Tingnan Zhang

Principles of appendage design in robots and animals determining terradynamic performance on flowable ground.

Natural substrates like sand, soil, leaf litter and snow vary widely in penetration resistance. To search for principles of appendage design in robots and animals that permit high performance on such flowable ground, we developed a ground control technique by which the penetration resistance of a dry granular substrate could be widely and rapidly varied. The approach was embodied in a device consisting of an air fluidized bed trackway in which a gentle upward flow of air through the granular material resulted in a decreased penetration resistance. As the volumetric air flow, Q, increased to the fluidization transition, the penetration resistance decreased to zero. Using a bio-inspired hexapedal robot as a physical model, we systematically studied how locomotor performance (average forward speed, v(x)) varied with ground penetration resistance and robot leg frequency. Average robot speed decreased with increasing Q, and decreased more rapidly for increasing leg frequency, ω. A universal scaling model revealed that the leg penetration ratio (foot pressure relative to penetration force per unit area per depth and leg length) determined v(x) for all ground penetration resistances and robot leg frequencies. To extend our result to include continuous variation of locomotor foot pressure, we used a resistive force theory based terradynamic approach to perform numerical simulations. The terradynamic model successfully predicted locomotor performance for low resistance granular states. Despite variation in morphology and gait, the performance of running lizards, geckos and crabs on flowable ground was also influenced by the leg penetration ratio. In summary, appendage designs which reduce foot pressure can passively maintain minimal leg penetration ratio as the ground weakens, and consequently permits maintenance of effective locomotion over a range of terradynamically challenging surfaces.

Walking and running on yielding and fluidizing ground

Presented at Robotics: Science and Systems VIII, July 09-July 13, 2012, University of Sydney, Sydney, NSW, Australia.

Ground fluidization promotes rapid running of a lightweight robot

We study the locomotor mechanics of a small, lightweight robot (DynaRoACH, 10 cm, 25 g) which can move on a granular substrate of 3 mm diameter glass particles at speeds up to 5 body length/s, approaching the performance of certain desert-dwelling animals. To reveal how the robot achieves this performance, we used high-speed imaging to capture its kinematics, and developed a numerical multi-body simulation of the robot coupled to an experimentally validated simulation of the granular medium. Average speeds measured in experiment and simulation agreed well, and increased nonlinearly with stride frequency, reflecting a change in propulsion mode. At low frequencies, the robot used a quasi-static “rotary walking” mode, in which the substrate yielded as legs penetrated and then solidified once vertical force balance was achieved. At high frequencies the robot propelled itself using the speed-dependent fluid-like inertial response of the material. The simulation allows variation of parameters which are inconvenient to modify in experiment, and thus gives insight into how substrate and robot properties change performance. Our study reveals how lightweight animals can achieve high performance on granular substrates; such insights can advance the design and control of robots in deformable terrains.

The effectiveness of resistive force theory in granular locomotiona)

Resistive force theory (RFT) is often used to analyze the movement of microscopic organisms swimming in fluids. In RFT, a body is partitioned into infinitesimal segments, each of which generates thrust and experiences drag. Linear superposition of forces from elements over the body allows prediction of swimming velocities and efficiencies. We show that RFT quantitatively describes the movement of animals and robots that move on and within dry granular media (GM), collections of particles that display solid, fluid, and gas-like features. RFT works well when the GM is slightly polydisperse, and in the “frictional fluid” regime such that frictional forces dominate material inertial forces, and when locomotion can be approximated as confined to a plane. Within a given plane (horizontal or vertical) relationships that govern the force versus orientation of an elemental intruder are functionally independent of the granular medium. We use the RFT to explain features of locomotion on and within granular media including kinematic and muscle activation patterns during sand-swimming by a sandfish lizard and a shovel-nosed snake, optimal movement patterns of a Purcell 3-link sand-swimming robot revealed by a geometric mechanics approach, and legged locomotion of small robots on the surface of GM. We close by discussing situations to which granular RFT has not yet been applied (such as inclined granular surfaces), and the advances in the physics of granular media needed to apply RFT in such situations.

AN AUTOMATED SYSTEM FOR SYSTEMATIC TESTING OF LOCOMOTION ON HETEROGENEOUS GRANULAR MEDIA

Particulate substrates like deserts or Martian terrain are often composed of collections of particles of different sizes and shapes. While much is known about how robots can effectively locomote on hard ground and increasingly on homogeneous granular ground, the principles of locomotion over heterogeneous granular substrates are relatively unexplored. In this study we test the locomotion performance of an open-loop controlled legged robot (Xplorerbot, 15 cm, 150 g) in a trackway filled with 3 mm diameter glass “fine grains”, with two parallel lines of eight 25.4 mm diameter large glass “boulders” embedded within. We also develop an experimentally validated Discrete Element Method (DEM) simulation. In experiment and simulation, we observe three distinct modes of robot leg-ground interaction which influence locomotion performance. To systematically investigate how robot leg frequency, particle size and boulder distribution affect the interaction modes and robot speed and stability, we develop an automated system which can vary the properties of the heterogeneous granular substrate, as well as record robot locomotion performance. The system allows collection of ~200 runs/day facilitating systematic parameter exploration and comparison to simulation.

A RESISTIVE FORCE MODEL FOR LEGGED LOCOMOTION ON GRANULAR MEDIA

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.