**4.3. Powered prosthesis with segmented foot**

PANTOE 1 is short for foot-prosthesis with Powered Ankle and Toe Joints. Our aim is to build an ankle-foot prosthesis with compliant powered joints and segmented foot to replicate the functionality of human foot as closely as possible. SEA 1 was designed based on the angle range of *<sup>θ</sup>*<sup>1</sup> from <sup>−</sup>16*<sup>o</sup>* to 27*o*. Spring 1 was constructed with three springs placed together in parallel. The stiffness of Spring 1 is about 500*N*/*cm*. The pitch of the ball screw Transmission 1 is 4*mm* per revolution, then the nut is self-locking. Because the ankle needs to provide high power output to propel the body, we chose a 83*W* FAULHABER brushed DC motor (with rotary encoder) as Motor 1. Figure 8 shows the CAD model and the prototype of PANTOE 1 in detail. In order to decrease the total weight, PANTOE 1 is made of aluminium-alloy. This design weighs 1.47*kg*, not including the rechargeable Li battery and the molded socket.

## **4.4. Lower-limb exoskeleton with segmented foot**

EXO-PANTOE 1 is short for below-knee exoskeleton with powered ankle and toe joints. It is designed for a subject suffering from some ankle pathology. The information of the subject is shown in Table 1. Figure 9 shows the CAD model and the prototype of EXO-PANTOE 1 in


**Table 1.** Information of the subject.

detail. The design concept of EXO-PANTOE 1 is similar to PANTOE 1. Two SEAs are used to drive the ankle and toe joints respectively.

558 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges Segmented Foot with Compliant Actuators and Its Applications to Lower-Limb Prostheses and Exoskeletons <sup>13</sup> Segmented Foot with Compliant Actuators and Its Applications to Lower-Limb Prostheses and Exoskeletons 559

**Figure 9.** The CAD model and the prototype of EXO-PANTOE 1 with compliant joints and segmented foot. The prototype is made of aluminium-alloy. The weight is 1.2*kg* (not including the Li rechargeable battery about 0.5*kg*), acceptable to the subject. The full angles of the ankle and the toe joints are 45*<sup>o</sup>* and 90*<sup>o</sup>* respectively.

#### **4.5. Sensors and control**

12 Will-be-set-by-IN-TECH

(a) (b)

**Figure 8.** The CAD model and the prototype of PANTOE 1 with compliant joints and segmented foot. The prototype is made of aluminium-alloy. The weight is 1.47 kg (not including the Li rechargeable battery about 1 kg), comparable to the weight of the subject's limb. The full angles of the ankle and the

PANTOE 1 is short for foot-prosthesis with Powered Ankle and Toe Joints. Our aim is to build an ankle-foot prosthesis with compliant powered joints and segmented foot to replicate the functionality of human foot as closely as possible. SEA 1 was designed based on the angle range of *<sup>θ</sup>*<sup>1</sup> from <sup>−</sup>16*<sup>o</sup>* to 27*o*. Spring 1 was constructed with three springs placed together in parallel. The stiffness of Spring 1 is about 500*N*/*cm*. The pitch of the ball screw Transmission 1 is 4*mm* per revolution, then the nut is self-locking. Because the ankle needs to provide high power output to propel the body, we chose a 83*W* FAULHABER brushed DC motor (with rotary encoder) as Motor 1. Figure 8 shows the CAD model and the prototype of PANTOE 1 in detail. In order to decrease the total weight, PANTOE 1 is made of aluminium-alloy. This design weighs 1.47*kg*, not including the rechargeable Li battery and the molded socket.

EXO-PANTOE 1 is short for below-knee exoskeleton with powered ankle and toe joints. It is designed for a subject suffering from some ankle pathology. The information of the subject is shown in Table 1. Figure 9 shows the CAD model and the prototype of EXO-PANTOE 1 in

> level distance of the ankle joint from the end of the heel *L*<sup>3</sup> 68*mm* height of the ankle joint from the ground *H*<sup>1</sup> 83*mm* maximal plantar flexion angle of the ankle joint *θ<sup>p</sup>* 27◦ maximal dorsiflexion angle of the ankle joint *θ<sup>d</sup>* 16◦ maximal angle of the toe joint *θ<sup>t</sup>* 90◦

detail. The design concept of EXO-PANTOE 1 is similar to PANTOE 1. Two SEAs are used to

Parameter Value length of the foot *L*<sup>1</sup> 265*mm* length of the forefoot *L*<sup>2</sup> 79*mm*

toe joints are 45*<sup>o</sup>* and 90*<sup>o</sup>* respectively.

