**1. Introduction**

### **1.1. Force control**

Over the years, the premise for constructing machines and actuators is "Stiffer is better" since a stiffer actuator has larger bandwidth force control and accurate position control. On the other

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hand, the force control is difficult since it develops high forces from small displacement and a little position error can result in a large force error. For this reason, the sensor has to be very precise with good resolution. Moreover, a stiffer actuator can lead to accidents with humans in a non-structured environment.

The majority of standard robot actuation systems cannot create precise force on the robotic joints due to friction, stick-slip, backlash and reflected inertia through the transmission, cogging in motors, and pressure drop in hydraulic circuits, among others. However, even with these nonlinearities and noises on force measurements, some robots are well aligned for a position or trajectory control since the mass of the robot and actuators acts as a low-pass filter for the force on position output (Robinson, 2000).

In some tasks, such as precise load positioning and human joints actuation, a good force control is required. In this case, the force noise on the actuators will hinder the application of the standard robot actuation. To achieve a good force-controlled system, some parameters have to be measured which are force bandwidth, mechanical output impedance, dynamic range and force density. All these parameters are related with each other and are further discussed in Section 4.

Although standard robots and stiff actuators are not good in force control, the humans are. Moreover, humans have no problems in contact hard surfaces and perform precise operations. Based on this bioinspiration, Williamson (1995) began to sacrifice the bandwidth and the stiffness for more stable force control. The method applied is to place an elastic element in series with the power source which are, commonly, a DC motor with gear reduction or a hydraulic cylinder (**Figure 1**).

**Figure 1.** Series elastic actuator schematic (Williamson, 1995).

### **1.2. Series elastic actuators**

Series elastic actuator (SEA) has been successfully applied in a number of applications for almost 20 years (Pratt and Williamson, 1995). As widely reported by a number of researchers (see Pratt and Williamson, 1995; Arumugom et al., 2009; Paluska and Herr, 2006; Paine et al., 2013), SEA provides many benefits in force control of robots. Series elastic actuators have an elastic element attached with the mechanical energy source output. This configuration presents advantages over rigid actuators such as low mechanical output impedance, tolerance to impact loads, increased peak power output, and passive mechanical energy storage. These properties enable the application of SEAs in legged actuation systems and human orthotics (Pestana et al., 2010; Parietti et al., 2011).

hand, the force control is difficult since it develops high forces from small displacement and a little position error can result in a large force error. For this reason, the sensor has to be very precise with good resolution. Moreover, a stiffer actuator can lead to accidents with humans in

The majority of standard robot actuation systems cannot create precise force on the robotic joints due to friction, stick-slip, backlash and reflected inertia through the transmission, cogging in motors, and pressure drop in hydraulic circuits, among others. However, even with these nonlinearities and noises on force measurements, some robots are well aligned for a position or trajectory control since the mass of the robot and actuators acts as a low-pass filter

In some tasks, such as precise load positioning and human joints actuation, a good force control is required. In this case, the force noise on the actuators will hinder the application of the standard robot actuation. To achieve a good force-controlled system, some parameters have to be measured which are force bandwidth, mechanical output impedance, dynamic range and force density. All these parameters are related with each other and are further discussed in

Although standard robots and stiff actuators are not good in force control, the humans are. Moreover, humans have no problems in contact hard surfaces and perform precise operations. Based on this bioinspiration, Williamson (1995) began to sacrifice the bandwidth and the stiffness for more stable force control. The method applied is to place an elastic element in series with the power source which are, commonly, a DC motor with gear reduction or a

Series elastic actuator (SEA) has been successfully applied in a number of applications for almost 20 years (Pratt and Williamson, 1995). As widely reported by a number of researchers (see Pratt and Williamson, 1995; Arumugom et al., 2009; Paluska and Herr, 2006; Paine et al., 2013), SEA provides many benefits in force control of robots. Series elastic actuators have an elastic element attached with the mechanical energy source output. This configuration presents advantages over rigid actuators such as low mechanical output impedance, tolerance to impact loads, increased peak power output, and passive mechanical energy storage. These properties enable the application of SEAs in legged actuation systems and human orthotics (Pestana et

a non-structured environment.

204 Recent Advances in Robotic Systems

hydraulic cylinder (**Figure 1**).

**1.2. Series elastic actuators**

al., 2010; Parietti et al., 2011).

**Figure 1.** Series elastic actuator schematic (Williamson, 1995).

Section 4.

for the force on position output (Robinson, 2000).

**Figure 2.** Electric SEA (1) DC motor with gearbox; (2) moving sub assembly, (3) ball nut plate, (4) ball screw, (5) guide rod, (6) support plate, (7) load connection terminal, (8) moving rod, (9) and springs (10) motor angle and rods plate (Pratt et al., 2002).

