**1. Introduction**

The grounds of construction sites or factories are often muddy or scattered with debris. Under such circumstances, wheeled vehicles used for material handling might be easily blockaded by obstacles or experience skidding on the muddy grounds. Hence, this inspires us to pursue the development of a hexapod robot to replace a wheeled vehicle. However, robots are complex and expensive machines, consisting of many actuators, sensors, transmissions, and hardware. Therefore, a method of developing a hexapod robot to reduce the cost by means of using a minimal number of actuators is proposed. In this article, a hexapod robot was conceived, designed, and built.

In the development of a legged robot, there are two primary concerns, i.e., how to generate a stable gait, so that the robot can walk without tumbling, and how to perpetually generate stable gaits. Regarding the first concern, McGhee and Frank [1,2] proposed the COG (center of gravity projection) method in 1968, stating that the legged robot is statically stable if the horizontal projection of its COG lies within the support polygon, which is defined as the convex polygon formed by connecting the footprints. Orin [3] generalized the COG method in 1976, proposing the COP (center of pressure) method, where a robot is dynamically stable if the projection of the COG, along the direction of the resultant force acting on the COG, lies within the support polygon. In 1969, Vukabratovic and Juricic [4,5] further proposed a method in favor of the biped robot called the ZMP (zero moment point) method, where a robot is stable if the moment about the COP, at its supporting foot, is zero. As to the second concern, many rhythmic movements such as locomotion, respiration, swallowing, etc., in animals, have been found to be produced by a CPG (central pattern generator) [6–11].

Neuroscientists [12] have employed a variety of techniques, including anatomical, behavioral, physiological methods, etc., to investigate the specific neural circuits and discover the mapping function in those circuits. One notable study on the locomotion of the salamander [13] proposed the CPG model based on nonlinear oscillators instead of neural network oscillators, presented numerical as well as mechanical simulations, and successfully constructed a salamander-like robot. Some studies [14–16] have addressed to the locomotion of hexapods with CPG and established mathematical models not only including the rhythmic generator, but also the interlimb coordinator, so that the hexapod can adapt to variant terrains by gait transition. Beyond bio-inspiration, a new trend of research that is noteworthy is the merging of natural and artificial components, which is defined as bio-hybrid organisms [17,18], also called bio-robots, in which an artificial component or a biological organ is incorporated into an animal or robot, respectively. These studies even investigate how the artificial agen<sup>t</sup> interacts with an animal individual or a population. So far, all studies have relied on electronic circuits or processors to implement the locomotion of legged robots.

Computers have always been thought of as nothing more than electronic devices, which is not necessarily the case. Recalling the evolution of computer science, the earlier computing devices, called calculators, invented by Blaise Pascal of France (1642) and G.W. Leibniz of Germany (1671), were built with the technology of gears. In fact, they were mechanical calculators, where data was represented through gear positioning and entered mechanically, by adjusting the initial gear positions. The output of the calculators was achieved by observing the final gear positions. Therefore, mechanical devices can be regarded as computational processors, as long as they execute certain mathematical operations. This was the inspiration to create a mechanism, or mechanical computational processor, to complement the electronic processors.

Moreover, neuroscience discovered that the CPG, located in the spinal cord, is an autonomous device, almost requiring neither the peripheral sensor feedback, nor the regulation command from the brain-stem. Therefore, a hexapod robot with biomimetic legs was built, to implement such a distributed control system, where a mechanism is proposed to serve as the CPG and a computer acts as the brain-stem, to command the autonomous device through wireless communication. In a sense, we are trying to implement the locomotion of a robot by means of a hybrid computational system, including a mechanism and electronic computers. The proposed mechanism comprises two modules, i.e., the tripod gait generator and the Theo Jansen Linkage. The tripod gait generator is a device that uses a single motor to generate a tripod gait that couples the middle leg on one side with the front and rear leg on the other side, while the TJL (Theo Jansen Linkage) rhythmically executes the legged motion.

The TJL was first introduced by Theo Jansen in 1990, where he presented a strandbeest [19], elegantly achieving a bio-inspired locomotion. This soon drew the attention of robotics researchers [20–25]. The TJL adopted in this paper is an eight-bar linkage. The interesting point is that the foot movement is a complex mathematical function, from a crank to a rocker. Nonetheless, it can be simply realized by the combination of these eight links. Consider that, if the same function is processed by an electronic device, it will consume a grea<sup>t</sup> amount of computational time and memory resources. Therefore, our proposed mechanism can alleviate the computational burden. Moreover, most hexapods are designed with collocated actuators, i.e., each joint is mounted with an actuator, so the number of actuators is usually high, reaching even 18, in number. Using a high number of actuators leads to many adverse e ffects, including increased challenge for the algorithms to control legged motions, degradation of the loading capacity, and increase of the construction cost. Hence, the present proposed design is based on non-collocated actuators, so as to minimize the number of actuators while reducing the building cost of the robot.

## **2. Mechanical Structure**

The TJL can be built using either 8 or 12 links, depending on the fabrication method of two triangular links of the TJL. If each triangular link is machined into a whole piece, the TLJ is an 8-bar linkage, whereas if each of them is assembled by three straight bars, the TLJ is a 12-bar linkage. The TJL, as adopted in this paper, is the eight-bar linkage option. It can be considered as a device to implement the mathematical function for the legged motion, as will be presented in the Kinematics section. As illustrated in Figure 1, the complexity of the foot movement implementation is not in any way reduced, but rather a passing from the computer to the mechanism occurs, i.e., coding is replaced by component designing. Once the ensemble of links is determined, it can generate a deterministic orbit.

**Figure 1.** (**a**) Assembly drawing. (**b**) Mechanical components.

The hexapod robot (Figure 2a) is divided into three modules, i.e., an upper deck, a bottom deck, and a swivel connecting the both of them (Figure 2b). In regard to manufacturing or maintenance, we should avoid diversifying the components design-wise. Instead, it is more practical to design the components shared by different modules. Hence, both decks are designed according to the same structure except their legs, which are mounted with opposing orientation. Therefore, it is adequate to study just one of them, while the bottom deck will be used for illustration purposes.

**Figure 2.** (**a**) Completed hexapod robot. (**b**) Three major modules.

The bottom deck consists of one tripod gait generator and three TJLs. The tripod gait generator is a module dispatching power from a motor to three legs (Figure 3a), each of which is a TJL.

**Figure 3.** (**a**) The module of a tripod gait generator. (**b**) Theo Jansen leg with four phases.

Let the crank of a TJL pose at four different angles, i.e. 0◦, 90◦, 180◦ and 270◦. Consequently, these four postures of the TJL are superimposed, showing the motion of the rocker in relation to the crank. In Figure 3b, the tip of the rocker draws an orbit, in a sense opposite to the rotation of the crank, as the four phase angles of the crank, labeled at the foot trajectory, help acknowledge how the rocker is related to the crank during motion.

The tripod gait module is also a device which couples the middle leg on one side with the front and rear on the other side, to rhythmically generate tripod gaits. The locomotion of the hexapod is achieved by alternating two support polygons, each being the triangle connecting the tips of the rockers (Figure 4).

**Figure 4.** (**a**) Lateral view of two support triangles. (**b**) Bottom view of two support triangles.
