In this paper, we present a method for an animated human agent to construct motion plans to achieve 3D-space postural goals, e.g. a goal of a hand, while avoiding collisions. we us the potential field approach by providing mechanisms to handle the problem of local minimum. Given a conjunctive goal of multiple control points on the body, the potential field approach tries to minimize the objective function typically defined to be a weighted sum of individual goals. The local minimum problem arises as the planner tries to locally minimize the weighted sum of individual goals, even when multiple goals of the control points do not conflict with each other in 3D space. Our approach handles this problem by trying to achieve multiple goals individually, not by means of a weighted sum. To do so, the planner uses a qualitative kinematic model, which specifies what joint motions move what body parts in which directions in 3D space. The model is used to suggest joint motions for individual goals, and to explicitly detect and remove conflicts between the suggested joint motions. The local minimum problem arises more obviously when the original goals and collision-avoidance constraints, i.e.repulsive potential fields due to obstacles conflict with each other in 3D space. Our approach avoids this conflict by finding intermediate postural goals of the endangered body parts, based on the kinematic simulation of the current plan.