State dependent model predictive control for orbital rendezvous using pulse-width pulse-frequency modulated thrusters

• A scheme of PWPF based SDMPC is proposed in ARPO using on-off thrusters.
• The resulting optimal control problem is formulated into a series of constrained quadratic programming problems and solved at sampling instants.
• The effectiveness of the newly proposed integration of SDMPC and PWPF modulation is proved to be more energy efficient.

This paper studies the pulse-width pulse-frequency modulation based trajectory planning for orbital rendezvous and proximity maneuvering near a non-cooperative spacecraft in an elliptical orbit. The problem is formulated by converting the continuous control input, output from the state dependent model predictive control, into a sequence of pulses of constant magnitude by controlling firing frequency and duration of constant-magnitude thrusters. The state dependent model predictive control is derived by minimizing the control error of states and control roughness of control input for a safe, smooth and fuel efficient approaching trajectory. The resulting nonlinear programming problem is converted into a series of quadratic programming problem and solved by numerical iteration using the receding horizon strategy. The numerical results show that the proposed state dependent model predictive control with the pulse-width pulse-frequency modulation is able to effectively generate optimized trajectories using equivalent control pulses for the proximity maneuvering with less energy consumption.