Computer Methods in Biomechanics and Biomedical Engineering, 2015 /'T'N Tavlor & . Francis Vol. 18, Nos. 5-8, 829-838, http://dx.doi.org/10.1080/10255842.2013.849341 TayioriFrancsc^p Local versus global optimal sports techniques in a group of athletes Aurore Hucheza*, Diane Haeringbl, Patrice Holvoef2, Franck Barbierc3 and Mickael BegonM “Laboratoire d’Automatique de Mecanique et d’Informatique Industrielles et Humaines and Faculte des Sciences du Sport et de Veducation physique, Universite de Lille 2, 9 rue de I’Universite, 59790 Ronchin, France; bLaboratory of Simulation and Movement Modelling, Department of Kinesiology, Universite de Montreal, 1700 rue Jacques Tetreault Laval, Quebec, H7N OB6, Canada; cLaboratoire d ’Automatique de Mecanique et d ’Informatique Industrielles et Humaines and Faculte des Sciences et Metiers du Sport, Universite du Hainaut Cambresis, Le Mont Houy, 59313 Valenciennes Cedex 9, France (.Received 30 March 2013; accepted 24 September 2013) Various optimization algorithms have been used to achieve optimal control of sports movements. Nevertheless, no local or global optimization algorithm could be the most effective for solving all optimal control problems. This study aims at comparing local and global optimal solutions in a multistart gradient-based optimization by considering actual repetitive performances of a group of athletes performing a transition move on the uneven bars. Twenty-four trials by eight national- level female gymnasts were recorded using a motion capture system, and then multistart sequential quadratic programming optimizations were performed to obtain global optimal, local optimal and suboptimal solutions. The multistart approach combined with a gradient-based algorithm did not often find the local solution to be the best and proposed several other solutions including global optimal and suboptimal techniques. The qualitative change between actual and optimal techniques provided three directions for training: to increase hip flexion-abduction, to transfer leg and arm angular momentum to the trunk and to straighten hand path to the bar. Keywords: simulation; optimization; algorithms; gymnastics; technique 1. Introduction Optimal control of sports movement has been one of the major objectives of sports biomechanics (Hatze 1984; Yeadon and Mikulcik 1992; Lee et al. 2012). Thirty years after Hatze’s overview on this topic (Hatze 1984), ‘the development of software [remains] an extremely laborious and expensive task’ to provide feedback to coaches. Movement optimization is considered as a nonlinear problem with nonlinear physiological constraints (e.g. joint range of motion or strength capacities) and geometrical constraints due to the environment. Various optimization algorithms have been used, either local optimization - such as simplex (van den Bogert and van Soest 1983; Sheets and Hubbard 2009), direct multiple shooting (Mombaur et al. 2010) and sequential quadratic programming (SQP; Pandy 2001; Leboeuf et al. 2006; Jackson et al. 2012) - or global optimization - such as simulated annealing (Ashby and Delp 2006; Hiley and Yeadon 2008) and genetic algorithm (Begon et al. 2009; Ohshima et al. 2010; Jackson et al. 2011). The choice of the algorithm is often motivated by the emphasis of the study: for example, personalization of the computer simulation model (Wilson et al. 2006; Mills et al. 2008), speed and easiness to improve the technique (Sprigings et al. 1997), improvement of an athlete-specific technique (Begon et al. 2009) versus generic optimal technique(s) (Cheng and Hubbard 2008). The expected impact of the research is also a factor to choose the algorithm; for example, create applied knowledge (Koh and Jennings 2007) or design a tool for coaches and athletes (Chakravorti et al. 2012) where the computational time becomes a constraint. Consequently, no algorithm is likely to be the most effective method for solving all optimal control problems in human movement analyses (Neptune and Hull 1999). Hence, development of original algorithms and their application remain a research interest. To improve the performance of a single athlete (Hiley and Yeadon 2012), the research effort is placed on the biofidelity of the dynamic model and its constraints; generic model would not lead to a feasible movement by the athlete (Wilson et al. 2006; Sheets and Hubbard 2008). Experimental measurement is carried out on this athlete to accurately determine his/her segment inertial parameters (Yeadon 1990), as well as maximal active (Forrester et al. 2011) and passive (Begon et al. 2009) joint torques. A (local) gradient-based optimization algorithm is often preferred since the changes between actual and optimal performances lead to specific instructions to the athlete (Hatze 1984). A global search with restricted bounds (Hiley and Yeadon 2013) is an alternative approach when constraints are not continuous (i.e. variability of the movement induced by noise in the neuromuscular system or the environment) or the objective function is non-smooth, since several simulations with random ^Corresponding author. Email: aurore.huchez@univ-lille2.fr ©2013 Taylor & Francis