**Table 1.** Information of the subject.

drive the ankle and toe joints respectively.

**4.3. Powered prosthesis with segmented foot**

**4.4. Lower-limb exoskeleton with segmented foot**

Sensors and control method used in PANTOE 1 and EXO-PANTOE 1 are similar. The sensor system includes two touch sensors, a angle sensors, a linear-potentiometer and a force sensor. The reactions between the ground and the foot are detected by touch sensors 1 and 2. The angle sensor is used to measure the rotation angle of the ankle joint. Assembled in parallel with series Spring 2 (see Fig. 9(a)), the linear-potentiometer is utilized to measure the rotation angle of the toe joint and the force of the Spring 2 at the same time. The force between the subject and the system is measured by the force sensor.

For gait identification, we divide the walking gait cycle into seven phases. Each phase represents a unique state where the system will be controlled by a specific control strategy and perform a specific behavior. Besides, a state can switch to one another if the triggering transition requirements are meet. This method can be called finite-state control and can be describe as follows [46]:

$$A\_{\bar{l}} = f\_a(\mathbb{S}\_{\bar{l}}) \tag{19}$$

where *fa* is the action function indicating the specific output behavior *Ai* of the specific state *Si*.

$$S\_{i+1} = f\_s(S\_{i\prime}I\_i) \tag{20}$$

where *fs* is the transition function indicating the transition between two adjacent states and *Ii* represents the input triggering information.

As described, a level ground walking gait cycle begins with the heel strike of one foot and ends with the next heel strike of the same foot [20]. It is generally divided into the stance phase when the foot is on the ground and the swing phase when the foot is off the ground. To get a more accurate description of the prosthesis state, we divide each phase into different sub-phases:

1) Stance Phase:

**Controlled plantar flexion of ankle (CPA):** CPA begins at heel-strike when the ankle joint begins to plantar flex and ends at foot-flat when toe-strike occurs. The behavior of the ankle joint at this state is consistent with a linear spring response since the output joint torque is proportional to the joint angle.

**Controlled dorsiflexion of ankle (CDA):** CDA begins at foot-flat when the ankle joint begins to dorsiflex and ends when the ankle reaches the maximum dorsiflexion angle. The behavior of the ankle joint at this state can be described as a nonlinear spring.

**Powered plantar flexion of ankle (PPA):** PPA begins after CDA when the ankle joint begins to plantar flex again and ends at the instant of toe-off. The function of the ankle joint at this state is the superposition of a nonlinear spring and a torque source. This phase is the main phase that can reflects the dynamical characteristics of the ankle joint.

**Controlled dorsiflexion of toe (CDT):** CDT begins after heel-off when the toe joint is compressed and begin to plantar flex. It ends when the toe joint is compressed to specific extent. The behavior of the toe joint at this state can be modeled as a linear spring.

**Powered plantar flexion of toe (PPT):** PPT begins when the toe joint angle reaches a specific value and the toe joint begins to dorsiflex to push the body forward and upward together with the ankle joint. It ends at toe-off. The toe joint's behavior at this state can be modeled as the superposition of a linear spring and a torque source.

#### 2) Swing Phase:

**Early swing (ESW):** ESW begins at toe-off when the ankle joint and the toe joint begin to return to the equilibrium position and ends after a predefined time period when the two joints have reached back to the equilibrium position. Both of the two joints play the role of position source to reset the prosthesis to equilibrium position.

**Late swing (LSW):** LSW begins just after the ESW and ends at the next heel-strike. The toe joint and the ankle joint just keep the balanced state and get ready for the beginning of the next gait cycle. The function of the two joints can also be modeled as a position source.

