**2.1. Human normal walking gaits**

Human walking is a cyclic pattern of bodily movements that is repeated over and over, step after step. Every gait cycle starts with heel-strike (HS) when the heel initially touches the ground and ends with the next HS of the same leg. As shown in Fig. 1, each cycle can be divided into two main phases: stance phase and swing phase [44]. The stance phase begins at the moment of HS and ends at the moment of toe-off (TO) when the forefoot pushes off the ground. The swing phase begins at the moment TO and ends at the next HS. The stance phase takes up 60% of the gait cycle and includes four subphases: 1) Hs to foot-flat (FF); 2) FF to midstance (MS); 3) MS to heel-off (HO); 4) HO to TO.

As introduced in [44], at the moment of HS, the ankle has to endure the impact force when the heel initially contacts the ground. From HS to FF, the ankle stores elastic energy within plantarflexor muscles. During FF to MS, the energy stored during the preceding period is released to help the body change the center of gravity from the support leg to the foreleg. At MS, the ankle begins to store elastic energy to dorsiflexor muscles and at HO the ankle reaches a state of maximum dorsiflexion. Then in the period HO to TO, ankle releases the energy stored in the last period to propel the body. However, the stored energy is much less than the energy needed. Then the ankle has to output much more net positive work. Meanwhile, the forefoot is bent to store energy. At the end of the period HO to TO, the toe joint releases the stored energy and supplements some net work to propel the body. During swing phase, the main function of the ankle and toe joints is to adjust the position of the foot to prepare for the next stance phase.
