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Quasi-static object manipulation using a wheeled mobile robot is studied. For a mobile robot, as a typical set-up for transportation of objects, dynamic grasp problem is defined. It is assumed that the robot moves along a straight path and carries an object on its upper surface and the object should not move relative to the robot (dynamic grasp problem). It is also assumed that the robot has limited wheel motors torque. It is shown that to preserve dynamic grasp between the object and the robot, acceleration of the robot has to remain in a specified range. A third order polynomial for position equation of the mobile robot is selected and dynamic grasp and torque conditions are sketched as a constraint on acceleration of the robot. An optimization problem is proposed to find the optimal motion of the robot. A genetic algorithm is proposed to solve the optimization problem. The solutions are validated by simulations in MSC-ADAMS and MATLAB in general case of the optimization problem and also in minimum time, maximum distance and minimum energy problems as special cases of the general problem.