# A Hexapod Robot with Non-Collocated Actuators
## 1 Introduction  
Wheeled robots can efficiently move on flat surfaces, but they become ineffective as soon as they encounter rough and uneven environments, which comprise the majority of the Earth's surface. For such terrains, legged robots simply always outperform wheeled robots. Hence, the development of a legged robot is motivated by the need to maneuver over rough terrains for outdoor activities.  
The challenge of developing a legged robot lies in one primary fact: how to generate the legged motion without tumbling. In 1968, [PERSON] and [PERSON] [1; 2] proposed the center of gravity projection (COG) method, where the legged robot is statically stable if the horizontal projection of its COG lies inside the support polygon, defined as the convex polygon formed by connecting footprints. [PERSON] [3] proposed a generalized COG in 1976 called the COP (center of pressure) method, wherein a robot is dynamically stable if the projection of the COG along the direction of the resultant force acting on the COG lies inside the support polygon. A variety of legged robots, including quadruped, hexapod, and octopod robots commonly practice the above methods [4; 5; 6]. On the other hand, bipedal robots favor the ZMP (zero moment point) method, first defined by [PERSON] and [PERSON] [7; 8] in 1969, stating that a robot is stable if the moment about the COP at its supporting foot is zero.  
Meanwhile, two distinct methodologies evolved and were later introduced into robotics-- that is, fuzzy theories and neural networks. Fuzzy theories [9; 10; 11] address the imprecision of systems by defining the fuzzy numbers or fuzzy sets that can be expressed in linguistic terms. For instance, the technology for finding the best value of foot acceleration for a given trajectory can be achieved by using a very simple Mamdani fuzzy inference system [12]. Once the foot acceleration function has been obtained, the real-time implementation of the fuzzy reasoning process can be optimized [13; 14]. Neural networks [15; 16; 17] are able to represent complex nonlinear relationships and are good at classifying patterns into preselected categories used in the training process. One important observation from neuroscience is that the CPG (central pattern generator) [18; 19] located in the spinal cord is an autonomous device generating rhythmic behaviors such as locomotion, requiring neither peripheralsensor feedback nor the regulation command from the brain-stem. Hybrid schemes using either fuzzy controllers or neural networks to implement bionic control are appealing, and have been conducted extensively in many articles (e.g., [20; 21; 22; 23; 24; 25; 26; 27]).  
We found that all of the legged robots under discussion are designed with collocated actuators. That is, each joint is mounted with an actuator so that the number of actuators is usually high. The adverse effects of using a great number of actuators include increasing the challenge of algorithms to control legged motions, degrading the loading capacity, and raising the cost of construction. This inspired us to overcome these weaknesses before resorting to other techniques. Hence, we designed an innovative mechanism to lessen the number of actuators. Since stable tripod gaits are generated by mechanism instead of computer, a great amount of computing resources can be released and diverted to engineering applications. In this paper, we will briefly discuss some design issues, elaborate the mechanism of reducing the number of actuators, establish the mathematical model, and introduce the relevant hardware as well as software.