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This paper provides a prototype of an intelligent robotic walking assistance system named Walkmate with force sensor interface and a motion control algorithm for it. Our human-machine interface with the force sensors embedded in handlebars offers a nature negative feedback loop of the motion control. In the algorithm we defined two motion control modes. In the Force-Velocity Mode, the velocity of the robot is set proportional to the force applied to the force sensor interface in the handlebars. The Force-Acceleration Mode is a stimulation of a passive type cart-like dynamics. Based on the input force signal, the system amplifies the signal and outputs the desired acceleration of each wheel to stimulate the dynamics of a real cart. By detecting the user's intentions though physical interaction, the force sensor interface offers a naturally and intuitively way to control the Walkmate. We did two experiments about the two different modes to show our motion control algorithm can simulate a cart-like dynamics and control the robot to perform some typical walking assistance tasks.