# Aging Affects Multi-Objective Optimal Control Strategies during Obstacle Crossing
## 4 Discussion  
The current study aimed to use multi-objective optimal control techniques with a mechanical model of the human body in the sagittal plane to study the control strategies adopted by healthy young and older adults when crossing obstacles of different heights. The older group was found to cross obstacles with significantly increased weightings to the heel- and toe-clearances, but decreased energy expenditure weightings when compared with the young group (Figure 3), supporting the hypothesis posed in the current study. These best-compromise weighting sets were not affected by obstacle height, suggesting that the observed strategy was one at the central nervous system level. The current findings suggest that the older adults adopted a crossing strategy that is different from that of the young, emphasizing the foot clearance to reduce the risk of tripping over the obstacle at the expense of increased energy expenditure. The older subjects crossed obstacles with altered end-point control when compared with the young, as indicated by the increased leading toe-obstacle clearance and trailing toe-obstacle distance, but decreased leading heel-obstacle distance. Similar age effects on toe-obstacle clearances were also found in the literature [13; 15; 36; 37; 38]. Increased leading toe-obstacle clearance appears to be helpful for reducing the risk of tripping during obstacle crossing in older people [13; 15]. For an increased leading toe-obstacle clearance, an efficient approach would be to cross the obstacle with the trailing stance foot closer to the obstacle [37]. However, the older subjects were found to cross with increased trailing toe-obstacle distance, but with subsequently reduced heel-obstacle distance when com \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Obstacle Height (\% Leg Length)**} & \multicolumn{2}{c}{**Group Effect**} & \multicolumn{2}{c}{**Height Effect**} \\ \cline{2-5}  & **10** & **20** & **30** & \multicolumn{2}{c}{\(p\)**-Value**} \\ \hline \multicolumn{5}{l}{Ankle trajectory (mm)} \\ \hline Older & 7.1 (3.1) & 7.1 (2.9) & 7.8 (1.7) & 0.4 & 0.63 \\ Young & 6.7 (1.9) & 6.7 (2.3) & 7.3 (2.3) & 0.4 & 0.63 \\ \hline \multicolumn{5}{l}{Swing hip angle (\({}^{\circ}\))} \\ \hline Older & 0.84 (0.22) & 0.81 (0.36) & 0.98 (0.29) & 0.11 & 0.11 \\ Young & 0.64 (0.19) & 0.66 (0.28) & 0.74 (0.23) & & \\ \hline \multicolumn{5}{l}{Swing knee angle (\({}^{\circ}\))} \\ \hline Older & 1.71 (0.49) & 1.39 (0.62) & 1.40 (0.33) & & \\ Young & 1.41 (0.39) & 1.29 (0.43) & 1.26 (0.38) & 0.08 & 0.09 \\ \hline \multicolumn{5}{l}{Trailing ankle moment (Nm)} \\ \hline Older & 3.13 (0.72) & 3.77 (1.64) & 3.90 (0.81) & & \\ Young & 3.44 (0.76) & 3.71 (1.18) & 4.00 (0.97) & 0.73 & 0.11 \\ \hline \multicolumn{5}{l}{Trailing knee moment (Nm)} \\ \hline Older & 3.08 (0.84) & 3.05 (1.68) & 2.99 (0.80) & & \\ Young & 2.75 (0.50) & 3.39 (0.85) & 3.53 (0.88) & 0.59 & 0.37 \\ \hline \multicolumn{5}{l}{Trailing hip moment (Nm)} \\ \hline Older & 3.63 (0.90) & 4.02 (1.96) & 3.98 (1.11) & & \\ Young & 4.35 (0.74) & 4.59 (1.08) & 4.46 (1.02) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Means (standard deviations) of the RMSEs of the kinematic data of the leading swing limb and the trailing joint moments between the best-compromise solutions of the Multi-Objective Optimal Control (MOOC) and the experimental data. pared with the young (Table 2). Reduced heel-obstacle distance may increase the risk of stumbling, although heel or midsole contact has been suggested to carry less risk for a fall than toe contact [11]. On the other hand, increased trailing toe-obstacle distance may increase the separation of the body's center of mass relative to the center of pressure, increasing the risk of loss of balance [39]. The observed obstacle-height-independent end-point trajectories for obstacle crossing were a result of the best compromise between minimizing mechanical energy and maximizing the toe-obstacle and heel-obstacle clearances.