  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.
