**4.1. Compliant actuators in joints**

8 Will-be-set-by-IN-TECH

**0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9**

**foot ratio [−]**

**Figure 4.** Adaptability of the rigid foot model with different foot ratios. The normalized foot length is

similar to the trend of walking velocity. In case of short hindfoot and long forefoot (foot ratio is 0.2), the walker can return to stable motion cycle after a ground disturbance larger than 0.7 percent of leg length. However, the maximum disturbance the model can overcome decreases below 0.2 percent of leg length when the lengths of hindfoot and forefoot are comparable (foot ratio is 0.8). The relationship between the maximal allowable ground disturbance and foot ratio of segmented foot model also shows a great resemblance to the trend of walking velocity (Fig. 5 shows the results). The maximum value is obtained when the foot ratio is 0.3.

**0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9**

**foot ratio [−]**

In that case the model can overcome ground disturbance larger than 0.6 percent of leg length. The adaptability of the segmented foot model decreases significantly if the foot ratio changes to other values. The results indicate that there exists a best foot structure of the segmented

**Figure 5.** Adaptability of the segmented foot model with different foot ratios. The normalized foot

**2**

0.1875. The ground disturbance is also normalized by leg length.

**1**

length is 0.1875. The ground disturbance is also normalized by leg length.

foot model, which achieves both excellent adaptability and walking velocity.

**2**

**3**

**4**

**normalized ground disturbance [−]**

**5**

**6**

**x 10−3**

**3**

**4**

**5**

**normalized ground disturbance [−]**

**6**

**7**

**x 10−3**

In practice, a combination of sophisticated nonlinear control strategies and analytical methods is required to deal with the uncontrollable and underactuated degrees of freedom introduced by joint compliance. As a result, many robotic applications have used stiff actuation schemes and high-stiffness materials. However, mechanically compliant systems, such as elastic joints, may be used for shock absorbtion and be exploited to store energy and decrease control complexity. As a new trend in robotics, various kinds of compliant actuators and compliant joints have been introduced to real robot applications, for instance, hexapod robot [28], quadruped system [29] and bipedal walking [30].

According to the composition of the elastic elements, compliant actuators can be roughly divided into several main classes. The first category is the spring based compliance. The well-known examples are the Series Elastic Actuators (SEA) developed by Pratt and Williamson [31] and the two-legged robot Spring Flamingo [32]. Starting from the Series Elastic Actuators, various legged robot applications have been equipped with motor-spring systems. Yamaguchi *et al* [33] used a non-linear spring mechanism to make predefined changes in stiffness of biped robot possible. Meyer *et al* [34] described a simple and low-cost humanoid leg with compliant joints and springy feet, aiming for a repetitive jumping system. Hurst *et al* [35] designed the Actuator with Mechanically Adjustable Series Compliance (AMASC) which consists of a drive motor connected in series with a pair of large, variable stiffness springs. Van Ham *et al* [36] reported a controlled passive walker Veronica actuated with the Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator (MACCEPA) which uses a dedicated servo motor and solid springs to control the compliance and equilibrium position.

Another category is the pneumatic artificial muscles based compliance. The well-known artificial muscles in the field of dynamic walking are the pneumatic McKibben muscles [37]. In addition, the Pleated Pneumatic Artificial Muscle (PPAM) designed by [38], has been successfully implemented in the biped Lucy [30]. However, such air muscles based mechanisms may be the barrier that constrains the dynamic walking systems, especially the lower-limb prostheses and exoskeletons, in practical use. One of the disadvantages is that with air muscles, it is difficult to perform precise control. Other problems, for example, include the use of compressed air and the inefficient down-regulation of pressure of the onboard

**Figure 6.** Schematics diagram of the segmented foot with compliant joints. The two main components of the prosthesis are two SEAs, which are used to drive the ankle and toe joints respectively.

air storage system. Thus, several recent studies try to change air muscles into motor-spring systems as compliant actuators for dynamic walking systems, e.g. [39].

In addition, there are other types of compliant actuators in robotics. For example, shape memory alloys show impressive actuation characteristics, while suffer from slow response and motion constraints [40]. Other interesting compliant actuators include artificial muscle actuator using fluid [41], polymer materials [42], dielectric elastomers [43], etc. Most of them are used in particular environments and difficult to implement in autonomous systems, especially in lower-limb prostheses and exoskeletons.

As mentioned above, currently, spring based compliance is the most promising compliant actuators in the field of dynamic walking. By using the proper spring based elastic mechanisms, lower-limb prostheses and exoskeletons may be capable of performing stable walking on different terrains and with controllable walking velocity. Applying compliant actuators to lower-limb rehabilitation systems provides not only new challenges for bipedal locomotion but also improvement of practical use.
