No Arabic abstract
In this paper, we present an approach to study the behavior of compliant plates in granular media and optimize the performance of a robot that utilizes this technique for mobility. From previous work and fundamental tests on thin plate force generation inside granular media, we introduce an origami-inspired mechanism with non-linear compliance in the joints that can be used in granular propulsion. This concept utilizes one-sided joint limits to create an asymmetric gait cycle that avoids more complicated alternatives often found in other swimming/digging robots. To analyze its locomotion as well as its shape and propulsive force, we utilize granular Resistive Force Theory (RFT) as a starting point. Adding compliance to this theory enables us to predict the time-based evolution of compliant plates when they are dragged and rotated. It also permits more rational design of swimming robots where fin design variables may be optimized against the characteristics of the granular medium. This is done using a Python-based dynamic simulation library to model the deformation of the plates and optimize aspects of the robots gait. Finally, we prototype and test robot with a gait optimized using the modelling techniques mentioned above.
Soft robots, in contrast to their rigid counter parts, have infinite degrees of freedom that are coupled with their interaction with the environment. We consider the locomotion of an untethered robot, in the granular medium, comprised of multiple flexible flagella that rotate about an axis by a motor. Drag from the grains causes the flagella to deform and the deformed shape generates a net forward propulsion. This external drag force depends on the shape of the flagella, while the change in flagellar shape is the result of the competition between the external loading and elastic forces. We introduce a numerical tool that couples discrete differential geometry based simulation of elastic rods - our model for flagella - and a resistive force theory based model for the drag. In parallel with simulations, we conduct experiments to quantify the propulsive speed of this class of robots. We find reasonable quantitative agreement between experiments and simulations. Owing to a rod-based kinematic representation of the robot, the simulation runs faster than real-time, and, therefore, we can use it as a design tool for this class of soft robots. We find that there is an optimal rotational speed at which maximum efficiency is achieved. Moreover, both experiments and simulations show that increasing the number of flagella decreases the speed of the robot. We also gain insight into the mechanics of granular medium - while resistive force theory can successfully describe the propulsion at low number of flagella, it fails when more flagella are added to the robot.
Compared to agile legged animals, wheeled and tracked vehicles often suffer large performance loss on granular surfaces like sand and gravel. Understanding the mechanics of legged locomotion on granular media can aid the development of legged robots with improved mobility on granular surfaces; however, no general force model yet exists for granular media to predict ground reaction forces during complex limb intrusions. Inspired by a recent study of sand-swimming, we develop a resistive force model in the vertical plane for legged locomotion on granular media. We divide an intruder of complex morphology and kinematics, e.g., a bio-inspired robot L-leg rotated through uniform granular media (loosely packed ~ 1 mm diameter poppy seeds), into small segments, and measure stresses as a function of depth, orientation, and direction of motion using a model leg segment. Summation of segmental forces over the intruder predicts the net forces on both an L-leg and a reversed L-leg rotated through granular media with better accuracy than using simple one-dimensional penetration and drag force models. A multi-body dynamic simulation using the resistive force model predicts the speeds of a small legged robot (15 cm, 150 g) moving on granular media using both L-legs and reversed L-legs.
Granular media (e.g., cereal grains, plastic resin pellets, and pills) are ubiquitous in robotics-integrated industries, such as agriculture, manufacturing, and pharmaceutical development. This prevalence mandates the accurate and efficient simulation of these materials. This work presents a software and hardware framework that automatically calibrates a fast physics simulator to accurately simulate granular materials by inferring material properties from real-world depth images of granular formations (i.e., piles and rings). Specifically, coefficients of sliding friction, rolling friction, and restitution of grains are estimated from summary statistics of grain formations using likelihood-free Bayesian inference. The calibrated simulator accurately predicts unseen granular formations in both simulation and experiment; furthermore, simulator predictions are shown to generalize to more complex tasks, including using a robot to pour grains into a bowl, as well as to create a desired pattern of piles and rings. Visualizations of the framework and experiments can be viewed at https://youtu.be/OBvV5h2NMKA
We study a simple model of periodic contraction and extension of large intruders in a granular bed to understand the mechanism for swimming in an otherwise solid media. Using an event-driven simulation, we find optimal conditions that idealized swimmers must use to critically fluidize a sand bed so that it is rigid enough to support a load when needed, but fluid enough to permit motion with minimal resistance. Swimmers - or other intruders - that agitate the bed too rapidly produce large voids that prevent traction from being achieved, while swimmers that move too slowly cannot travel before the bed re-solidifies around them i.e., the swimmers locally probe the fundamental time-scale in a granular packing.
Granular media (GM) present locomotor challenges for terrestrial and extraterrestrial devices because they can flow and solidify in response to localized intrusion of wheels, limbs, and bodies. While the development of airplanes and submarines is aided by understanding of hydrodynamics, fundamental theory does not yet exist to describe the complex interactions of locomotors with GM. In this paper, we use experimental, computational, and theoretical approaches to develop a terramechanics for bio-inspired locomotion in granular environments. We use a fluidized bed to prepare GM with a desired global packing fraction, and use empirical force measurements and the Discrete Element Method (DEM) to elucidate interaction mechanics during locomotion-relevant intrusions in GM such as vertical penetration and horizontal drag. We develop a resistive force theory (RFT) to account for more complex intrusions. We use these force models to understand the locomotor performance of two bio-inspired robots moving on and within GM.