Adaptive multi-objective control explains how humans make lateral maneuvers while walking
Fig 4
Conceptual Depiction of Task Performance.
A) When viewed in the [zL, zR] plane, goals to maintain constant position (zB*) or step width (w*) each form linear Goal Equivalent Manifolds (GEMs) that are diagonal to the zL and zR axes and orthogonal to each other. Deviations (δzB and δw) with respect to both the zB* and w* GEMs characterize the stepping distribution at a given step and reflect the relative weighting of zB and w regulation. In steady-state walking, humans strongly prioritize regulating w over zB, producing stepping distributions strongly aligned to the w* GEM. B) Any maneuver would then involve a substantial change from some initial (green) to some new final (blue) stepping goals that will displace these GEMs diagonally in the [zL, zR] plane, such as the theoretical rightward shift in zB* (ΔzB*) and increase in w* (Δw*) depicted here. To accomplish such a maneuver requires changing both zL and zR. This cannot be achieved in any single step. C) At least two consecutive steps (either ‘a’: zR→zL, or ‘b’: zL→zR) at minimum are required to execute a lateral maneuver (ΔzB* and/or Δw*). Each possible intermediate step (‘a’ or ‘b’) has its own distinct stepping goals. D-F) For any given intermediate step, numerous feasible strategies to execute the maneuver are theoretically possible. D) One such strategy might be to maintain strong prioritization of w over zB regulation (i.e., as in A) at the intermediate step. Enacting this strategy would produce a stepping distribution at the intermediate step that would remain strongly aligned to the new constant step width GEM (w*a) at that intermediate step. E) Another feasible strategy might be to simply put the first (here, right) foot at its new desired location (zR). This would produce a stepping distribution at the intermediate step that would be strongly aligned to that new desired location (here, zR) for that step. F) A third feasible strategy might be to maximize maneuverability. Here, foot placement at the intermediate step should be as accurate as possible. This would produce an approximately isotropic (i.e., circular) stepping distribution at the intermediate step.