There are life forms with incredibly effective locomotion mechanisms, sensing and computation capabilities, which are invaluable sources of inspiration for researchers. One of these bio-inspired designs is snake-like robots, which their small body cross-section, intrinsic stability, manoeuvrability and hyper-redundancy make them ideal for locomotion in challenging environments. However, design, modelling and control of a snake-like robotic mechanism for effective locomotion on surfaces with irregularities is a challenging task, which requires extensive research work.

In this thesis, the design of a cost-effective modular snake robot is presented for generating pedal wave locomotion (undulatory motion in the vertical plane) on surfaces with irregularities, where the robot lifts its body parts to climb over obstacles. To design the motor torque measurement unit as a reliable and robust environmental sensing mechanism, an elastic element with the desired shape and stiffness has been designed and manufactured using easily accessible Polyurethane sheets and attached between the links and the motors to turn a conventional servo into a Series Elastic Actuator (SEA). The designed torque sensor is calibrated and the resolution and stiffness of the sensor are obtained to be 0.01𝑁. 𝑚 and 1.74 𝑁. 𝑚. 𝑟𝑎𝑑−1, respectively. In addition to the design of the SEAs, the snake robot modules are also designed and manufactured using cost-effective 3D printing method with Acrylonitrile Butadiene Styrene (ABS), which unlike existing snake robot designs are not equipped with wheels allows effective pedal wave locomotion on surfaces with irregularities. Experimentation results are also provided showing the effectiveness of the developed snake robot with SEAs for effective pedal wave motion generation.

Moreover, this thesis introduces the equations of motion of modular 2D snake robots moving in vertical plane employing SEAs for the first time. The kinematics of such 2D modular snake robot is presented in an efficient matrix form and the Euler-Lagrange equations have been constructed to model the robot. Moreover, using a spring-damper (Kelvin-Voigt) contact model, external contact forces, necessary for modelling pedal wave motion are taken into account, which unlike existing methods enables to model the effect of multiple contact points on surfaces with irregularities. Using the constructed model, pedal wave motion of the robot is simulated and the torque signals measured with the elastic element from the simulation and experimentation are compared. The correlation coefficient indicating the similarity between the signals is calculated to be 83.36% showing the validity of the dynamical model. Using the simulated and the physical robot, the effect of friction on the motion of the robot is investigated, which showed that the average speed of the pedal wave is positively correlated with the friction coefficient of the surface.

Additionally, this thesis presents Local Stiffness Control strategy, which with the help of an admittance controller, enables active control of the joint stiffness to achieve adaptive, snake robot pedal wave locomotion. The effectiveness of the proposed controller in comparison to an open-loop control strategy is shown by several experiments, which demonstrates the capability of the robot to successfully climb over an obstacle with the height of more than 55% of the diameter of the snake robot modules, which was not possible with the open-loop gait based control strategy due to side instability of the robot. Moreover, to enable the snake robot to effectively use pedal wave locomotion pattern in more challenging environments, the extend Local Stiffness Control strategy, named Tail-leading Stiffness Control (TSC) strategy is also proposed, which allows propagation of the position feedback signal along the snake body. The experimental results showing the superiority of the TSC strategy compared to both open-loop controllers and the Local Stiffness Control strategy are provided, which proved that TSC strategy with the use of both position feedback between neighbouring joints and the stiffness control concept increases the side stability of the snake robot pedal wave motion. Therefore, enables the developed snake robot with SEAs to successfully use pedal wave motion to move forward in environments with multiple irregularities.