Obstacle Avoidance Path Planning for Worm-like Robot Using Bézier Curve.

Worm-like robots have demonstrated great potential in navigating through environments requiring body shape deformation. Some examples include navigating within a network of pipes, crawling through rubble for search and rescue operations, and medical applications such as endoscopy and colonoscopy. In this work, we developed path planning optimization techniques and obstacle avoidance algorithms for the peristaltic method of locomotion of worm-like robots. Based on our previous path generation study using a modified rapidly exploring random tree (RRT), we have further introduced the Bézier curve to allow more path optimization flexibility. Using Bézier curves, the path planner can explore more areas and gain more flexibility to make the path smoother. We have calculated the obstacle avoidance limitations during turning tests for a six-segment robot with the developed path planning algorithm. Based on the results of our robot simulation, we determined a safe turning clearance distance with a six-body diameter between the robot and the obstacles. When the clearance is less than this value, additional methods such as backward locomotion may need to be applied for paths with high obstacle offset. Furthermore, for a worm-like robot, the paths of subsequent segments will be slightly different than the path of the head segment. Here, we show that as the number of segments increases, the differences between the head path and tail path increase, necessitating greater lateral clearance margins.

An Analysis of Peristaltic Locomotion for Maximizing Velocity or Minimizing Cost of Transport of Earthworm-Like Robots.

Earthworm-like peristaltic locomotion has been implemented in >50 robots, with many potential applications in otherwise inaccessible terrain. Design guidelines for peristaltic locomotion have come from observations of biology, but robots have empirically explored different structures, actuators, and control waveform shapes than those observed in biological organisms. In this study, we suggest a template analysis based on simplified segments undergoing beam deformations. This analysis enables calculation of the minimum power required by the structure for locomotion and maximum speed of locomotion. Thus, design relationships are shown that apply to peristaltic robots and potentially to earthworms. Specifically, although speed is maximized by moving as many segments as possible, cost of transport (COT) is optimized by moving fewer segments. Furthermore, either soft or relatively stiff segments are possible, but the anisotropy of the stiffnesses is important. Experimentally, we show on our earthworm robot that this method predicts which control waveforms (equivalent to different gaits) correspond to least input power or to maximum velocity. We extend our analysis to 150 segments (similar to that of earthworms) to show that reducing COT is an alternate explanation for why earthworms have so few moving segments. The mathematical relationships developed here between structural properties, actuation power, and waveform shape will enable the design of future robots with more segments and limited onboard power.

Rapidly Exploring Random Tree Algorithm-Based Path Planning for Worm-Like Robot.

Inspired by earthworms, worm-like robots use peristaltic waves to locomote. While there has been research on generating and optimizing the peristalsis wave, path planning for such worm-like robots has not been well explored. In this paper, we evaluate rapidly exploring random tree (RRT) algorithms for path planning in worm-like robots. The kinematics of peristaltic locomotion constrain the potential for turning in a non-holonomic way if slip is avoided. Here we show that adding an elliptical path generating algorithm, especially a two-step enhanced algorithm that searches path both forward and backward simultaneously, can make planning such waves feasible and efficient by reducing required iterations by up around 2 orders of magnitude. With this path planner, it is possible to calculate the number of waves to get to arbitrary combinations of position and orientation in a space. This reveals boundaries in configuration space that can be used to determine whether to continue forward or back-up before maneuvering, as in the worm-like equivalent of parallel parking. The high number of waves required to shift the body laterally by even a single body width suggests that strategies for lateral motion, planning around obstacles and responsive behaviors will be important for future worm-like robots.

Turning in Worm-Like Robots: The Geometry of Slip Elimination Suggests Nonperiodic Waves.

Inspired by earthworms, soft robots have demonstrated locomotion using segments with coupled length-wise elongation and radial contraction. However, peristaltic turning has primarily been studied empirically. Surface-dependent slip, which results in frictional forces that deform the body segments, makes accurate models challenging and limited to a specific robot and environment. Here, instead of modeling specific surfaces and segments, we take a geometric approach to analyzing the constraints that result from elimination of slip for the general case of peristaltic locomotion. Thus, our abstract two-dimensional model applies to many different mechanical designs (e.g., fluidic actuation, origami, woven mesh). Specifically, we show how turning is limited by segment range of motion, which means that more than one wave will be required to completely reorient the body in an environment where slip is not possible. As a result, to eliminate slip, segments must undergo nonperiodic shape changes. By representing segments as isosceles trapezoids with reasonable ranges of motion, we can determine control waves that in simulation do not require slip. These waves follow from an initial "reach" (i.e., kinematic movement range) of the second segment. A strategy for choosing the second segment reach is proposed based on evaluating long-term turn stability. To demonstrate the value of the approach, we applied the nonperiodic waveform (NPW) to our earthworm-inspired soft robot, Compliant Modular Mesh Worm with Steering (CMMWorm-S). With the NPW, the robot slips less when compared with a naive periodic waveform, where each segment of the robot has the same kinematic reach of each wave, as indicated by the difference between predicted and actual body position over multiple waves. Using an NPW for turning, we observe a decrease in prediction error compared with a naive periodic waveform by 66%. Thus, while our model ignores many factors (inertial dynamics, radial deformation, surface forces), the resulting turn strategies can improve kinematic motion prediction for planning. The theoretical constraints on NPWs that eliminate slip during turning will help robot designers make application-specific design choices about body stiffness, frictional properties, body length, and degrees of freedom.

Design and Actuation of a Fabric-Based Worm-Like Robot.

Soft-bodied animals, such as earthworms, are capable of contorting their body to squeeze through narrow spaces, create or enlarge burrows, and move on uneven ground. In many applications such as search and rescue, inspection of pipes and medical procedures, it may be useful to have a hollow-bodied robot with skin separating inside and outside. Textiles can be key to such skins. Inspired by earthworms, we developed two new robots: FabricWorm and MiniFabricWorm. We explored the application of fabric in soft robotics and how textile can be integrated along with other structural elements, such as three-dimensional (3D) printed parts, linear springs, and flexible nylon tubes. The structure of FabricWorm consists of one third the number of rigid pieces as compared to its predecessor Compliant Modular Mesh Worm-Steering (CMMWorm-S), while the structure of MiniFabricWorm consists of no rigid components. This article presents the design of such a mesh and its limitations in terms of structural softness. We experimentally measured the stiffness properties of these robots and compared them directly to its predecessors. FabricWorm and MiniFabricWorm are capable of peristaltic locomotion with a maximum speed of 33 cm/min (0.49 body-lengths/min) and 13.8 cm/min (0.25 body-lengths/min), respectively.