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Kinematic models and motion control algorithms for a two-axle compliant frame mobile robot are examined. General kinematics describing the compliantly coupled nonholonomic kinematics are derived using velocity constraints that minimize traction forces and consider foreshortening of the frame. Given the complexity of these equations, the steering ratio a is defined to describe the relative heading angles of the front and rear axles. Simplified kinematic models are developed based upon a (Types I, II, and III) and the reference point used to guide the robot. Physical limitations and performance metrics (lateral mobility and maneuverability per unit of traction force) are derived to evaluate the models. Six groups of simulations and 24 experimental tests consisting of 120 trials evaluate the performance of the algorithms on carpet, sand, and sand with rocks. Results indicate that Type I (curvature-based steering) provides superior maneuverability and regulation accuracy, whereas Type II provides excellent lateral mobility at the cost of high traction forces, reduced accuracy, and potential singularities. Both models offer significant reductions in complexity for simplified control using standard curvature-based unicycle control algorithms. These results support expectations derived from performance metrics and physical limitations. Experimental results also demonstrate the efficacy of the robot to adapt to and maneuver over extremely rugged rocky terrain.