Spacecraft Attitude Control with Nonconvex Constraints: An Explicit Reference Governor Approach

TL;DR

This work tackles constrained spacecraft attitude control under actuator saturation and exclusion-cone constraints by deploying an Explicit Reference Governor (ERG) with a two-layer design. The control layer pre-stabilizes the plant using $\tau = -k_P \tilde{q}_I - k_D \omega$, while the navigation layer updates the auxiliary reference via $\dot{v}=\Delta(\tilde{q},\omega)\rho(v,r)$ to enforce constraints without online optimization. Key contributions include a quaternion-specific ERG construction with a dynamic safety margin based on Nagumo-like arguments, a destabilization term to remove saddle points, and formal proofs of forward invariance and global asymptotic stability to $r$ for admissible references. Numerical simulations illustrate fast responses under actuator saturation and successful constraint satisfaction even with multiple exclusion cones, demonstrating practical viability for onboard implementation.

Abstract

This paper introduces a novel attitude controller for spacecraft subject to actuator saturation and multiple exclusion cone constraints. The proposed solution relies on a two-layer approach where the first layer prestabilizes the system dynamics whereas the second layer enforces constraint satisfaction by suitably manipulating the reference of the prestabilized system. In particular, constraint satisfaction is guaranteed by taking advantage of set invariance properties, whereas asymptotic convergence is achieved by implementing a non-conservative navigation field which is devoid of undesired stagnation points. Multiple numerical examples illustrate the good behavior of the proposed scheme.

Figures (7)

• Figure 1: Qualitative representation of the invariant set \ref{['eq:ActInvSet']}, shown in cyan. The set boundaries are $\|\tau\|=\tau_{\max}$, in red, and $V=\Gamma_a$, in black. The invariance of the set can be deduced from the fact that the system trajectories point inward, thus satisfying the Nagumo theorem blanchini. For the sake of comparison, the invariant set obtained by solving \ref{['eq:ActGamma_No']} is reported in green; it is smaller and hence a dynamic safety margin based on it will lead to more conservative performance.
• Figure 2: Qualitative representation in $\mathbb{R}^2$ of the exclusion cone constraint and the various components in the navigation field \ref{['eq:NavigationField']}. The red circle identifies the constraint boundary \ref{['eq:ExclusionCone']}. The blue dotted line is the boundary of \ref{['eq:Unaffected']}, which depends on the influence margin $\zeta$. The black dashed line is the boundary of \ref{['eq:SSAdmissible']}, which depends on the static safety margin $\delta$. Within the influence region, $\rho_r$ is a term that points from $v$ to $r$, $\rho_e$ is a term that points away from the center of the exclusion cone constraint, and $\rho_d$ is a term that is always tangent to the constraint and does not increase the distance between $v$ and $r$. By construction, $\rho_d$ and $\rho_e$ are zero outside the influence margin $\zeta$ and have a modulus of one whenever the angular distance between $v$ and $r$ is equal to the static safety margin $\delta$.
• Figure 3: Closed-loop response in the presence of only actuator saturation constraints. Top: The satellite orientation (solid) and auxiliary reference (dotted) converge to the desired steady-state. Middle: The angular velocities closely resemble the behavior of a trapezoidal trajectory planner. Bottom: The control inputs satisfy the constraint $|\tau|\leq1\,Nm$.
• Figure 4: Closed-loop response of the satellite subject to an exclusion cone constraint. In the absence of the destabilization term (left), the system settles in an undesired equilibrium point. In the presence of the destabilization term (right) the obstacle is successfully overcome.
• Figure 5: Closed-loop response in the presence of actuator saturation constraints and a single exclusion cone constraint. The effect of the exclusion cone can be seen starting from time $t=78\,s$, which is when the auxiliary reference enters the influence region. Top: The satellite orientation (solid) and auxiliary reference (dotted) circumnavigate the exclusion cone and converge to the desired steady-state. Middle: Angular velocities. Bottom: The control inputs satisfy the constraint $|\tau|\leq1\,Nm$.

Theorems & Definitions (12)

• Proposition 1
• proof
• Remark 1
• Remark 2
• Proposition 2
• proof
• Proposition 3
• proof
• Corollary 1
• proof