# Aging Affects Multi-Objective Optimal Control Strategies during Obstacle Crossing
## 4 Discussion
However, the strategy was multi-objective and specific to different age groups, which was in contrast to the single-objective and possibly age-independent control strategy for unobstructed level walking (i.e., minimization of energy expenditure, [22]). Note that the best-compromise weighting sets in both groups were not affected by obstacle height, suggesting that the control strategies for obstacle crossing were stored and executed at the central nervous system level [12] according to the central pattern generator theory [40]. This best-compromise MOOC strategy was found to change with aging. The current results indicate that the older adults placed more emphasis on foot-obstacle clearances than on energy expenditure compared with the healthy young group. The significantly increased weightings for the foot-obstacle clearance corresponded to the increased values of the toe-obstacle clearances, irrespective of obstacle heights, suggesting a strategy for reduced risk of tripping during obstacle crossing. However, this comes with the expense of increased mechanical energy expenditure (decreased weighting for minimization of mechanical energy) owing to the conflicting nature of the objectives for obstacle crossing (Table 2). Increased mechanical energy expenditure indicated increased muscular work at the lower limb joints was needed for the stability of the stance limb (Equation (2)) when the swing limb was lifted to increase toe-obstacle clearance. This is a challenge to older people who often have reduced muscle strength during the aging process [41; 42; 43]. It has been noted that obstacle negotiation is a precise end-point control task [9; 13; 18; 44; 45]. Sufficient foot-obstacle clearance and necessary body stability provided mainly by the stance limb are essential to a successful and safe obstacle crossing [13]. It appears that the MOOC strategy adopted by the older group would rely on not only the muscular strength of the lower extremities for stance stability, but also the ability of precision end-point control for the increased toe-obstacle clearance. Both the ability of end-point control and muscle strength are important components for preventing falls in older people [46; 47; 48; 49]. Fall risks may be increased if an older person has muscle weakness [41; 42; 43] or compromised limb position control [11; 41; 50], or increased variability in performing motor tasks [15; 51; 52], which are common in the process of aging. Therefore, apart from factors such as vision, spatial cognition, and fear of tumbling, maintaining or improving muscle strength and the ability of limb position control are critical for safe and successful obstacle crossing in the older population. The current study approached the complicated control problem of obstacle crossing with the multi-objective optimal control technique considering the laws of kinematics and kinetics. The small RMSEs of the ankle trajectories, leading joint angles, and trailing joint moments indicate that the iterative solution process converged and that the best-compromise solutions for the MOOC problems were obtained with a high degree of accuracy. This enabled the study of the effects of aging on the control strategies of obstacle crossing via a reliable comparison of the best-compromise weighting sets between the older and young groups. In the current study, the crossing strategies over the swing phase of the leading limb during obstacle crossing were studied. Further investigation will be needed to test whether different objective functions would be involved during obstacle crossing with the trailing limb. Furthermore, further inclusion of motion components of the frontal and transverse planes may be needed to study the motor control of obstacle crossing, especially for people with neuromuscularsokeletal disorders. In the current study, both subject groups were healthy adults without any neuromuscularsokeletal dysfunction and with normal or corrected vision.