Robust finite-time control approach for spacecraft rendezvous and formation reconfiguration in Earth orbits

In response to the need for a reliable and robust strategy that ensures finite-time convergence of the spacecraft’s relative attitude and orbital state during critical missions, such as rendezvous and docking, this paper proposes a new Finite-Time Control (FTC) approach. First, a nonlinear feedback control is introduced and analyzed through the Lyapunov method. Thereafter, by introducing the technique of “variation of parameters” to solve the resulting Lyapunov differential equation, the necessary conditions for finite time convergence are derived, resulting in a new strategy that transforms the problem of designing an FTC into determining a positive and differentiable function that diverges as time approaches to any predefined finite/fixed time, and converges to zero at considered initial time. The stability, convergence, robustness, and effectiveness of this new FTC approach are demonstrated through a comparative analysis with the asymptotic stability demonstration methods. Four candidate functions that satisfy the proposed finite-time stability criteria are further studied. Demonstrating that this new approach encompasses the advantages of Lyapunov-based and time transformation-based FTC approaches. This approach improves upon existing FTC methods in terms of simplicity, exponential convergence, and independence from the plant’s nature and initial state. The simulation results corroborate that this approach drives the system to the reference state within any predefined finite-time constraint, indicating the potential applications of these research findings in space exploration. Moreover, the approach is developed based on a general description of a perturbed nonlinear dynamic plant, which suggests that these findings are not limited to spacecraft relative motion control and are therefore applicable to any control problem with finite-time constraints.