https://users.dimi.uniud.it/~antonio.dangelo/Robotica/2012/helper/leggedRobot/Ijspeert08NN.pdf

2008 Special Issue: Central pattern generators for locomotion control in animals and robots: A review

The spring mass model for running and hopping

Several physico-mechanical designs evolved in fish are currently inspiring robotic devices for propulsion and maneuvering purposes in underwater vehicles. Considering the potential benefits involved, this paper presents an overview of the swimming mechanisms employed by fish. The motivation is to provide a relevant and useful introduction to the existing literature for engineers with an interest in the emerging area of aquatic biomechanisms. The fish swimming types are presented, following the well-established classification scheme and nomenclature originally proposed by Breder. Fish swim either by body and/or caudal fin (BCF) movements or using median and/or paired fin (MPF) propulsion. The latter is generally employed at slow speeds, offering greater maneuverability and better propulsive efficiency, while BCF movements can achieve greater thrust and accelerations. For both BCF and MPF locomotion, specific swimming modes are identified, based on the propulsor and the type of movements (oscillatory or undulatory) employed for thrust generation. Along with general descriptions and kinematic data, the analytical approaches developed to study each swimming mode are also introduced. Particular reference is made to lunate tail propulsion, undulating fins, and labriform (oscillatory pectoral fin) swimming mechanisms, identified as having the greatest potential for exploitation in artificial systems.

/pdf/review-of-fish-swimming-modes-for-aquatic-locomotion-12dkkh88vr.pdf

Review of fish swimming modes for aquatic locomotion

Recent advances in integrative studies of locomotion have revealed several general principles. Energy storage and exchange mechanisms discovered in walking and running bipeds apply to multilegged locomotion and even to flying and swimming. Nonpropulsive lateral forces can be sizable, but they may benefit stability, maneuverability, or other criteria that become apparent in natural environments. Locomotor control systems combine rapid mechanical preflexes with multimodal sensory feedback and feedforward commands. Muscles have a surprising variety of functions in locomotion, serving as motors, brakes, springs, and struts. Integrative approaches reveal not only how each component within a locomotor system operates but how they function as a collective whole.

https://science.sciencemag.org/content/sci/288/5463/100.full.pdf

How Animals Move: An Integrative View

In this paper, the authors describe the design and control of RHex, a power autonomous, untethered, compliant-legged hexapod robot. RHex has only six actuators—one motor located at each hip— achieving mechanical simplicity that promotes reliable and robust operation in real-world tasks. Empirically stable and highly maneuverable locomotion arises from a very simple clock-driven, open-loop tripod gait. The legs rotate full circle, thereby preventing the common problem of toe stubbing in the protraction (swing) phase. An extensive suite of experimental results documents the robot’s significant “intrinsic mobility”—the traversal of rugged, broken, and obstacle-ridden ground without any terrain sensing or actively controlled adaptation. RHex achieves fast and robust forward locomotion traveling at speeds up to one body length per second and traversing height variations well exceeding its body clearance.

/pdf/rhex-a-simple-and-highly-mobile-hexapod-robot-2ektix8klv.pdf

RHex: A Simple and Highly Mobile Hexapod Robot:

The basic mechanics of human locomotion are associated with vaulting over stiff legs in walking and rebounding on compliant legs in running. However, while rebounding legs well explain the stance dynamics of running, stiff legs cannot reproduce that of walking. With a simple bipedal spring–mass model, we show that not stiff but compliant legs are essential to obtain the basic walking mechanics; incorporating the double support as an essential part of the walking motion, the model reproduces the characteristic stance dynamics that result in the observed small vertical oscillation of the body and the observed out-of-phase changes in forward kinetic and gravitational potential energies. Exploring the parameter space of this model, we further show that it not only combines the basic dynamics of walking and running in one mechanical system, but also reveals these gaits to be just two out of the many solutions to legged locomotion offered by compliant leg behaviour and accessed by energy or speed.

/pdf/compliant-leg-behaviour-explains-basic-dynamics-of-walking-1qg4aimnf7.pdf

Compliant leg behaviour explains basic dynamics of walking and running

Despite impressive variation in leg number, length, position and type of skeleton, similarities of legged, pedestrian locomotion exist in energetics, gait, stride frequency and ground-reaction force. Analysis of data available in the literature showed that a bouncing, spring-mass, monopode model can approximate the energetics and dynamics of trotting, running, and hopping in animals as diverse as cockroaches, quail and kangaroos. From an animal's mechanical-energy fluctuation and ground-reaction force, we calculated the compression of a virtual monopode's leg and its stiffness. Comparison of dimensionless parameters revealed that locomotor dynamics depend on gait and leg number and not on body mass. Relative stiffness per leg was similar for all animals and appears to be a very conservative quantity in the design of legged locomotor systems. Differences in the general dynamics of gait are based largely on the number of legs acting simultaneously to determine the total stiffness of the system. Four- and six-legged trotters had a greater whole body stiffness than two-legged runners operating their systems at about the same relative speed. The greater whole body stiffness in trotters resulted in a smaller compression of the virtual leg and a higher natural frequency and stride frequency.

Similarity in multilegged locomotion: Bouncing like a monopode

https://www.cs.cmu.edu/~hgeyer/Publications/SeyfarthEA02JBiomech.pdf

A movement criterion for running.

The storage and recovery of elastic energy in muscle-tendon springs is important in running, hopping, trotting, and galloping We hypothesized that animals select the stride frequency at which they behave most like simple spring-mass systems If higher or lower frequencies are used, they will not behave like simple spring-mass systems, and the storage and recovery of elastic energy will be reduced We tested the hypothesis by having humans hop forward on a treadmill over a range of speeds and hop in place over a range of frequencies The body was modeled as a simple spring-mass system, and the properties of the spring were measured by use of a force platform Our subjects used nearly the same frequency (the "preferred frequency," 22 hops/s) when they hopped forward on a treadmill and when they hopped in place At this frequency, the body behaved like a simple spring-mass system Contrary to our predictions, it also behaved like a simple spring-mass system when the subjects hopped at higher frequencies, up to the maximum they could achieve However, at the higher frequencies, the time available to apply force to the ground (the ground contact time) was shorter, perhaps resulting in a higher cost of generating muscular force At frequencies below the preferred frequency, as predicted by the hypothesis, the body did not behave in a springlike manner, and it appeared likely that the storage and recovery of elastic energy was reduced The combination of springlike behavior and a long ground contact time at the preferred frequency should minimize the cost of generating muscular force

Reinhard Blickhan

Papers

The spring mass model for running and hopping

Compliant leg behaviour explains basic dynamics of walking and running

Similarity in multilegged locomotion: Bouncing like a monopode

A movement criterion for running.

Hopping frequency in humans: a test of how springs set stride frequency in bouncing gaits.