By Suresh Ramasamy

A majority of mobile robots that operate in the world around us either use wheels or legs for locomotion. The reason for this is the inherent simplicity of operation in the case of wheels and easy access to environments of societal interests like buildings, stores, and warehouses in the case of legs. These modes of locomotion generally perform poorly in environments with either heterogeneous ground or deformable substrates like sand, mud, and soil. The diversity of locomotion methods employed successfully by different animals in these harsh environments suggest alternative modes of locomotion are critical for robots to operate efficiently in these environments.

A major stumbling block while studying robots which employ novel methods of locomotion is that most strong results are limited by a set of assumptions (such as the quasi-static assumption, which is essentially assuming all the forces on the robot are always in balance) or are applicable to only a particular robot morphology (like bipeds or quadrupeds). The lack of a universal framework impedes comparison of different approaches to locomotion and hinders discovering fundamental principles that apply to all locomoting systems. One approach to developing a unifying framework to analyze, design and control robotic locomotion is to determine the normal form or a small set of normal forms of the equations of motion, that can capture the mechanics of a very large class of locomoting systems. With this goal in mind, a normal form of the equations that describe mechanics of locomotion when the interaction with the environment is described by a nonholonomic constraint (In locomotion analysis, a constraint is holonomic if it relates the shape of the robot to the position of the robot. All other types of constraints are classied as nonholonomic constraints.) was presented in [1]. My long term research goal is to develop, understand and use these normal forms to create frameworks that simplify locomotion analysis and help identify optimal locomotion strategies for robotic systems that employ novel methods of actuation.

For robots operating in a fluid, the origin of the drag force it experiences lies in the need to displace the particles of the fluidout of the way of a moving object. At low velocities, the movement of the fluid is smooth and the faster the object moves, the greater is the amount of fluid it has to displace. This leads to a linear relationship between the velocity of the robot and the drag force it experiences. This causes the equations of motion to take the form presented in [1]. The motion of paramecia-like vehicles (which move by an interaction of a periodically vibrating boundary and the fluid) can also be described by equations that take the form presented in [1]. So the normal form presented in [1] is already representative of a large class of locomoting systems. My short term research goal is taking advantage of the structure introduced by the normal form introduced in [1] to develop a framework that identifies optimal gaits for locomoting systems.

References
[1] J.P. Ostrowski and J.W. Burdick. The geometric mechanics of undulatory robotic locomotion. Interna-
tional Journal of Robotics Research, 17(7):683{702, 1998.

Suresh Ramasamy is pursuing a dual doctoral degree in robotics and mechanical engineering at Oregon State University.
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