1.1. Design and Morphology

• Number of degrees of freedom (DOF): determines the operating space of the robot. By increasing of DOFs, the robot can achieve more complex trajectories. The number of DOFs also has a direct impact on robot characteristics, such as its autonomy, mass, and cost. Therefore, the number of DOFs should not be neglected in the design process. Currently, insect-inspired robotic legs are designed with between one and five DOFs per leg.
  With one DOF per leg, the robot’s maneuverability is highly limited. Depending on both leg and control designs, a one DOF per leg robot can perform a straight line walk [55] and also achieve simple rough terrain navigation if is equipped with whegs [46,56,57], comprising elements of both wheels and legs. These whegs equipped robots cannot really be considered as insect-like robots regarding their body structure. Their development tends to target navigation tasks over locomotion studies.
  With two DOFs per leg, a simplified hexapod robot can be built [58]. This choice is a good compromise between energetic cost and mobility. However, this type of robot walks mainly over flat terrains and can only perform curved leg trajectories, generating body oscillations.
  Previously, insect-based hexapod robots were built with three DOFs per leg (Table 1, in which the trochanter segment joint is merged with the femur and each joint only comprises one DOF, see Figure 2). Reflecting the standard insect leg model [59], this type of leg permits roaming in a slightly rough or slopped terrain in addition to a flat terrain walk.
   
   
  Table 1. Overview of the state-of-the-art hexapod robots developed over the last 20 years in the range 1∼27 kg. The size, given in meters, corresponds to the largest dimension between width and height. DOF stands for Degrees Of Freedom for the entire robot (note that this can include extra actuation for head control and body control). The speed represents the maximum speed measured, in meters per second. The symbol “-” represents missing data.
  
  
  More DOFs in leg morphology improve maneuverability and adaptation to challenging terrains [39,60]. Additional actuators help to adjust robot orientation according to the slope in order to increase stability [26]. Experiments have shown that 4 or 5 joints per leg enable robots to cope with high gradient slopes in any orientation (e.g., up to 50∘ slopes, see [26,61], or up to 43∘ slopes, see [14]). Unfortunately, these improvements increase the level of complexity of control commands and the robot’s price and weight (Table 2), they also concomitantly, reduce autonomy due to the high power consumption of numerous actuators.
  To sum up, from the large number of robots based on three-DOF legs, this appears to be the right compromise to walk on a flat terrain. Despite the three DOFs per leg trend, from a biological point of view, an insect possesses more than three joints with one DOF per joint [62,63], allowing it to overcome large obstacles and cross sloped and rough terrain (e.g., up to 54∘ see [64]). More complex models based more closely on insect leg kinematics are being developed [65]. Dung beetle like legs were built in 2018, the leg design was based on micro-CT scans of a real dung beetle [66]. A pair of beetle-like legs comprising four DOFs, allowing both manipulation and transportation was tested [66].
  In 2017, a hexapod robot, called Cassino Hexapod III (∼3 kg), composed of hybrid legs on a modular anthropomorphic architecture with omni-wheels, as feet at the extremities, was designed and built [67]. Each hybrid leg was built with three DOFs with the third being dedicated to rotating the wheel at the tip of the leg. This kind of hybrid locomotion is relevant for efficient rolling mobility on moderate terrain and walking mobility on extreme terrain, such as non-terrestrial exploration [68]. Hybrid locomotion by walking or by rolling allows hexapod robots to save energy, and this hybrid locomotion is a combination of an engineering approach and a bio-inspired approach. Hybrid locomotion has not been developed in this review, which is focused on the biomimetic approach.
• Structure type: this describes how leg joints are linked to each other. Two major leg designs are used on inspect-inspired robots: serial multi-shaped legs or single shape legs.
  Serial multi-shaped legs are the most common structures encountered for locomotion and navigation. By definition, an insect leg is composed of five segments (coxa, trochanter, femur, tibia, and tarsus), arranged in a particular toggled zig-zag shape, forming a sprawled posture, reducing and distributing the forces on every joint of the leg [69,70]. However, in most robotic cases, this structure is simplified to three segments per leg (coxa, femur, tibia) comprising three joints per leg, each one with only one DOF (see previous point). In this arrangement, the trochanter segment of the leg is merged with the femur, and the tarsus is generally removed. However, the tarsus makes an important contribution to the insect’s walk, serving as an adhesive pad [62,71] and allowing a better ground forces transmission with a passive spring effect. Moreover, some insects (e.g., leafhoppers) possess particular tarsal structures allowing them to jump from smooth surfaces [72]. Looking over the last decade of hexapod robots, presented in Table 1, the tarsus is often neglected, even though it represents more than 30% of the leg length [73]. Currently, few artificial tarsus designs have been developed to efficiently walk on complex terrains [74].
  Single shape legs are used on whegs robots, origami, and compliant joint robots. The specifications of these types of robots, require the absence of most tiny mechanical parts such as bearings, shafts, screws, and nuts, and involves a simplicity of manufacturing, scale and cost reduction and, backlash and structural robustness improvements. The development of single shape legs follows the advances in new materials and manufacturing techniques such as multi-material 3D printing, which allows the building of soft joint robots [75]. Particularly, the 3D printing of legs appears to be a good way to develop and simplify standard joint designs by using properties of these new materials, such as flexibility or heat deformation [76]. In this way, hexapod robot legs are tending to become closer to real insect legs, in terms of relative dimensions and mass. An important point to notice for insects, e.g., cockroaches, is that a leg corresponds to approximately 2% of the body mass [77], allowing them low inertia, high frequency strides during a walk. In comparison, insect-like robot legs represent at least 10% of the overall mass (estimated for a 2 kg robot, from Table 1). Apart from 3D printing, some materials could take over from standard aluminum or molded plastic legs, e.g., chitosan–fibroin material, inspired by insect cuticle structure [78].
  Furthermore, some other original structures have been designed; they were mainly developed when a specific animal behavior, such as jumping [79,80], is to be replicated or to satisfy some sought after design specifications like posture changes [81].
  At first glance, leg design is highly dependent on actuator technologies. However, an impressive number of improvements are still possible through subtle structural modifications, allowing huge performance improvements. Independently of the structure type, observing the current state of the art in leg design, a question presents itself: why are all the legs of a hexapod robots the same? Insect legs are different in size (Figure 3, see [82]), and not built like robot legs, wherein the six are often identical, except for a few robots mimicking insect morphology in detail (Drosophibot [18,19] and MantisBot [30,31]). In response to this question and with the technologies now available, in the 2020s, leg design is likely to become increasingly based on available micro-CT scans of real insects (e.g., [66,83] dung beetles, [84] flies, or [65] ants) in order to improve the level of complexity, fidelity, and bio-inspiration.

