Shadmehr R (1991), Issues of actuator and kinematic redundancy in
biological motor control. In: Research Notes in Neural Computing: Visual
Structures and Integrated Functions, M. A. Arbib, J-P
Springer, pp. 239-254.
Abstract A task must be specified in terms of both the position and stiffness of the limb before muscle forces and activations are unambiguously assigned. To illustrate this, we begin with the problem of how to control an inverted pendulum with a pair of muscles. An active state model of the frog's gastrocnemius is used to derive three criteria for the stiffness characteristics of the system during posture and movement. The differential equation representing this model is solved to indicate the relation between force and stimulation frequency. This result leads to an interesting prediction of muscle forces in a minimum stiffness equilibrium point control scheme: neural activity in the agonist muscle should decrease as the joint rotates the limb against gravity. For the case where the number of joints exceeds the task's degrees of freedom, an algorithm for mapping end-effector
position and stiffness to the lengths of the muscles is considered. We show that previously proposed algorithm for control of multi-joint limbs (Berkinblit et al. 1986a, Hinton 1984) is in fact a special case of this mapping. We contend that these kinematic maps must be augmented by a mechanism that takes into account the dynamics of the muscle-load-feedback system. We suggest an adaptive control scheme where the derived kinematic relationships are used to set the bias of the stretch reflex feedback loop, while a learning mechanism produces a virtual equilibrium trajectory that compensates for the second order dynamics of the load, as well as the dynamics of the muscles.