# A Synthetic Nervous System Controls
## 1 Introduction  
Insects are excellent models for walking robots, for two reasons. First, insects are highly successful animals that can walk through a variety of terrains. Second, decades of behavioral and neurobiological research have revealed many of the neuromechanical mechanisms that underlie this adaptive behavior. The legs of walking animals propel the body by alternating between stance and swing phases. A leg is in contact with the ground in stance phase, during which it supports and propels the body. A leg is not in contact with the ground in swing phase, during which it is returned from its position at the end of stance phase (posterior extreme position, or PEP) to its position at the beginning of stance phase (anterior extreme position, or AEP). This alternating activity is supported by central pattern generators (CPGs), networks that are capable of producing endogenous oscillatory output. Each leg joint appears to be controlled by its own CPG [1; 2]. Although periods of coordinated behavior can be observed [3], each leg joint's activity is generally decoupled from that of the others [2]. CPGs' phases are adjusted by inter-joint signals from load [4; 5; 6] and proprioceptive [7; 8] sensors, giving rise to the coordination seen during walking. When walking in different directions, some of these inter-joint reflexes are modified [9; 10], giving rise to different coordination patterns that better serve locomotion in a particular direction. Indeed, stimulating populations in the insect central complex (CX) that encode locomotion direction can change the sign and phase of inter-joint reflexes as observed in intact animals [11]. There is an interdependent relationship between neuroscience, mathematical modeling, and robotics. The neuroscience of insects promises to inspire new and adaptive robot control systems(for a review, see [12]). However, mathematical modeling of the nervous system and the body's mechanics is often a necessary intermediate step between neuroscience and robotics. First, despite decades of wonderful work, there still exist many gaps in our understanding of how insects walk. Thus, a mathematical model can be constructed that incorporates what is known, and suggests how to bridge gaps in understanding [13; 14]. Second, it is valuable to test the control method first in a simulated agent before controlling a robot. This enables a more thorough study of the function and stability of the system in a simplified environment before deploying it on a hardware system in the real world. Many models exist to address specific questions about motor control in insects. Walknet, for example, has developed into a highly successful model. It uses a combination of finite state machine (FSM) and artificial neural network (ANN) elements to coordinate the walking of kinematic models [15] and hardware robots [16]. While Walknet is a capable walking controller, it is based on behavioral, not neurobiological data, making it difficult to test neurobiological hypotheses. Another model used similar FSM elements to demonstrate how decoupled CPGs could be coordinated into stepping motions via sensory feedback [17]. This model was even used to control a single robotic leg [18]. These works were important proofs of concept for the control of a leg via sensory-coupled CPGs. However, the simplicity of the model made it difficult to produce fine-tuned motions necessary for walking. In addition, the FSM implementation leaves out the details of neural dynamics, which can produce more complicated and potentially more capable motor patterns. More recently, Hodgkin-Huxley neural models of networks in insect nervous systems have been constructed to explore the effect of such neural dynamics on locomotion [13; 19; 20; 21]. These models have enabled scientists to suggest neural and synaptic mechanisms underlying animal behavior.