Analysis and Simulation of Optimal Motions in Rock Climbing. (Analyse et simulation des mouvements optimaux en escalade)

How optimal are human movements ? This thesis tackles this issue by focusing especially on climbing movements, studied here under three complementary aspects which are the experimental gathering of climbing sequences, the biomechanical analysis of these data, and the synthesis of gestures by timing optimization. Walking has been largely studied, with good results in animation [Mordatch 2013]. We are interested here especially in the original question of climbing motions, whose diversity and multicontact aspect present an interesting complexity for the evaluation of the human motion characteristics. The heterogeneity of climbing gestures can be linked to several factors which are the variety of wall shapes, the multiplicity of climber skill levels, and di erent climbing categories, namely bouldering, route climbing or speed climbing. Our exploratory approach of this sport consists in three steps: the data collection by multicamera marker-based motion capture, combined with a set of force sensors mounted on an in-laboratory bouldering wall; a gesture analysis by inverse dynamics, taking only kinematic data as inputs, based on the minimization of internal torques to resolve the multicontact ambiguity, intrinsic to the climbing activity, validated by comparison with sensor measurements; and nally, the use of the energy e ciency criterion for synthesizing the best timing associated with a given sequence of movements. Experimental recordings were made at McGill University which has a climbing wall instrumented of 6 force sensors, and a motion capture device of 24 cameras, which allowed us to collect data on a population of nine subjects. The analysis of these data is the second part of this thesis. The addressed challenge is to nd the external forces and internal torques from the climber's movements only. To this end we assume an optimal distribution of internal torques. After analysis, the distribution turns out to be rather uniform than proportional to the muscle capacity associated to each body joint. Finally, in a third and last part, we focus on the timing of climbing gestures, taking as input the path of the climber, possibly after inverse kinematics in order to overcome the need for a capture with markers and infrared cameras. As output, an optimal timing for this path is found. This timing is realistic, but lacks of a modelization for hesitation and decision making instants, as well as a model for the contact establishment, with the associated temporal delay currently not taken into account.