Reach-and-hold at a musculoskeletal arm posture is an unstable-equilibrium stabilization problem: the limits of fixed equilibrium-point and impedance controllers

Abstract

Holding a redundant limb at a commanded posture against gravity is a basic problem in musculoskeletal motor control. Whether fixed, biologically grounded controllers can achieve it remains unclear. Using the MyoSuite myoArm under a frozen-criterion, hash-provenanced protocol, we evaluate fixed, non-learning controllers: an equilibrium-point/referent (lambda) reflex, a reflex with co-contraction, an endpoint Cartesian impedance controller, a gravity-compensation feedforward, and an exact inverse-statics gravity-balancing command. None achieves a stable near-task hold. The tested referent reflex placed a near-target equilibrium (best 0.048 m at the lowest target), but sustained a structural limit cycle that velocity damping did not cure; endpoint impedance settled at far false equilibria; and an exact gravity-balancing activation can exist while deployment falls away. At posture-matched targets evaluated in both the 34- and 63-muscle models, the reduced acceleration-position Jacobian has positive real eigenvalues, indicating locally unstable second-order modes. In the 34-muscle model, the full fixed-controller grid also fails to produce a stable near-task hold. In the 63-muscle model, measured endpoint stiffness spans human-scale magnitudes and human-like ellipse axis ratios across a co-contraction sweep, so the failure is not explained by a limp or non-biological plant. We conclude that reach-and-hold is an unstable-dynamics stabilization problem: the tested fixed equilibrium-point/referent controller can place a near-target equilibrium, but does not stabilize it. These results motivate learned selective impedance and predictive/internal-model control as the next class of mechanisms, separating equilibrium placement from stabilization.