Figure 10 shows the finite-state control scheme for level-ground walking with segmented foot. We define the ankle joint angle to be zero when the shank is perpendicular to the foot. From the zero position, the angle will be negative if the ankle plantar flexs and positive if the ankle dorsiflexs. The toe joint angle is defined to be zero when the joint is not compressed and to be positive we compressed to dorsiflex. To accurately identify each gait state and decide the transition between different states, we collect the information below: a) Heel contact (*H*), *H=0* indicates that the heel is off the ground and vice versa; b) Heel pressure (*FH*), *FH* indicates the pressure that the ground exerts to the heel; c) Toe contact (*T*), *T=0* indicates that the toe is off the ground and vice versa; d) Toe pressure (*FT*), *FT* indicates the pressure that the ground exerts to the toe; e)Ankle joint angle (*θa*); f) Ankle joint's angular velocity ( ˙ *θa*), ˙ *θ<sup>a</sup>* indicates the rotatory direction of the ankle joint; g) Toe joint angle (*θt*); h) Ankle torque (*Ta*); i) Stance phase time period (Δ*tstance*), Δ*tstance* can be used as an indicator of the walking speed; j) Swing phase time period (Δ*tswing*), Δ*tswing* can be used as an indicator of the walking speed. Figure 11 shows the hardware of the proposed control platform.

### **5. Experimental results**

#### **5.1. Walking performance**

For PANTOE 1, we have done several preliminary experiments to evaluate the functionality of the prototype. The amputee subject was 45 years of age, 1.70m in height and 71kg in weight.

**Figure 10.** Finite-state control for level-ground walking with segmented foot.

**Figure 11.** The hardware of the control platform.

14 Will-be-set-by-IN-TECH

joint at this state is consistent with a linear spring response since the output joint torque is

**Controlled dorsiflexion of ankle (CDA):** CDA begins at foot-flat when the ankle joint begins to dorsiflex and ends when the ankle reaches the maximum dorsiflexion angle. The behavior

**Powered plantar flexion of ankle (PPA):** PPA begins after CDA when the ankle joint begins to plantar flex again and ends at the instant of toe-off. The function of the ankle joint at this state is the superposition of a nonlinear spring and a torque source. This phase is the main

**Controlled dorsiflexion of toe (CDT):** CDT begins after heel-off when the toe joint is compressed and begin to plantar flex. It ends when the toe joint is compressed to specific

**Powered plantar flexion of toe (PPT):** PPT begins when the toe joint angle reaches a specific value and the toe joint begins to dorsiflex to push the body forward and upward together with the ankle joint. It ends at toe-off. The toe joint's behavior at this state can be modeled as the

**Early swing (ESW):** ESW begins at toe-off when the ankle joint and the toe joint begin to return to the equilibrium position and ends after a predefined time period when the two joints have reached back to the equilibrium position. Both of the two joints play the role of position source

**Late swing (LSW):** LSW begins just after the ESW and ends at the next heel-strike. The toe joint and the ankle joint just keep the balanced state and get ready for the beginning of the next gait cycle. The function of the two joints can also be modeled as a position source.

Figure 10 shows the finite-state control scheme for level-ground walking with segmented foot. We define the ankle joint angle to be zero when the shank is perpendicular to the foot. From the zero position, the angle will be negative if the ankle plantar flexs and positive if the ankle dorsiflexs. The toe joint angle is defined to be zero when the joint is not compressed and to be positive we compressed to dorsiflex. To accurately identify each gait state and decide the transition between different states, we collect the information below: a) Heel contact (*H*), *H=0* indicates that the heel is off the ground and vice versa; b) Heel pressure (*FH*), *FH* indicates the pressure that the ground exerts to the heel; c) Toe contact (*T*), *T=0* indicates that the toe is off the ground and vice versa; d) Toe pressure (*FT*), *FT* indicates the pressure that the ground

the rotatory direction of the ankle joint; g) Toe joint angle (*θt*); h) Ankle torque (*Ta*); i) Stance phase time period (Δ*tstance*), Δ*tstance* can be used as an indicator of the walking speed; j) Swing phase time period (Δ*tswing*), Δ*tswing* can be used as an indicator of the walking speed. Figure

For PANTOE 1, we have done several preliminary experiments to evaluate the functionality of the prototype. The amputee subject was 45 years of age, 1.70m in height and 71kg in weight.

