Optimizing principles underlying the shape of trajectories in goal oriented locomotion for humans
- 1 December 2006
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 131-136
- https://doi.org/10.1109/ichr.2006.321374
Abstract
This paper addresses the problem of understanding the shape of the locomotor trajectories for a human being walking in an empty space to reach a goal defined both in position and in direction. Among all the possible trajectories reaching a given goal what are the fundamental reasons to chose one trajectory instead of another? The underlying idea to attack this question has been to relate this problem to an optimal control problem: the trajectory is chosen according to some optimization principle. This is our basic starting assumption. The subject being viewed as a controlled system, the question becomes what criteria is optimized? Is it the time to perform the trajectory? the length of the path? the minimum jerk along the path?... In this study we show that the human locomotor trajectories are well approximated by the geodesics of a differential system minimizing the L2 norm of the control. Such geodesics are made of arcs of clothoids. The clothoid or Cornu spiral is a curve, whose curvature grows with the distance from the origin. The study is based on an experimental protocol involving 7 subjects. They had to walk within a motion capture room from a fixed starting point, and to cross over distant porches from which both position in the room and orientation were changing over trials.Keywords
This publication has 21 references indexed in Scilit:
- Guidelines in nonholonomic motion planning for mobile robotsPublished by Springer Science and Business Media LLC ,2006
- Optimality principles in sensorimotor controlNature Neuroscience, 2004
- Time Optimal Trajectories for Bounded Velocity Differential Drive VehiclesThe International Journal of Robotics Research, 2002
- Minimum-jerk, two-thirds power law, and isochrony: converging approaches to movement planning.Journal of Experimental Psychology: Human Perception and Performance, 1995
- Near-optimal nonholonomic motion planning for a system of coupled rigid bodiesIEEE Transactions on Automatic Control, 1994
- Optimal paths for a car that goes both forwards and backwardsPacific Journal of Mathematics, 1990
- Formation and control of optimal trajectory in human multijoint arm movementBiological Cybernetics, 1989
- The law relating the kinematic and figural aspects of drawing movementsActa Psychologica, 1983
- Nonlinear regulator theory and an inverse optimal control problemIEEE Transactions on Automatic Control, 1973
- On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and TangentsAmerican Journal of Mathematics, 1957