Recent experimental and theoretical work [1] investigated the neural control of contact transition between motion and force during tapping with the index finger as a nonlinear optimization problem. Such transitions from motion to well-directed contact force are a fundamental part of dexterous manipulation. There are 3 alternative hypotheses of how this transition could be accomplished by the nervous system as a function of changes in direction and magnitude of the torque vector controlling the finger. These hypotheses are 1) an initial change in direction with a subsequent change in magnitude of the torque vector; 2) an initial change in magnitude with a subsequent directional change of the torque vector; and 3) a simultaneous and proportionally equal change of both direction and magnitude of the torque vector. Experimental work in [2] shows that the nervous system selects the first strategy, and in [1] we suggest that this may in fact be the optimal strategy. In [4] the framework of Iterative Linear Quadratic Optimal Regulator (ILQR) was extended to incorporate motion and force control. However, our prior simulation work assumed direct and instantaneous control of joint torques, which ignores the known delays and filtering properties of skeletal muscle.
In this study, we implement an ILQR controller for a more biologically plausible biomechanical model of the index finger than [4], and add activation-contraction dynamics to the system to simulate muscle function. The planar biomechanical model includes the kinematics of the 3 joints while the applied torques are driven by activation?contraction dynamics with biologically plausible time constants [3]. In agreement with our experimental work [2], the task is to, within 500 ms, move the finger from a given resting configuration to target configuration with a desired terminal velocity. ILQR does not only stabilize the finger dynamics according to the objective function, but it also generates smooth joint space trajectories with minimal tuning and without an a-priori initial control policy (which is difficult to find for highly dimensional biomechanical systems).
Furthemore, the use of this optimal control framework and the addition of activation-contraction dynamics considers the full nonlinear dynamics of the index finger and produces a sequence of postures which are compatible with experimental motion data [2]. These simulations combined with prior experimental results suggest that optimal control is a strong candidate for the generation of finger movements prior to abrupt motion-to-force transitions.
This work is funded in part by grants NIH R01 0505520 and NSF EFRI-0836042 to Dr. Francisco J. Valero- Cuevas
1 Venkadesan M, Valero-Cuevas FJ.
Effects of neuromuscular lags on controlling contact transitions.
Philosophical Transactions of the Royal Society A: 2008.
2 Venkadesan M, Valero-Cuevas FJ.
Neural Control of Motion-to-Force Transitions with the Fingertip.
J. Neurosci., Feb 2008; 28: 1366 - 1373;
3 Zajac. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit Rev Biomed Eng, 17
4. Weiwei Li., Francisco Valero Cuevas: ?Linear Quadratic Optimal Control of Contact Transition with Fingertip ? ACC 2009