Gyro-free attitude observer of rigid body via only time-varying reference vectors

Finite‐time constrained attitude regulation for spacecraft formation with disturbances on SO(3)$$ SO(3) $$

“…Remark Inspired by References 39‐42, the following control strategy is used to design the control law $$$ {u}_i $$$ (44). When the modified finite‐time communication‐delayed distributed observer estimate the desired attitude for $$$ t<{T}_r $$$, the control law is set to zero and then the control law $$$ {u}_i $$$ (44) can be switched to the $$$ {u}_i^{\ast } $$$ (43) required by the mission after the time moment $$$ {T}_r $$$.…”

“…) , (41) where 𝜍 1 , 𝜍 2 > 0 and i = 1, 2, ..., n. According to the works in Reference 35, we can obtain the following lemma.…”

“…Theorem 3. Consider the sliding mode observer (41). Assume that the communication graph is fixed and the leader has directed paths to all follower spacecraft.…”

“…Then according to Theorem 3, it is easy to see that T r = 10.5s. Moreover, to decrease the chattering caused by the signum operator in sliding mode observer (41) 5, and c 0 (t) = 1000 𝜋 arctan(10 −6 (t − 10.5) 2 + 10 −6 (t − 10.5)). Figure 13 shows the results of attitude error vector changing with time in the leader-following attitude regulation process of 100 times simulation experiments with stochastic initial attitudes on SO (3).…”