**Figure 2** shows a linear electric driven SEA (Pratt et al., 2002). The DC motor with gearbox (1) drives the ball screw (4) which moves the ball nut plate (3). Ball nut plate (3) then moves the springs (9) against the moving sub-assembly (2) which is fixed to the moving rods (8), thus causing the displacement of the load connection terminal (7) and then moves the load. The guide rods (5) are fixed to the motor flange (10) and to the support plate (6) through plain bearings for the ball screw and for the moving rods (8). They move together with the moving sub-assembly (2) in which they are fixed. It follows that all the force exerted by the spindle motor assembly on the load is directly supported by the springs, which are the elastic element purposely inserted to lower the stiffness of the actuator load interface.

The SEA's designs are made under various trade-offs, and the decision parameters often are power output, volumetric size, weight, efficiency, Back-drivability, impact resistance, passive energy storage, backlash, and torque ripple. Furthermore, iterations may be necessary on components design of a SEA. Curran and Orin (2008), Hutter et al. (2009), Kong et al. (2009), and Ragonesi et al. (2011) propose rotary designs based primarily on commercially available off-the-shelf components. Lagoda et al. (2010) and Diftler et al. (2011) design a compact rotary SEA using a harmonic drive and a high-stiffness planar spring. A compact actuator can be achieved by placing linear springs coupled to rotary shafts between the motor and the chassis ground as presented in Hutter et al. (2011) and Torres-Jara and Banks (2004). Furthermore, this compact actuator employs springs with low stiffness. In order to reduce the torque require‐ ment on the spring, Kong et al. (2012) and Taylor (2011) placed the spring within the reduction phase. A promising design for SEA that is widely researched throughout the years is to apply ball screws as the primary reduction mechanism followed by a cable drive which remotely drives a revolute joint. This design takes advantage of the ball screw high efficiency even for large speed reductions (85–90%), backdrivability, impact tolerance, and do not introduce torque ripple (Edsinger-Gonzales and Weber, 2004; Gregorio et al., 1997; Pratt and Pratt, 1998). Paine et al. (2013) presented a good review of some recent progress in series elastic actuators. In this chapter, we presented a different design of SEA. In order to avoid accidents risks and components contamination, the internal components were encapsulated in a unique hollow tubular structure. This allows the substitute of the heavy structure of solid steel tubes of the reference model (Pratt et al., 2002), permitting the applications in wearable robots, exoskeletons and prostheses.

Regarding the control of series elastic actuators, as can be expected, the design of the controller is closely related to the hardware employed. Therefore, a controller parameter such as the output force can be estimated by measuring spring deflection (Kong et al., 2010), or by applying strain gauges (Pratt and Williamson, 1995). Nevertheless, a PID approach for force control suffers from stability issues if friction and backlash are too large. For this reason, an impedance control is developed, which basically is an innermost control structure with position feedback to treat the force control as a simple position or velocity control (Pratt et al., 2004; Lagoda et al., 2010). In this chapter, such idea was adopted to develop the proposed SEA controller.

### **1.3. Series elastic actuator background**

The first robot designed with SEA was the Spring Flamingo (Pratt and Pratt, 1998) which is a planar bipedal walking robot. The SEAs drive six degrees of freedom mechanism which has three degree of freedom in each leg representing hip, knee and ankle. **Figure 3** shows the Spring Flamingo, it can walk at 1.25m/s on flat terrain. Moreover, it can walk over uphill and downhill terrains up to 15 degrees slope.

**Figure 3.** Spring Flamingo (Pratt and Pratt, 1998).

The extension of the work started with the Spring Flamingo is the M2 (Robinson et al., 1999) which is a three-dimensional bipedal walking robot. For this reason, it has twelve degrees of freedom, six on each leg. Regarding one leg, the M2 has three degrees of freedom on the hip, two degrees of freedom on the ankle, and one degree of freedom on the knee. This configura‐ tion provides three-dimensional movements with the same characteristics of the Spring Flamingo. The M2 project is far more complex than the Spring Flamingo, as can be seen in **Figure 4**.

**Figure 4.** M2 (Robinson et al., 1999).

risks and components contamination, the internal components were encapsulated in a unique hollow tubular structure. This allows the substitute of the heavy structure of solid steel tubes of the reference model (Pratt et al., 2002), permitting the applications in wearable robots,

Regarding the control of series elastic actuators, as can be expected, the design of the controller is closely related to the hardware employed. Therefore, a controller parameter such as the output force can be estimated by measuring spring deflection (Kong et al., 2010), or by applying strain gauges (Pratt and Williamson, 1995). Nevertheless, a PID approach for force control suffers from stability issues if friction and backlash are too large. For this reason, an impedance control is developed, which basically is an innermost control structure with position feedback to treat the force control as a simple position or velocity control (Pratt et al., 2004; Lagoda et al., 2010). In this chapter, such idea was adopted to develop the proposed SEA controller.

