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.