【摘要】 对散开现象提出了一种新的解释,并对姿态控制提出了一种新的PD型控制。实际应用中常用四元数来表示一刚体运动的姿态。可是四元数的状态空间S3对姿态集合SO(3)是双重覆叠的,即每一个姿态对应两个不同的四元数向量。这样,当采用四元数来进行反馈控制时,四元数的非唯一性会在q∈S3和-q∈S3的邻域分别形成一个吸引域和一个排斥域,从而导致了姿态控制的散开现象。文中用一个姿态控制的实例来说明这个不稳定现象。为了避免出现散开现象,提出了一个PD型的非线性控制器。这种控制器还有一个特点是能够以最小转角来回归平衡状态。更多还原

【Abstract】 A new exposition of the unwinding phenomenon was presented and a new type of PD controller for attitude control was proposed. The quaternions are often used in practical applications to represent rigid- body attitude. However,the quaternion state space S3 double covers the set of attitudes SO( 3) in the sense that each attitude corresponds to two different quaternion vectors. Thus,in the case of feedback control using quaternions,this nonunique representation can give rise to regions of attraction and repulsion in the neighborhood of q∈S3and- q∈S3,respectively,and cause the unwinding phenomenon of attitude control. A practical attitude control example was presented to illustrate this unstable behavior. A PD- type nonlinear controller was proposed to avoid the unwinding phenomenon. This controller also has an advantage of retuning to the equilibrium state with minimum angle of rotation.更多还原