In this paper, we consider the general problem of obstacle avoidance based on dynamical system. The modulation matrix is developed by introducing orthogonal coordinates, which makes the modulation matrix more reasonable. The new trajectory's direction can be represented by the linear combination of orthogonal coordinates. A orthogonal coordinates manipulating approach is proposed by introducing rotating matrix to solve the local minimal problem and provide more reasonable motions in 3-D or higher dimension space. The proposed method also provide a solution for patrolling around a convex shape. Experimental results on several designed dynamical systems demonstrate the effectiveness of the proposed approach.
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