**1. Introduction**

546 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

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Thomson, W. (1971). Theory of vibration with applications. George Allen and Unwin. Tonoli A., Bonfitto A., Silvagni M., Suarez L.D., Zenerino E. (2011) Active Isolation and Damping of Vibrations for High Precision Laser Cutting Machine. In: Vibration In recent years, there has been an increasing interest in the functionality of the foot in human normal walking. Different from the existing methods that represent the foot as a single rigid bar, several multi-segmented foot models have been studied to evaluate the effects of the segmented foot structures on human walking for clinical applications [1], adolescent gaits [2] and pediatric gaits [3]. The results show that the segmented foot with a toe joint has several advantages compared to the rigid foot in: walking step, walking speed, range of joint angle, change in angular velocity and joint energy-output. In addition, biomechanical studies conducted on ten donated limbs [4] indicate that the human foot can not be considered as a single rigid body with no intrinsic motion.

Inspired by biological investigations, several studies implemented segmented feet in robotic systems to improve walking performance. One of the main applications is in humanoid robots. Simulations and experiments on prototypes showed that adding toe joints could increase the walking speed of biped robots [5, 6]. These works were carried on humanoid robots based on the trajectory-control approach [7]. By controlling joint angles precisely, the robots can achieve static equilibrium postures at any time during motion. However, this kind of bipedal walking features low resemblance to human normal gaits and high energy consumption [8]. In contrast to the active-control bipedal walking mentioned above, passive dynamic walking [9] has been developed as a possible explanation for the efficiency of the human gait. Investigations on the effects of segmented foot, which are based on passivity-based model, may reveal more insights on real human walking. Though several efforts have been made in adding flat feet to passivity-based models [10–15], only a few studies have investigated passive dynamic bipedal walking model with segmented feet. Recently, [16] proposed a passive dynamic walking model with toed feet. Specifically, in the work, the authors contributed to the investigation of the passive bipedal walking behavior under toe joint rotation. The toe-rotation phase is initiated by ankle-strike. Simulation results showed that the advantages of the proposed walker come from its relation to arc-feet walker.

©2012 Wang et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

However, the effects of heel-strike and toe-strike during normal walking are ignored, which may influence the characteristics of bipedal walking [12]. In addition, the phase of rotation of the stance foot about the toe tip is ignored in this model, which makes the bipedal walking gait far from natural human-like gait.

Another area that can use segmented foot is rehabilitation robotics, e.g. lower-limb prostheses and exoskeletons. Although foot prosthesis was invented thousands of years ago, the development of foot prostheses is not as fast as people expect. Most of today's commercial foot prosthesis are passive and do not comprise segmented foot. In 1998, [17] first built a powered ankle-foot prosthesis which was powered by a pneumatic actuator. Then, several pneumatic actuated prostheses have been developed [18, 19]. Though the pneumatic actuator is lightweight, inherently compliant and capable of generating high forces, its control difficulties, large size and noise restrain the development of pneumatic driven prosthesis. Recently, [20] developed a powered ankle-foot prosthesis driven by a DC motor. The motor implemented compliant actuation and was placed on the ankle joint. The prosthesis can provide net positive work to propel the body upward and forward during the stance period. Experimental results show that the prosthesis can decrease the amputee's metabolic cost by 14% on average as compared to the conventional passive-elastic prosthesis. However, the prosthesis functionality is not comparable to that of the human foot because of the absence of segmented foot with toe joint. Similarly, although exoskeletons were invented several decades ago [21], there is no powered toe joint implemented in existing exoskeleton systems, e.g. [22, 23].

In this chapter, we discuss the effects and applications of adding segmented feet with compliant joints to lower-limb prostheses and exoskeletons. To analyze the effects of segmented foot and compliant joints on energetic efficiency and stability of bipedal walking, we first propose a passivity-based dynamic bipedal model which shows resemblance to human normal walking. Phase switching is determined by the direction of ground reaction force. The push-off phase includes rotation around toe joint and rotation around toe tip, which show a great resemblance to natural human gait. The effects of foot structure on motion characteristics including energetic efficiency and walking stability is investigated through simulation experiments. Starting from the theoretical analysis, we introduce segmented foot with toe joint in both ankle-foot prosthesis and exoskeleton prototypes. Both the ankle and toe joints are driven by two series-elastic actuators (SEA), which not only provide the required torque, but also shock tolerance and energy storage during walking. Preliminary studies on sensory based feedback control are carried out to improve the movement of the proposed systems. Experimental results validate the effectiveness of the proposed structure and actuation method.

The rest of the chapter is organized as follows. In section 2, we introduce the idea of adding segmented feet with compliant actuators placed on ankles and toes. Specifically, a theoretical model with segmented feet is proposed which is based on the simplest walking model. In Section 3, detailed investigations are presented to analyze the effects of segmented foot with joint compliance on dynamic walking. Then, starting from the theoretical analysis, the applications of segmented feet to lower-limb prostheses and exoskeletons are introduced in Section 4. After an overview of current compliant actuators in robotics, the development of a lower-limb prosthesis and an exoskeleton with powered compliant ankle and toe joints is presented. In section 5, the basic control method and related experiments on the prototypes are described. Experimental results validate the effectiveness of the proposed systems.

**Figure 1.** One typical gait cycle. Each cycle includes two main subdivisions: (a) stance phase, (b) swing phase. The four important instants in every cycle are heel-strike (HS), foot-flat (FF), heel-off (HO) and toe-off (TO).
