System and method suitable for controlling operations of a spacecraft based on an isoperimetric reformulation of constraints

A method for controlling an operation of a vehicle subject to constraints based on continuously parametrized sets (CPS), comprising:

• determining a trajectory for the vehicle using an isoperimetric reformulation of the constraints based on the CPS, wherein the trajectory is iteratively updated with successive approximations of the CPS using linearized dynamics of the vehicle corresponding to a current trajectory iterate, wherein the CPS are robust controllability sets (RCS) that are continuously parametrized by propagation time for trajectory horizon (t) and safety horizon (τ), and wherein the isoperimetric reformulation presents constraints based on the RCS as a double integral over the trajectory horizon and the safety horizon of a distance between the vehicle and a keep-away zone and reformulates the double integral as a boundary value problem over the trajectory horizon;
• and
• controlling the vehicle according to the trajectory.

A non-transitory computer-readable storage medium embodied thereon a program executable by a processor for performing a method for controlling an operation of a vehicle subject to constraints based on continuously parametrized sets (CPS), the method comprising:

• determining a trajectory for the vehicle using an isoperimetric reformulation of the constraints based on the CPS, wherein the trajectory is iteratively updated with successive approximations of the CPS using linearized dynamics of the vehicle corresponding to a current trajectory iterate, wherein the CPS are robust controllability sets (RCS) that are continuously parametrized by propagation time for trajectory horizon (t) and safety horizon (τ), and wherein the isoperimetric reformulation presents constraints based on the RCS as a double integral over the trajectory horizon and the safety horizon of a distance between the vehicle and a keep-away zone and reformulates the double integral as a boundary value problem over the trajectory horizon;
• and
• controlling the vehicle according to the trajectory.