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Reaction force manipulation is one of the key issues on the motor control of legged systems, which moves with a number of joints cooperated on the unactuated floating baselink under the discontinuously varying contact status. This paper presents two solutions to this problem both in strict and approximate forms. A mass-concentrated model which the latter is based on represents the core dynamics of the legged system by a relationship between the center of gravity (COG) and the zero moment point (ZMP) . The desired reaction force under the dynamical constraint is equivalently converted to COG acceleration, and COG Jacobian which implicitly involves unactuated coordinates maps the desired acceleration to the movement of the whole actuated joints. Although it is a pragmatic approach, requirement of less computational cost encourages a realtime implementation. A highly-precise ZMP manipulation by the acceleration offset with an estimation of the effect of neglected moment around COG is also proposed.

Whole-body Cooperative Reaction Force Manipulation on Legged Robots with COG Jacobian involving Implicit Representation of Unactuated Coordinates