Ross L. Hatton

Design of a modular snake robot

Many factors such as size, power, and weight constrain the design of modular snake robots. Meeting these constraints requires implementing a complex mechanical and electrical architecture. Here we present our solution, which involves the construction of sixteen aluminum modules and creation of the Super Servo, a modified hobby servo. To create the Super Servo, we have replaced the electronics in a hobby servo, adding such components as sensors to monitor current and temperature, a communications bus, and a programmable microcontroller. Any robust solution must also protect components from hazardous environments such as sand and brush. To resolve this problem we insert the robots into skins that cover their surface. Functions such as climbing the inside and outside of a pipe add a new dimension of interaction. Thus we attach a compliant, high-friction material to every module, which assists in tasks that require gripping. This combination of the mechanical and electrical architectures results in a robust and versatile robot.

Parameterized and Scripted Gaits for Modular Snake Robots

Snake robots, sometimes called hyper-redundant mechanisms, can use their many degrees of freedom to achieve a variety of locomotive capabilities. These capabilities are ideally suited for disaster response because the snake robot can thread through tightly packed volumes, accessing locations that people and conventional machinery otherwise cannot. Snake robots also have the advantage of possessing a variety of locomotion capabilities that conventional robots do not. Just like their biological counterparts, snake robots achieve these locomotion capabilities using cyclic motions called gaits. These cyclic motions directly control the snake robots internal degrees of freedom which, in turn, causes a net motion, say forward, lateral and rotational, for the snake robot. The gaits described in this paper fall into two categories: parameterized and scripted. The parameterized gaits, as their name suggests, can be described by a relative simple parameterized function, whereas the scripted cannot. This paper describes the functions we prescribed for gait generation and our experiences in making these robots operate in real experiments.

Generating gaits for snake robots: annealed chain fitting and keyframe wave extraction

Snake robots have many degrees of freedom, which makes them both extremely versatile and complex to control. They are often controlled with gaits, coordinated cyclic patterns of joint motion. Using gaits simplifies the design of high-level controllers, but shifts the complexity burden to designing the gaits. In this paper, we address the gait design problem by introducing two algorithms: Annealed chain fitting and Keyframe wave extraction. Annealed chain fitting efficiently maps a continuous backbone curve describing the three-dimensional shape of the robot to a set of joint angles for a snake robot. Keyframe wave extraction takes joint angles fit to a sequence of backbone curves and identifies parameterized periodic functions that produce those sequences. Together, they allow a gait designer to conceive a motion in terms three-dimensional shapes and translate them into easily manipulated wave functions, and so unify two previously disparate gait design approaches. We validate the algorithms by using them to produce rolling and sidewinding gaits for crawling and climbing, with results that match previous empirical investigations.

Geometric motion planning: The local connection, Stokes' theorem, and the importance of coordinate choice

The locomotion of articulated mechanical systems is often complex and unintuitive, even when considered with the aid of reduction principles from geometric mechanics. In this paper, we present two tools for gaining insights into the underlying principles of locomotion: connection vector fields and connection height functions . Connection vector fields illustrate the geometric structure of the relationship between internal shape changes and the system body velocities they produce. Connection height functions measure the curvature of their respective vector fields and capture the net displacement over any cyclic shape change, or gait , allowing for the intuitive selection of gaits to produce desired displacements. Height function approaches have been previously attempted, but such techniques have been severely limited by their basis in a rotating body frame, and have only been useful for calculating planar rotations and infinitesimal translations. We circumvent this limitation by introducing a notion of optimal coordinates defining a body frame that rotates very little in response to shape changes, while still meeting the requirements of the geometric mechanics theory on which the vector fields and height functions are based. In these optimal coordinates, the height functions provide close approximations of the net displacement resulting from a broad selection of possible gaits.

