Explore the fascinating intersection of biology and robotics in this 50-minute lecture from the Society for Industrial and Applied Mathematics. Delve into the mathematics behind biologically inspired design, examining how natural systems like crawling snails, digging clams, and swimming microorganisms have evolved to perform tasks optimally within physical constraints. Learn how these biological principles can guide engineering design and provide insights into the form and function of living organisms. Discover the development of novel robotic diggers and crawlers based on snail and clam mechanics, and investigate the crucial role of mathematics in designing, controlling, and evaluating unconventional robotic systems. Follow along as the lecturer covers topics such as optimization, bio-inspired dynamic anchoring, genetic algorithms, and optimal kinematics, culminating in practical applications like the RoboSnail and strategies for recognizing outstanding engineering design.