Predictive simulation: minimal-effort optimal control

Predicts the movement a limb model would produce to go from one posture to another while minimising control effort (integral of squared joint torque) – a direct-collocation optimal-control problem. Each joint trajectory is a boundary-satisfying quintic plus interior basis functions whose amplitudes are optimised; the required torque at each node is obtained by inverse dynamics.

Usage

predictiveSimulation(
  model,
  q0,
  qT,
  duration,
  n_nodes = 60L,
  n_basis = 3L,
  maxit = 200L
)

Arguments

model

A planar_limb_model.

q0, qT

Start and target joint configurations (length ndof); velocity is zero at both ends.

duration

Movement time (s).

n_nodes

Collocation nodes for the effort integral (default 60).

n_basis

Interior basis functions per joint (default 3).

maxit

Optimiser iterations (default 200).

Value

a predictive_sim: time, q, qd, qdd, tau (node x ndof), effort (optimised) and effort_baseline (the minimum-jerk quintic), the effort reduction, and boundary error.

References

Todorov & Jordan (2002); Ackermann & van den Bogert (2010) predictive simulation.

See also

forwardDynamics()

Examples

m <- planarLimbModel(c(2.1, 1.4), c(0.3, 0.25), g = 0)   # horizontal reach
ps <- predictiveSimulation(m, q0 = c(0.2, 0.3), qT = c(1.1, 0.6),
                           duration = 0.6, n_basis = 2, maxit = 80)
ps$effort <= ps$effort_baseline                          # optimisation helps
#> [1] TRUE