Why the seahorse tail is square

The curious tale of the square tail Appendages in animals are typically round, but the seahorse tail has a square cross section. Porter et al. hypothesize that this shape provides better functionality and strength than a round cross section (see the Perspective by Ashley-Ross). Three-dimensional printed models show that square cross section shapes behave more advantageously when subjected to compressive forces. By allowing greater deformation without damage and accommodating twisting deformations, square appendages passively return to their original configurations. The added flexibility of the square cross section enhances the tails ability to grasp objects. Science, this issue 10.1126/science.aaa6683; see also p. 30 3D-printed models show that square profile seahorse tails have better crush resistance and grasping ability than do circular ones. [Also see Perspective by Ashley-Ross] INTRODUCTION Although the predominant shapes of most animal tails are cylindrical, seahorse tails are square prisms. The skeleton of their tails consists of a bony armor arranged into several ringlike segments composed of four L-shaped plates that surround a central vertebra. These plates articulate with specialized joints that facilitate bending and twisting, as well as resist vertebral fracture from crushing. Muscles attached to the vertebral column transmit forces to the bony plates to provide motion for grasping and holding on to objects such as sea grasses, mangrove roots, and coral reefs, which allows them to hide and rely on camouflage when evading predators and capturing prey. RATIONALE We hypothesize that the square cross-sectional architecture of a seahorse tail improves mechanical performance in prehension (grasping ability) and armored functions (crushing resistance), relative to a cylindrical one. To test this hypothesis, we evaluated the mechanics of two three-dimensional (3D)–printed prototypes composed of articulating plates and vertebrae that mimic the natural (square prism) and a hypothetical (cylindrical) tail structure. We compared the bending, twisting, and compressive behavior of the biomimetic prototypes to show that the square profile is better than the circular one for two integrated functions: grasping ability and crushing resistance. RESULTS Seahorse tails (and the prototypes) have three primary joints that enable motion: ball-and-socket, peg-and-socket, and gliding. The ball-and-socket joints connect adjacent vertebrae and constrain bending in both the square and cylindrical prototypes to the same degree, exhibiting a behavior similar to that of a natural seahorse tail. The peg-and-socket joints connect the plates of adjacent segments and substantially restrict twisting in the prototype with a square profile, as compared with the circular one. The square geometry limits excessive torsion and preserves articulatory organization, which could provide seahorses a natural safety factor against torsion-induced damage and assist in tail relaxation. Further, the square architecture is flat (increasing surface contact) and undergoes an exterior shape change when twisted, which could allow seahorses to grasp objects with more control. Gliding joints are present at the plate overlaps along all four sides of both prototypes. Under transverse compression and impact (with a rubber mallet), the plates of the square prototype slide past one another with one degree of translation freedom (analogous to the crushing behavior of a natural seahorse tail), exhibiting a response that is stiffer, stronger, and more resilient than its cylindrical counterpart, whose plates translate and rotate on impact. CONCLUSION Exploration of these biologically inspired designs provides insight into the mechanical benefits for seahorses to have evolved prehensile tails composed of armored plates organized into square prisms. Beyond their intended practical applications, engineering designs are convenient means to answer elusive biological questions when live animal data are unavailable (for example, seahorses do not have cylindrical tails). Understanding the role of mechanics in these prototypes may help engineers to develop future seahorse-inspired technologies that mimic the prehensile and armored functions of the natural appendage for a variety of applications in robotics, defense systems, or biomedicine. Engineering designs answer biological questions. 3D-printed models that mimic a seahorse tail were designed not only for potential engineering applications but also to answer the biological question, why might tails organized into square prisms be better than cylinders? A mechanical comparison of the prototypes shows that articulated square prisms perform better than do cylinders for grasping and resistance to crushing. Whereas the predominant shapes of most animal tails are cylindrical, seahorse tails are square prisms. Seahorses use their tails as flexible grasping appendages, in spite of a rigid bony armor that fully encases their bodies. We explore the mechanics of two three-dimensional–printed models that mimic either the natural (square prism) or hypothetical (cylindrical) architecture of a seahorse tail to uncover whether or not the square geometry provides any functional advantages. Our results show that the square prism is more resilient when crushed and provides a mechanism for preserving articulatory organization upon extensive bending and twisting, as compared with its cylindrical counterpart. Thus, the square architecture is better than the circular one in the context of two integrated functions: grasping ability and crushing resistance.

Sidewinding on slopes

Sidewinding is an efficient translation gait used by snakes over flat ground. When implemented on snake robots, it retains its general effectiveness, but becomes unstable on sloped surfaces. Flattening the sidewinding motion along the surface to provide a more stable base corrects for this instability, but degrades other performance characteristics, such as efficiency and handling of rough terrain. In this paper, we identify stability conditions for a sidewinder on a slope and find a solution for the minimum aspect ratio of the sidewinding pattern needed to maintain stability. Our theoretical results are supported by experiments on snake robots. In constructing our stability analysis, we present a new, tread-based model for sidewinding that is both consistent with previous models and provides new intuition regarding the kinematics of the gait. This new interpretation of sidewinding further admits a symmetry-based model reduction that simplifies its analysis. Additionally, an intermediate stage of the theoretical work contains a comprehensive analysis of the behavior of an ellipse in rolling contact with a sloped surface.

Geometric Swimming at Low and High Reynolds Numbers

Several efforts have recently been made to relate the displacement of swimming three-link systems over strokes to geometric quantities of the strokes. In doing so, they provide powerful, intuitive representations of the bounds on a systems locomotion capabilities and the forms of its optimal strokes or gaits. While this approach has been successful for finding net rotations, noncommutativity concerns have prevented it from working for net translations. Our recent results on other locomoting systems have shown that the degree of this noncommutativity is dependent on the coordinates used to describe the problem and that it can be greatly mitigated by an optimal choice of coordinates. Here, we extend the benefits of this optimal-coordinate approach to the analysis of swimming at the extremes of low and high Reynolds numbers.

Optimizing coordinate choice for locomoting systems

Gait evaluation techniques that use Stokess theorem to integrate a systems equations of motion have traditionally been limited to finding only the net rotations or small translations produced by gaits. Recently, we have observed that certain choices of generalized coordinates allow these techniques to be extended to gaits that produce large translations. In this paper, we present a method for finding the optimal coordinate choice for this purpose, based on a Hodge-Helmholtz decomposition of the system constraints, and demonstrate the efficacy of the Stokess theorem approach over a wide variety of gaits when using the optimized coordinate choice.

Geometric visualization of self-propulsion in a complex medium.

Combining geometric mechanics theory, laboratory robotic experiment, and numerical simulation, we study the locomotion in granular media of the simplest noninertial swimmer, the Purcell three-link swimmer. Using granular resistive force laws as inputs, the theory relates translation and rotation of the body to shape changes (movements of the links). This allows analysis, visualization, and prediction of effective movements that are verified by experiment. The geometric approach also facilitates comparison between swimming in granular media and in viscous fluids.

Generating gaits for snake robots by annealed chain fitting and Keyframe wave extraction

Snake robots have many degrees of freedom, which makes them both extremely versatile and complex to control. In this paper, we address this complexity by introducing two algorithms. Annealed chain fitting efficiently maps a continuous backbone curve to a set of joint angles for a snake robot. Keyframe wave extraction takes joint angles fit to a sequence of backbone curves, and identifies parameterized periodic functions which produce those sequences. Together, they allow a designer to conceive a gait in terms three-dimensional shapes and translate them into easily manipulated wave functions. We validate the algorithms by using them to produce rolling gaits for crawling and climbing.