1.2. Cost of Transport

1.3. Actuation of the Legs

• Servomotors: the main issues with servomotors are their weight and energy efficiency. A servomotor heats up easily until it surpasses its maximum operating temperature of 70 °C, then it stops working. In addition, a servomotor is composed by definition, of a motor with high ratio gearing used to make it as stiff as possible. In this sense, such servo-based actuators differ significantly from biological actuators that may have variable stiffness and adaptable compliance. One way to implement variable stiffness is to use springs to make variable impedance actuators (VIA). As summarized in [91], VIA actuators can be classified into three categories: spring pre-loaded variation, transmission ratio changing and spring physical property alteration. VIA is certainly an approach of great interest for the design of future hexapod robots able to dynamically change the stiffness of their joints.
• Brushless motors: recent developments in smart rotating actuators based on brushless motors will permit the design of direct drive joints without gearing. The maximum specific power of electric motors with permanent magnets is 300 W/kg, which is about the same order as biological muscle [92]. Companies, such as HEBI Robotics [17] or IQ Motion, have developed integrated rotating actuators for robotic applications and for the development of mobile robots of various sizes. As the electronic driver and angular sensor are integrated into the motor, it drastically simplifies the wiring and complexity of the overall hardware architecture, which can be crucial when designing robots like hexapods that require the control of 18 actuators.
• Artificial muscles: the design of future insect-inspired robots will certainly depend on the availability of actuators able to mimic the functionalities of biological muscles. Their properties of viscoelasticity and energy dissipation leading to high compliance is the holy grail of insect-inspired actuators. Among the broad repertoire of new artificial actuators for robots (see review by [93]), non-conventional actuators like pneumatic artificial muscles (PAMs), shape memory alloys (SMAs), and electroactive polymers (EAPs) are of great interest. One particular case is HASEL actuators, which are composed of a series of pouches made of a flexible and inextensible shell that is filled with a liquid dielectric. Electrodes cover a portion of each pouch so as to progressively close when a voltage is applied thus squeezing the pouches to increase their volume [94]. HASEL actuators can be implemented in different ways and can feature a bandwidth as high as 126 Hz for the quadrant-donut HASEL and even a specific energy twice as high as mammalian skeletal muscles for the planar HASEL actuator [94]. HASEL actuators mimic the muscle-like performance of dielectric actuators (DEAs), which can be highly effective for robotic applications. They can lift more than 200 times their weight and have a peak specific power of 585 W/kg [95]. Moreover, it is worth noting that a toolkit has been developed to aid designs using HASEL actuators [96]. In addition, electro-ribbon technology, with an ability of lifting 1000 times its own weight and a contraction by 99.8% of its length, is also very promising [97]. Finally, five-DOF soft dielectric elastomer actuators have been shown to be very useful in the implementation of soft legged robots [98] which are able to walk with an alternative tripod gait as fast as 52 mm/s for a 7 Hz actuation frequency.

1.4. Force Sensing in Robotic Legs

• Leg tip/TARSE sensing: sensing at the end of the leg can be done by a tactile sensor, a pressure sensor, a three-axis force/torque sensor [100], or a compliant force sensor made with a spring [15,39]. Leg tip sensing can be easily implemented by adding an attachment point to the leg tip without requiring any modification of the robot’s structure. The cost of these tip sensors can be expensive depending on the chosen technology, but recent research has developed low-cost designs [100]. Tip force sensing is useful because it provides the robot with a terrain description. Force measurements allow the robot to understand which of its legs are in contact with the ground, or to evaluate the terrain slope, in order to both adjust its gait and plan its path [101].
• Force sensing in actuators: sensing coming from the state of actuators by current measurement [26,29,37,43] or dedicated sensors in the joints. This category of sensors simplifies the robot’s design, since the sensor is integrated within the actuator forming a compact structure. The complexity of the estimation of forces from the currents generated by the actuators is based on the robot’s leg model. To obtain an accurate leg movement, the mathematical model should reflect the robot as closely as possible, and take account of any structural deformation under various loads since no material is perfectly rigid.
• Legs with compliant structures: compliant mechanisms exploit the deformation properties of the leg segments, deformations that could be a disadvantage in other legs. Stiffer legs appear to narrow the region of stable gaits while preventing tripod contact with the ground. However, compliant legs are more capable of absorbing energy even if the leg touches down early, thus minimizing the severity of ground reaction on legs. This solution had been developed for one-joint C-shaped legs [44,45,54]. Whegs do not possess any force sensors on their legs. Compliant legs offer the possibility of placing the force sensors along the segments (such as the femur or the tibia) [101,102]. This type of sensor placement mimics the force measurements in insects, as done by campaniform sensilla mechanoreceptors [103,104].

2.1. Body Morphology

2.2. Scale Effect on Level of Performance