Adaptive Control and Estimation of the Center of Mass of a 5-degree-of-freedom Spacecraft Testbed

In space applications, on-ground experimentation is an essential step in control algorithm validation before real mission application. However, on-ground conditions greatly differ from space ones, where satellites operate under extremely low gravity and friction conditions. A common way to simulate these conditions is with air-bearing-based testbeds. These testbeds reduce friction significantly to almost space-like conditions. Air-bearing technology can provide virtually frictionless translational and rotational motion. However, when frictionless rotational motion is achieved, the testbed becomes highly sensible gravity torque. This external torque is produced by the offset between the predetermined geometrical center of rotation (CoR) and the center of mass (CoM) of the testbed, which makes the system behave like a three-dimensional pendulum. Testbeds with rotational degrees of freedom must be designed to minimize this offset. However, manufacturing and assembly precision is limited, usually leading to a residual gravity torque that needs to be compensated for to obtain space-like conditions. The testbeds are designed to include sliding masses in the assembly, usually as stepper motors that can be commanded to a desired position to compensate the CoM to CoR offset. However, this offset is usually unknown, requiring an estimation process before offset compensation. The literature shows various methods that can be used to estimate the unknown offset, such as batch estimation methods, filtering techniques, and active control techniques. However, all these methods present either one of the following problems. On the one hand, methods that allow the estimate of all three components of the offset vector at the same time require the use of actuators such as thrusters or momentum exchange devices. On the other hand, those methods that utilize the sliding masses as the only source of control input lead to an under-actuated system and fail to estimate all three components of the offset vector. This work presents a novel reference model adaptive estimation and control law that ensures the estimation of all three components of the offset vector while taking into consideration a time-varying moment of inertia of a 5-degree-of-freedom (DOF) testbed. A reference model is designed to obtain a control law that ensures the control input can be obtained from moving mass control (MMC) only. The controller and estimation laws are demonstrated to produce asymptotic convergence of the error between system and desired states and asymptotic convergence of the estimation error to zero. Lyapunov stability theory concludes that the system's desired equilibrium point is stable, and Barbalat's Lemma is utilized to extend the conclusion to the asymptotic stability of the desired equilibrium point. The control is validated in a numerical simulation environment using a Runge-Kutta fourth-order integrator. The results display asymptotic stability of the system states and estimation errors, validating the results obtained in the stability proof.