Development and Optimization of a Rendezvous Manoeuvre for Robotic Facility Testing & Validation

Optimization of space maneuvers is becoming a key requirement for the evolution of the space market and paves the way towards new investigation scenarios: the purpose of this work is to optimize rendezvous maneuvers in the context of in-space logistics services, such as in-orbit maintenance, propellant depot and refueling, considering the spacecraft trajectory and the dispatching of the limited available resources. The aim is to plant more cost-effective, sustainable and performing missions, with the implementation of the optimized guidance algorithms. The optimized maneuver has been simulated online through Hardware-In-the-Loop (HIL) testing, to investigate the feasibility and robustness of the optimization problem, replicating the 6 degree-of-freedom motion of the spacecraft (in the context of rendezvous maneuvers, the so called “chaser”), through a cooperative robotic arm. In order to execute properly the simulations, the work envelope of the manipulator has been investigated, to overcome the issues related to the replication of a trajectory optimized for a spacecraft with a tool subjected to limitations over its maximum extension and to the risk of reaching singular configurations. From the point of view of the guidance of the chaser, the optimization strategy that has been applied is based on a Model Predictive Control (MPC) scheme, due to its capability of adjusting control inputs in real-time to respond to variations in the system's behaviour, adaptability (making it suitable for real-time implementations) and sensitivity to system's dynamics. The optimization problem has been formulated and solved in Matlab exploiting a toolbox developed in-house by SENER Aeroespacial, SENER Optimization Toolbox (SOTB), powered by an Interior-Point Method solver. For what concerns the control allocation and the optimization of the resources available on the spacecraft, such as fuel consumption, the problem has been optimized formulating a Quadratic Programming (QP) and developing an Active Set Method (ASM) based solver in Matlab. For the peculiar case of control allocation problems, the ASM provides rapid convergence when a warm start of the active set is provided and smooth transitions between consecutive optimizations, minimizing changing in control inputs and maintaining system stability. The designed solver doesn't recall any predefined Matlab function, and has been robustified to handle ill-conditioned Hessian matrices of the QP, exploiting Singular Value Decomposition. The accuracy of the ASM has been assessed with the applications to five different formulations of the problem under analysis, aiming at minimizing the error between the control actions generated by the actuators and the values of force and torque required to complete the optimized trajectory. In addition, the ASM has been evaluated on its capability to distribute homogeneously the control actions between the actuators. Finally, the optimal solution found with the ASM has been compared to the force and torque values commanded by the control loop of the robotic facility, while the correspondent execution time have been compared with SOTB, with the objective of verifying the applicability of the solver to online optimization of the control allocation problem and integration in the HIL simulation facility.