The Mathematical Model and Computer Simulation of a Quadruped Robot

Legged robots are capable of complex dynamic movements such as walking, running, and jumping. Quadruped robots have the minimum number of legs to produce a triangular support polygon that allows the robot to walk with a statically stable gait. To produce coordinated and effective motions for legged robots requires planning algorithms that exploit the natural dynamics of a system. In order to quantify performance of the motions generated by these algorithms, there is a need to develop a walking machine that can support such movements. The robot platform will help advance knowledge in locomotion by demonstrating the feasibility of novel gait patterns and strategic motions. In addition, it will promote the development of new control strategies to implement the required locomotion. However, mathematical models of the robot need to be developed to help determine important parameters and characteristics. A kinematic model was created by writing the forward and inverse kinematics of the robot. These were then used to simulate a crawl gait pattern using MATLAB programming and Solidworks modeling software. Leg designs created in SolidWorks were imported into MATLAB as standard transformation language (STL) files. The geometry was then plotted as a series of polygons in 3-D space, and animated using homogeneous transformations. The animations were used to calculate joint angles, foot trajectories, and visualize gait pattern movements. Additionally, the equations of motion for the robot were developed using Newtonian mechanics to determine the forces and torques necessary to hold its weight and achieve locomotion. By breaking down the model down to its most simple components, the torques in each joints were solved for in terms of the design parameters, reaction forces, joint positions, velocities, and accelerations. The results of the research provide a planar model of a quadruped robot that will be useful in the analysis and design of a locomotive robot platform.