**1. Introduction**

Robots are currently being designed based on human morphologies. Therefore, the most recent humanoid robots are technologically complex systems, with an extremely high level of mechanical and electronic integration. They are equipped with complete perceptive sys‐ tems, which enable them to interact with the human beings and to move in human environ‐ ments. However, controlling humanoid robots is difficult, particularly walking motions and balance when walking, during transitions from walking to stopping, or when the robot undergoes external thrusts. The walking and running abilities of humans have caused

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researchers to focus on muscular skeletal system properties, with a focus on improving the walking and interaction capabilities of robots.

One of the most significant properties of the mammalian muscle is compliance, that is, the capacity to adapt the muscle stiffness to various movements and interactions. When walking, the muscular compliance is implicated at a low level of control because it occurs in the muscle (the actuator) according to the required movement of the limb. Muscle compliance allows a muscle to optimize energy consumption by storing energy in passive phases and restoring energy for active phases. This intrinsic muscle stiffness control allows humans to run, walk, control walk‐halt‐walk transitions, and control posture related to external perturbations (other systems, such as the vestibular apparatus, are also involved in balancing, walking, and running processes).

### **1.1. Recent progress in articular compliance for legged robots**

Creating an artificial system that can mimic mammalian muscle behavior would represent significant progress in the field of humanoid robots [1]. This goal can be achieved via numerous advancements [2, 3].

### *1.1.1. Compliant actuators*

Special mechanical systems can be built that store and restore energy based on the walking phases. This approach, which is known as passive dynamic walking, was pioneered by McGeer more than a decade ago [4] and has been analyzed by several studies [5–8]. Passive dynamic walking is attractive due to its elegance and simplicity. However, active feedback control is necessary to achieve walking on the ground and varying slopes, for robustness related to uncertainties and disturbances, and to regulate the walking speed. The first active feedback control that exploits passive walking appeared for planar bipeds [6, 9–11]. Three‐dimensional (3‐D) passive walking was studied [12, 13], the results [11] of which were extended to the general case of 3‐D walking [8]. An interesting extension of these concepts uses geometric reduction methods to generate stable 3‐D walking from two‐dimensional (2‐D) gaits [14]. Robustness issues were addressed by using total energy as a storage function in the hybrid passivity framework [15].

Another manner in which to achieve compliance is to design actuators that reproduce the properties of mammalian muscles. These novel elastic actuators can be regarded as an artificial "muscle‐tendon" [16]. The McKibben pneumatic muscle actuator [17–19] produces a high force at low speeds, but these actuators are difficult to control because of their nonlinearity depend‐ ing on air temperature and pressure. However, artificial pneumatic muscles or elastic actuators can be used to actuate joints of bipedal robot and their natural compliance improves robustness to postural and motion in jumping experiments [20, 21].

Alternatives, such as piezoelectric actuator, electroactive polymers, or shape memory alloys, also possess energy disadvantages. Emerging technologies, such as those based on electroac‐ tive polymers, can provide high power density with reasonable energy efficiency [22]. Dielectric elastomer‐based linear actuators are interesting; however, their thrust profile can be improved in terms of stiffness characteristics [23]. These techniques are very promising, but no electroactive polymer has yet yielded a walk within a biped.

### *1.1.2. Compliant joint with mechanical elasticities*

researchers to focus on muscular skeletal system properties, with a focus on improving the

One of the most significant properties of the mammalian muscle is compliance, that is, the capacity to adapt the muscle stiffness to various movements and interactions. When walking, the muscular compliance is implicated at a low level of control because it occurs in the muscle (the actuator) according to the required movement of the limb. Muscle compliance allows a muscle to optimize energy consumption by storing energy in passive phases and restoring energy for active phases. This intrinsic muscle stiffness control allows humans to run, walk, control walk‐halt‐walk transitions, and control posture related to external perturbations (other systems, such as the vestibular apparatus, are also involved in balancing, walking, and running

Creating an artificial system that can mimic mammalian muscle behavior would represent significant progress in the field of humanoid robots [1]. This goal can be achieved via numerous

Special mechanical systems can be built that store and restore energy based on the walking phases. This approach, which is known as passive dynamic walking, was pioneered by McGeer more than a decade ago [4] and has been analyzed by several studies [5–8]. Passive dynamic walking is attractive due to its elegance and simplicity. However, active feedback control is necessary to achieve walking on the ground and varying slopes, for robustness related to uncertainties and disturbances, and to regulate the walking speed. The first active feedback control that exploits passive walking appeared for planar bipeds [6, 9–11]. Three‐dimensional (3‐D) passive walking was studied [12, 13], the results [11] of which were extended to the general case of 3‐D walking [8]. An interesting extension of these concepts uses geometric reduction methods to generate stable 3‐D walking from two‐dimensional (2‐D) gaits [14]. Robustness issues were addressed by using total energy as a storage function in the hybrid