*θa*), ˙

*θ<sup>a</sup>* indicates

exerts to the toe; e)Ankle joint angle (*θa*); f) Ankle joint's angular velocity ( ˙

11 shows the hardware of the proposed control platform.

**5. Experimental results**

**5.1. Walking performance**

extent. The behavior of the toe joint at this state can be modeled as a linear spring.

of the ankle joint at this state can be described as a nonlinear spring.

phase that can reflects the dynamical characteristics of the ankle joint.

superposition of a linear spring and a torque source.

to reset the prosthesis to equilibrium position.

proportional to the joint angle.

2) Swing Phase:

16 Will-be-set-by-IN-TECH 562 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

**Figure 12.** A sequence of photos captured during walking of the amputee subject.

He wore the proposed prosthesis during the experiment. The ratio between the length of the residual shank (the distance between patella to the amputated site) to that of the sound shank (measured from patella to malleolus lateralis) is 0.4m. Fig. 12 shows the walking performance.

EXO-PANTOE 1 is worn by a subject whose right ankle is injured and can not output sufficient power during walking. With the powered ankle and toe joints, EXO-PANTOE 1 is able to provide enough energy to the subject and help him relearn the normal walking gait (shown in Fig. 13).

(a) Stance phase

(b) Swing phase

**Figure 13.** Sequence pictures captured from the walking motion of the subject wearing EXO-PANTOE 1 in a walking gait cycle beginning with heel-strike. The result indicates that EXO-PANTOE 1 can assist the subject relearn the human walking gait.

562 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges Segmented Foot with Compliant Actuators and Its Applications to Lower-Limb Prostheses and Exoskeletons <sup>17</sup> Segmented Foot with Compliant Actuators and Its Applications to Lower-Limb Prostheses and Exoskeletons 563

#### **5.2. Energy consumption**

16 Will-be-set-by-IN-TECH

He wore the proposed prosthesis during the experiment. The ratio between the length of the residual shank (the distance between patella to the amputated site) to that of the sound shank (measured from patella to malleolus lateralis) is 0.4m. Fig. 12 shows the walking performance. EXO-PANTOE 1 is worn by a subject whose right ankle is injured and can not output sufficient power during walking. With the powered ankle and toe joints, EXO-PANTOE 1 is able to provide enough energy to the subject and help him relearn the normal walking gait (shown

(a) Stance phase

(b) Swing phase

**Figure 13.** Sequence pictures captured from the walking motion of the subject wearing EXO-PANTOE 1 in a walking gait cycle beginning with heel-strike. The result indicates that EXO-PANTOE 1 can assist

the subject relearn the human walking gait.

**Figure 12.** A sequence of photos captured during walking of the amputee subject.

in Fig. 13).

In order to analyze the effects of the segmented foot structure on the energetic efficiency during walking, we have measured the energy consumption of EXO-PANTOE 1 during the subject walking at his most comfortable speed (1.1*m*/*s*) in three cases. In the first case, the segmented foot is locked with a mechanical structure and the foot just acts as a single rigid plate. In the second case, Motor 2 does not work at all and the toe joint can only be bent passively. In the third case, the toe joint is active and it is able to output sufficient net positive work to the subject during the TO phase. In these three cases, the ankle joint always provides enough energy to the subject. Before the measurement of the energy consumption, in each case the subject is allowed to have a long enough training period to adapt to the exoskeleton.

As shown in Fig. 14, one can find that EXO-PANTOE 1 consumes the most energy in the first case (see Fig. 14(a)), which indicates that the segmented foot plays important role in improving energetic efficiency. The total energy consumed in the second case and the third case is close, where the segmented foot with active toe performs slightly better (see Fig. 14(b)

**Figure 14.** Energy consumption of EXO-PANTOE 1 in one stride cycle. (a)Energy consumption of EXO-PANTOE 1 when the foot is a single rigid plate. (b) Energy consumption of EXO-PANTOE 1 when the toe joint can only be bent passively. (c)Energy consumption of EXO-PANTOE 1 when the toe joint can output sufficient power.

and Fig. 14(c)). The ankle joint in the third case consumes much less energy than that in the second case. The result shows that powered toe joint can share the energy cost of the ankle joint, and enables the development of more efficient and effective powered lower-limb exoskeleton.
