This paper proposes a trajectory estimation method for a skid-steering mobile robot (SSMR) incorporating free wheels on uneven but smooth ground with different ground properties and distributed loads on wheel axes. We formulate a mathematical expression in terms of virtual work for evaluating the energy cost of all the wheel motions with skidding and slipping under the condition that each wheel is always in contact with the ground via a pivot suspension structure. Minimization of the expression for virtual work results in a unique solution for the new position of the robot after small movement of the wheels. Further, by iterating we calculate a continuous trajectory which is an important result for assigning powered wheel velocities for self-navigation. Trajectories demonstrated by a test robot confirm the validity of the method.
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