# Aging Affects Multi-Objective Optimal Control Strategies during Obstacle Crossing
## 1 Introduction  
Obstacle crossing challenges balance and is considered one of the daily activities that increases the risk of falls in older people [1, 2, 3]. Loss of balance and inability to recover balance are the main contributing factors to falling during obstacle crossing in older people [4]. For a successful obstacle crossing, necessary foot-clearance of the swing limb and stability of the body provided mainly by the stance limb are needed [5]. Insufficient foot-clearance will increase the risk of tripping, leading to loss of balance [6, 7, 8]. While increasing foot-clearance may help reduce the risk of tripping [9, 10, 11], the associated alteration of the whole-body posture may place greater challenges on body balance [6, 7]. In this case, extra muscular effort and work at the joints in the stance limb will be required to maintain body balance or recover balance in cases where imbalance occurs. A previous study has reported the overall strategies for the simultaneous control of foot-clearance, lower limb muscularwork, and total mechanical energy for successful obstacle crossing in young adults [12]. Similar knowledge in older adults will be helpful for developing intervention strategies for fall prevention in the older population. Older people have been shown to cross obstacles with increased leading toe-clearance [13; 14; 15], slower crossing speed, shorter step length, and smaller step width [11], as well as increased muscular moments at the lower limb joints [9], when compared with young controls. Altered kinematics of individual joints of the lower extremities were also reported in previous studies [5; 9; 10; 13; 16; 17; 18]. While increased toe-clearance helps reduce the risk of tripping [9; 10; 11], it remains unclear how the reported changes in individual variables together would contribute to the higher risk of falls in older people. To gain insight into the control strategies of obstacle crossing, relative phase analysis has been used to study the patterns and variability of the multi-joint coordination during obstacle crossing in older people, which were independent of obstacle height [15; 19; 20]. While the mechanics of and coordination between individual joints have been studied, difficulties still exist in synthesizing these data to uncover the overall control of the locomotor system for obstacle crossing in older people. For example, older people changed some joint angles or moments with increasing obstacle height, while keeping other variables unchanged [5; 9; 16]. From these results, it is difficult to test whether there exists an obstacle-height independent control strategy present at the level of the central control system. To tackle this problem, [PERSON] et al. proposed a multi-objective optimal control (MOOC) approach to study obstacle-crossing strategies in young adults from the perspective of the central control system [12]. Using the MOOC approach with a weighting method [21], the overall control strategy for obstacle crossing in young adults has been shown to be the best-compromise solution to an MOOC problem with conflicting objectives of maximizing foot clearance and minimizing mechanical energy expenditure. Minimizing energy expenditure has generally been accepted as the optimal control objective for normal walking [22; 23; 24; 25; 26], but not for obstacle crossing [9], even though both activities appear similar. During obstacle crossing, one has to lift the foot to cross the obstacle, so minimizing energy expenditure alone does not predict swing ankle trajectories that give the foot clearances observed in normal obstacle-crossing [9; 12]. For a successful obstacle crossing, the swing foot has to cross over the obstacle with sufficient foot-clearance [5]. Previous studies have shown that older people crossed obstacles with increased toe-obstacle clearance, presumably to reduce the risk of tripping because, the greater the foot-obstacle clearance, the less likely the foot is to hit the obstacle [13].