Models and control strategies for dynamic obstacle avoidance in visual guidance of mobile robot are presented. Characteristics that distinguish the visual computation and motion-control requirements in dynamic environments from that in static environments are discussed. Objectives of the vision and motion planning are formulated as: 1) finding a collision-free trajectory that takes account of any possible motions of obstacles in the local environment; 2) such a trajectory should be consistent with a global goal or plan of the motion; and 3) the robot should move at as high a speed as possible, subject to its kinematic constraints. A stochastic motion-control algorithm based on a hidden Markov model (HMM) is developed. Obstacle motion prediction applies a probabilistic evaluation scheme. Motion planning of the robot implements a trajectory-guided parallel-search strategy in accordance with the obstacle motion prediction models. The approach simplifies the control process of robot motion.