We derive a continuous nonlinear control law for spacecraft attitude tracking of arbitrary continuously differentiable attitude trajectories based on rotation matrices. This formulation provides almost global stabilizability, that is, Lyapunov stability of the desired equilibrium of the error system as well as convergence from all initial states except for a subset for which the complement is open and dense. This controller thus overcomes the unwinding phenomenon associated with continuous controllers based on attitude representations, such as quaternions, that are not bijective and without resorting to discontinuous switching. The controller requires no inertia information, no information on constant-disturbance torques, and only frequency information for sinusoidal disturbance torques. For slew maneuvers (that is, maneuvers with a setpoint command in the absence of disturbances), the controller specializes to a continuous, nonlinear, proportional-derivative-type, almost globally stabilizing controller, in which case the torque inputs can be arbitrarily bounded a priori. For arbitrary maneuvers, we present an approximate saturation technique for bounding the control torques.

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This paper presents a tracking control scheme for spacecraft formation flying with a decentralized collision avoidance scheme, using a virtual leader state trajectory. The configuration space for a spacecraft is the Lie group SE (3), which is the set of positions and orientations in three-dimensional Euclidean space. A virtual leader trajectory, in the form of attitude and orbital motion of a virtual satellite, is generated offline. Each spacecraft tracks a desired relative configuration with respect to the virtual leader in an autonomous manner, to achieve the desired formation. The relative configuration between a spacecraft and the virtual leader is described in terms of exponential coordinates on SE(3). A continuous-time feedback tracking control scheme is designed using these exponential coordinates and the relative velocities. A Lyapunov analysis guarantees that the spacecraft asymptotically

A deterministic attitude estimation problem for a rigid body in a potential field, with bounded attitude and angular velocity measurement errors is considered. An attitude estimation algorithm that globally minimizes the attitude estimation error is obtained. Assuming that the initial attitude, the initial angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and the size of the uncertainty ellipsoid measures the accuracy of the estimates. The point estimates and the uncertainty ellipsoids are propagated using a Lie group variational integrator and its linearization, respectively. The attitude and angular velocity estimates are optimal in the sense that the sizes of the uncertainty ellipsoids are minimized.

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