Another manner in which to achieve compliance is to design actuators that reproduce the properties of mammalian muscles. These novel elastic actuators can be regarded as an artificial "muscle‐tendon" [16]. The McKibben pneumatic muscle actuator [17–19] produces a high force at low speeds, but these actuators are difficult to control because of their nonlinearity depend‐ ing on air temperature and pressure. However, artificial pneumatic muscles or elastic actuators can be used to actuate joints of bipedal robot and their natural compliance improves robustness

Alternatives, such as piezoelectric actuator, electroactive polymers, or shape memory alloys, also possess energy disadvantages. Emerging technologies, such as those based on electroac‐ tive polymers, can provide high power density with reasonable energy efficiency [22]. Dielectric elastomer‐based linear actuators are interesting; however, their thrust profile can be

walking and interaction capabilities of robots.

**1.1. Recent progress in articular compliance for legged robots**

to postural and motion in jumping experiments [20, 21].

processes).

advancements [2, 3].

*1.1.1. Compliant actuators*

48 Recent Advances in Robotic Systems

passivity framework [15].

Other approaches consist of developing new mechanisms in the robot actuators. Springs can be attached across the knee joints in parallel with the knee actuators [24], or a spring can be inserted in series with the actuator and thus reduce the energy consumption [25–27, 45]. This has been demonstrated for running, where tendons may be responsible for half or more of the overall work of the musculo‐tendinous system [28]. However, the tendons could yield the required leg speed with only a small active work production, such as that from the transfer phase [29, 30] or from slow walking to fast running [31]. The necessary "push‐off" phase, which allows humans to walk at all speeds, also benefits from elastic energy storage in the Achilles tendon [32, 33]. The springs could also be arranged in parallel with the actuators so that no active force is required to initiate these springs. The Delft biped [36] applies this principle with springs (and MacKibben muscles) at the ankles, which provides extended support for the leg and helps reduce collision losses. Although these principles can reduce the energy consump‐ tion, they tend to be poorly suited for theoretical control law designs. Mechanical systems (stops, clutches, latches, etc.) introduce nonlinearities, which are generally incompatible with traditional control approaches. The linear springs that store and return the energy introduce natural oscillation modes, which must be further identified and controlled. Adding elastic knees to biped robots offers more elastic gaits [34]. Knee prosthesis including elastic actuators positioned in parallel to reproduce agonist‐antagonist muscle actions increases enhanced comfort of the human walking [35].

### *1.1.3. Compliant joint based on special control algorithms*

In contrast to the insert compliance of the mechanical limb or actuator design, the compliance effect can be achieved via a DC motor control algorithm [44]. Online controllers can be used for maintaining dynamic stability of humanoid robots. Mixing damping joint and damping controller increases the balance of the robot [37].

One such approach consists of adapting the proportional integral derivative (PID) gains of the DC motor control loop in real time, according to a specific control law that explains the compliance behavior. For example, if this law represents a muscle model, then it can theoret‐ ically reproduce responses that are similar to those observed in the musculo‐skeletal system. This approach then possesses the benefits of electric motors and those of human muscle without adding any physical elements to the robot. Nevertheless, this approach requires a muscle model.

Studies have mimicked muscle behavior using a DC motor and PID controller [38]. This muscle emulator (**Figure 1**) uses a muscle model developed based on a neural network autoregressive exogenous (NNARX) input structure. This NNARX was trained to learn data issued from experimentation described by Gollee and Donaldson et al. in [30, 39]. The PID parameters are tuned using an multi‐layer perceptron MLP network with a special indirect online learning algorithm. The learning algorithm calculation is performed based on a model of the DC motor. The NNARX muscle model output is used as a reference for the DC motor control loop, in a model following control loop. The results show that the physical system was successfully forced to behave like the muscle model within acceptable error margins. This technique was able to physically emulate a nonlinear muscle model based on a DC motor with a PID controller tuned by a neural network (NN), enabling a robot to walk like a human. Using neural actuator, identification is possible when the actuator model is uncertain.

The rest of this chapter analyses the walking efficiency of a 3D simulated biped robot when the muscle emulator is implemented or not implemented in the robot's knees. The work focuses on the robustness of the dynamic walk during walk‐halt‐stop transitions and when external unknown forces unbalance the walking robot. The simulation results show that articular trajectories with the muscle emulator approach human trajectories and that the total motor power consumption is significantly reduced.

This chapter is organized as follows. After this introduction, Section 2 presents the robot and simulator, and summarizes the walking control approach presented in [40, 41]. The control algorithm implementation is described and the results are analyzed in Section 3. In addition, the results are compared and discussed. Section 4 provides the conclusions.

**Figure 1.** Block diagrams of the muscle emulator. *y(t)* is the torque output of the DC motor, *yd(t)* is the output of the muscle model, *r(t)* is the articular command, and *I(t)* is the input signals vector based on *e(t),e(t-1),e(t-2)* and *ρ(t)* which provides information on the fast variations of *r(t)*.
