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This paper presents an algorithm for kinematic tracking of a trajectory in the presence of static and moving obstacles. The algorithm is designed so that the physical abilities of the robot system can be considered in tracking for practical applications. For these design goals, we formulate the problem as a constrained least-squares problem subject to time-dependent state and control constraints, where the state constraints are used to describe both the obstacle constraints and the workspace constraint of the robot, and the control constraint is used to describe the speed constraint of the robot. Then we present algorithms for the two cases when the obstacle trajectories are known and unknown. In addition to this theoretical derivation of the algorithm, we also consider several practical aspects which are important in designing applications. For example, we take into consideration the necessary conditions for allowable regions of configuration space and presence of sensor noise.