimal solutions to highly non-linear and constrained optimal control problems in real-time. The issues of robustness, tractability, and global optimality are still open problems.To this end, this thesis investigates robust and optimal planning and control schemes for space-robotics that leverage convex programming. Primarily, four theoretical advances have been made: 1.) Exact reformulation for control of deterministic, nonlinear robotic systems as a convex program; 2.) Sequential, emph{iteratively feasible} convex relaxations leading to locally optimal solutions using difference of convex functions programming; 3.) Hierarchy of convex relaxations of systems formulated exactly or approximated with polynomial dynamics with global optimality certificates and guaranteed convergence; and 4.) Robust controller synthesis for nonlinear polynomial systems using polynomial optimization in the framework of nonlinear disturbance observers for both matched and mismatched uncertainties. For applications, the thesis solves four challenging problems for trajectory planning and control during spacecraft proximity operation. First, quadratic programming based trajectory planning methods are formulated for free-floating space robots. Leveraging tools in analytical mechanics and differential geometry, a novel quadratic programming based trajectory planning scheme is developed for task-constrained end-effector motion which minimizes the base attitude disturbance, in addition to obstacle avoidance for both the unactuated base and manipulator. Second, the orbital station-keeping of spacecraft in the framework of the circular restricted three-body problem is solved using polynomial optimization in a receding horizon setting. Third, robust stabilization and tracking of spacecraft attitude motion in the presence of parametric uncertainties and external disturbances is explored in the framework of convex optimization based nonlinear disturbance observer synthesis. And fourth, an iteratively feasible convex programming based approach is proposed for solving optimal spacecraft guidance problems with non-convex constraints such as obstacle avoidance.