A considerable amount of experimental data suggests that neuromusculoskeletal control processes may be described basically by three functional mechanisms:

1. a feedforward control process which encodes an approximate solution to the inverse dynamics of the desired movement trajectory and the forces which act on the musculoskeletal system;

2. a feedback control process (reflexive system) which corrects for errors in the representation of the inverse dynamics and accounts for unexpected external forces;

3. the intrinsic impedance of a musculoskeletal system, meaning the areflexive stiffness and viscosity components induced by the muscles and other visco-elastic components of a musculoskeletal system.

Experiments in which the movement control of surgically deafferented animals, ischaemically deafferented healthy humans or patients deafferented due to sensory neuropathy were studied, show that deafferented subjects are capable to move (indicating feedforward control), but that the kinematics of these movements are affected and external loads cannot be effectively compensated for, indicating the lack of feedback control. Furthermore, measurement of intrinsic and reflexive impedance characteristics of 1 degree of freedom (dof) joints indicate that both components are functionally relevant in motor control tasks.

An influential hypothesis for movement control, the equilibrium-point (EP) hypothesis, stresses the latter two mechanisms. The EP hypothesis comes in two flavours, viz. the greek small letter alpha-version which is formulated in joint angles and the ?-version which emphasises muscle length as control variable, but in both versions the impedance generated by the neuromuscular system and a (virtual) trajectory of EPs are the keys to movement generation. An attractive feature of the EP hypothesis is the notion that complicated inverse dynamics calculations are not necessary if the neuromuscular stiffness is sufficiently high. However, data of Bennett et al. (1992) for 1 dof elbow movements, and of Gomi and Kawato, 1996 and Gomi and Kawato, 1997 for 2 dofs arm movements show that the stiffness during movement is rather low, such that complicated EP trajectories are necessary for moderate and high movement velocities. Since the calculation of these complicated EP trajectories requires knowledge of the inverse dynamics of the musculoskeletal system and there is no direct evidence that the generation of fast movements is based primarily on EP trajectories, the EP hypothesis now hinders rather than facilitates insight into the possible contribution of feedforward control mechanisms which encode inverse dynamics.

In spite of this criticism, it is agreed with the notion of Feldman (1986) that a good neuromuscular control model should take into account the (reflexive + intrinsic) impedance characteristics of the actual system. This means that a feedback control component should be a part of such a model. In addition to the feedback control component, a feedforward control component which represents the inverse dynamics in a direct manner rather than indirectly via a complex EP trajectory, is adhered to in this paper.

In the remainder of this paper a neuromuscular control model is discussed which includes a motor control system with feedback and feedforward control modes as well as Hill-type muscle models. The motor control system is optimized in a learning process which adapts both control modes. The neural control signals during movement and posture and impedance during posture control are calculated and compared with experimental results from the literature. The strengths and weaknesses of the model as well as possible applications are discussed in Section 4.

The arm model describes movements in the horizontal plane with 90° abduction of the upper arm. Both the shoulder and the elbow are modelled as 1 dof joints, the upper arm and the forearm are described by rigid links and the wrist is considered being fixed. The upper arm is moved by a pair of (lumped) monoarticular shoulder muscles and by a pair of biarticular muscles. Similarly, pairs of monoarticular and biarticular muscles act on the forearm. Nonlinear inertial, centrifugal and Coriolis forces are accounted for in the arm model. The movement ranges of the joints are limited by passive elasticities. The muscles are modelled basically according to the work of Winters and Stark (1985), with the main exception of the series element (SE) in their model. To reduce the computational load the SE was assumed infinitely stiff. It was shown in that this assumption affects the impedance of the muscle only minorly. In the model the force Fm exerted by a muscle depends on its activation a, its length lm and its velocity.