The first robot designed with SEA was the Spring Flamingo (Pratt and Pratt, 1998) which is a planar bipedal walking robot. The SEAs drive six degrees of freedom mechanism which has three degree of freedom in each leg representing hip, knee and ankle. **Figure 3** shows the Spring Flamingo, it can walk at 1.25m/s on flat terrain. Moreover, it can walk over uphill and downhill

The extension of the work started with the Spring Flamingo is the M2 (Robinson et al., 1999) which is a three-dimensional bipedal walking robot. For this reason, it has twelve degrees of freedom, six on each leg. Regarding one leg, the M2 has three degrees of freedom on the hip, two degrees of freedom on the ankle, and one degree of freedom on the knee. This configura‐ tion provides three-dimensional movements with the same characteristics of the Spring

exoskeletons and prostheses.

206 Recent Advances in Robotic Systems

**1.3. Series elastic actuator background**

terrains up to 15 degrees slope.

**Figure 3.** Spring Flamingo (Pratt and Pratt, 1998).

Another lower limb robot developed with SEA is the Corndog (Krupp, 2000) which is a planar running robot with one fore and one aft leg. Therefore, it represents only the half of a dog and employs electro-mechanical series elastic actuator (**Figure 5**).

```
Figure 5. The Corndog (Krupp, 2000).
```
Series elastic technology is also applied on upper limb robots. The COG robot is a humanoid with upper torso and head (Brooks et al., 1999). It has 6 degrees of freedom on its arms which are operated with SEAs. Moreover, COG has the ability to hammering and turning a crank (**Figure 6**).

**Figure 6.** COG humanoid robot (Brooks et al., 1999).

In addition to the application on dynamic robots, SEAs have been widely studied and applied on rehabilitation and assistive technologies. Regarding assistive technologies for gait rehabil‐ itation, a compact rotary SEA for knee joint assistive exoskeleton is developed (Kong et al., 2010). Unlike the majority of SEAs with motor and gear reduction as the motor part, a worm gear is used for motor reduction due to it compactness. However, it increases the friction of the system, which makes it more difficult to control (**Figure 7**). A robust control algorithm inspired by disturbance observer is implemented for the system control.

**Figure 7.** Proposed exoskeleton for knee assistance. (a) Rotary SEA module, (b) a thigh brace, (c) a calf brace, (d) a mo‐ tor driver, (e) a DC motor, and (f) an controller (Kong et al., 2010).

Lagoda et al. (2010) designed a Series elastic actuated joint for robotic gait rehabilitation training to be applied at LOPES (Lower Extremity Powered Exoskeleton) which helps an impaired patient to training his/her gait with an assisted-as-need (AAN) approach which only provides actuated torque as needed to help the patient to complete the gait cycle.

Series elastic actuator is also employed on assistive technologies, a prosthetic knee is developed and the stiffness adjustments are described to achieve the optimum values for peak power and energy consumption for walking and running (Grimmer and Seyfarth, 2011). Results have shown large reductions in peak power and energy requirements with the proper spring selection. Moreover, SEA can mimic the human knee behavior better than the passive ap‐ proaches.

Au et al. (2007) proposed a prosthetic ankle comprised of SEA that matches size and weight of the human ankle, comparing with the passive approaches, SEA ankle prosthesis enhances the capability of mimicking the human gait (**Figure 8**).

**Figure 8.** Ankle-foot prosthesis (Au et al., 2007).

**Figure 6.** COG humanoid robot (Brooks et al., 1999).

208 Recent Advances in Robotic Systems

tor driver, (e) a DC motor, and (f) an controller (Kong et al., 2010).

In addition to the application on dynamic robots, SEAs have been widely studied and applied on rehabilitation and assistive technologies. Regarding assistive technologies for gait rehabil‐ itation, a compact rotary SEA for knee joint assistive exoskeleton is developed (Kong et al., 2010). Unlike the majority of SEAs with motor and gear reduction as the motor part, a worm gear is used for motor reduction due to it compactness. However, it increases the friction of the system, which makes it more difficult to control (**Figure 7**). A robust control algorithm

**Figure 7.** Proposed exoskeleton for knee assistance. (a) Rotary SEA module, (b) a thigh brace, (c) a calf brace, (d) a mo‐

Lagoda et al. (2010) designed a Series elastic actuated joint for robotic gait rehabilitation training to be applied at LOPES (Lower Extremity Powered Exoskeleton) which helps an impaired patient to training his/her gait with an assisted-as-need (AAN) approach which only

Series elastic actuator is also employed on assistive technologies, a prosthetic knee is developed and the stiffness adjustments are described to achieve the optimum values for peak power and energy consumption for walking and running (Grimmer and Seyfarth, 2011). Results have shown large reductions in peak power and energy requirements with the proper spring

provides actuated torque as needed to help the patient to complete the gait cycle.

inspired by disturbance observer is implemented for the system control.

Another approach for human-friendly actuators for assistive robotic application is to add a variable damping in the SEA design as shown in **Figure 9**. It can be achieved with magneto‐ rheological fluids (MR fluids).

**Figure 9.** Series elastic actuator with controlled damping (Iyer, 2012).

Although this configuration allows a human-friendly device that can be applied to design legs with agile locomotion (Garcia et al., 2011), the investigation of such devices are beyond this chapter analysis, but will be investigated in further works.
