Procedures used to calculate solutions for a model of legged locomotion on natural terrain are discussed in this chapter. The equations of motion are solved in their original form for efficiency and adaptability to combinations of imposed boundary conditions (i.e., specified joint forces and trajectories). An Euler predictor-corrector scheme is applied to the differential equations and the estimated local error is used for global error control and variable stepsize definition. The non-linear algebraic equations obtained by discretizing the equations of motion are solved with a combination of full Newton, altered Newton and chord iterative methods. A difference approximation is used to calculate the system Jacobian because unloading characteristics and intermittent contact of the foot-soil modeling preclude symbolic evaluation. Relevant details of the solution implementation are described.
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