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Pure-R static optimization of muscle activations

Source: R/static-optimization.R
staticOptimizationR.Rd

Distributes the net joint moment at each time frame across muscles by minimising the sum of squared activations (a quadratic muscle-effort criterion), subject to the moments being reproduced exactly and each activation staying within its bounds: $$\min_a \sum_i w_i a_i^2 \quad \text{s.t.} \quad \tau_j = \sum_i a_i F^{max}_i r_{ji}, \; 0 \le a_i \le 1.$$ Each frame is an independent convex quadratic program (solved with quadprog), giving the unique minimum-effort activations. This mirrors the OpenSim Static Optimization tool (Anderson & Pandy 2001) and is used by runStaticOptimization() when OpenSim is unavailable.

Usage

staticOptimizationR(
  moment_arms,
  max_force,
  joint_moments,
  activation_bounds = c(0, 1),
  weights = NULL,
  passive_moments = NULL
)

Arguments

moment_arms

Muscle moment arms: either a single n_dof x n_muscle matrix r (moment arm of muscle i about degree-of-freedom j, reused for every frame) or a list of such matrices, one per frame.

max_force

Numeric vector of muscle maximum isometric forces (F_max, length n_muscle).

joint_moments

Net joint moments to reproduce: a length-n_dof vector (single frame) or an n_frames x n_dof matrix (one row per frame).

activation_bounds

Length-2 numeric c(lower, upper) activation bounds (default c(0, 1)).

weights

Optional length-n_muscle positive weights w_i for the effort criterion (default all 1).

passive_moments

Optional passive/gravity joint moments subtracted from joint_moments before optimization (same shape as joint_moments).

Value

A static_optimization_r object: a list with activations (n_frames x n_muscle), moments (the reproduced net joint moments, n_frames x n_dof), residual (max absolute moment error per frame), effort (sum of squared activations per frame), feasible (logical per frame), and the muscle / DOF counts.

References

Anderson FC, Pandy MG (2001). "Static and dynamic optimization solutions for gait are practically equivalent." J Biomech 34(2):153-161.

See also

runStaticOptimization()

Examples

if (requireNamespace("quadprog", quietly = TRUE)) {
  # Two muscles with unit moment arm and F_max reproduce a moment of 30.
  r <- matrix(c(1, 1), nrow = 1)
  so <- staticOptimizationR(r, max_force = c(100, 100), joint_moments = 30)
  so$activations
}
#>      [,1] [,2]
#> [1,] 0.15 0.15