Energy Comparison Between Trot, Bound, and Gallop Using a Simple Model

Power Systems Research Dept., General Motors R&D Center, Warren, Ml 48090, USA.
Journal of Biomechanical Engineering (Impact Factor: 1.78). 12/1995; 117(4):466-73. DOI: 10.1115/1.2794209
Source: PubMed


In this paper, the dynamics of quadruped trot, gallop, and bound will be examined using a simple model for the quadruped. The body of the quadruped is modeled as a uniform bar and the legs are modeled by massless springs. It will be shown that symmetry can be used to study the locomotion of this system. Using symmetry, a technique will be developed to obtain periodic solutions for each of the gaits of the quadruped model. These periodic solutions will be computed at various speeds. The energy levels will be compared for each of the gaits. The exchange of energy between its different forms will be shown for different gaits. It will be shown that even without body flexibility, there are significant savings in energy due to gait transition from trot to gallop. The energy levels will be used to predict the trot-gallop transition speed. These results will be compared with the experimental results for horses and dogs.

56 Reads
  • Source
    • "Mechanical efficiency of locomotion of the existing walking machines is very low in comparison to the living animals and low in comparison to the wheeled locomotion. Referred to the living world the expectation is that in the future the artificial legged locomotion will be one of the most energetically effective sources of transportation [3]. The designer of a walking machine must analyze of the energy consumption which determines the choice of mechanical structure, and the propulsion and powering systems. "
    [Show abstract] [Hide abstract]
    ABSTRACT: An improvement of the computer technology caused the progress in building of the developed machines, indispensable in some works which are too dangerous or onerous for humans. The article deals with prototyping problems in constructing autonomous walking machines including design problems, evaluation of required motor power, evaluation of expecting walking velocity as well as the control system design considerations etc., presenting themselves as key factors which must be taken into account while walking robots prototyping.
    Bulletin of the Polish Academy of Sciences, Technical Sciences 01/2010; 58(3). DOI:10.2478/v10175-010-0042-2 · 0.91 Impact Factor
  • Source
    • "Animals select gaits at various speeds based mainly on energy considerations, and trotting is the most energy-efficient gait for a wide range of intermediate speeds between walking and highspeed galloping [2]. Bounding algorithms have been studied [3], [4], but very few animals naturally bound due in part to its higher energy cost per stride when compared to trotting [5]. Figure 2 shows representative data taken for a dog trotting at a constant speed [7]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, an attitude control strategy is developed for a high-speed quadruped trot. The forces in the trot are redistributed among the legs to stabilize the pitch and roll of the system. An important aspect of the strategy is that the controller works to preserve the passive dynamics of quadruped trotting that are accurately predicted by the spring-loaded inverted pendulum (SLIP) model. A hybrid control strategy is presented which allows the quadruped to reach a speed of 4.75 m/s and turn at a rate of 20 deg/s in simulation under operator control. The discrete part of the controller runs once per trot step and outputs a stance thrust energy and hip angles for touchdown. The stance thrust energy accounts for losses during the step, especially at touchdown. Both the stance thrust energy and hip angles dictate the natural dynamics during stance. The force redistribution algorithm continuously operates during stance to stabilize the body's tilt axes, roll and pitch, with minimal effect on the prescribed natural dynamics. The 1.0 m/s increase in speed over previously presented work is largely due to the more dynamically-consistent force redistribution algorithm presented in this paper. The controller also tracks desired changes in heading, for which the biomimetic method of banking into a high-speed turn is also realized.
    Robotics and Automation, 2007 IEEE International Conference on; 05/2007
  • Source
    • "In nature, cursorial quadrupeds select gaits at various speeds based mainly on energy considerations. Although many animals gallop at top speeds, there is a significant range of intermediate speeds for which trotting is the most energy efficient gait [1], [2]. A number of researchers have studied the quadruped bound as a high-speed dynamic gait [3], [4], [5], but very few animals naturally bound. "
    [Show abstract] [Hide abstract]
    ABSTRACT: During a complete running stride, which involves significant periods of flight during which no legs are contacting the ground, a quadruped cannot employ static stability techniques. Instead, the corrective forces necessary to maintain dynamic stability must be applied during the short stance intervals inherent to high-speed running. Because of this complexity and the large coupled forces required to run, much of the research on the control of quadruped running has focused on planar systems which are not required to simultaneously control attitude in all three dimensions. The 3D trot controller presented here overcomes these and other complexities to control a trot up to 3.75 m/s, approximately 3 body lengths per second, and turning rates up to 20 deg/s. The biomimetic method of banking into a high-speed turn is also investigated here. Along with the details of the attitude control algorithm, a set of control principles for high-speed legged motion is presented. These principles, such as the need to counteract the disturbance of swing leg return and the usefulness of force redistribution during stance, are not dependent on a particular scale or actuation scheme and can be applied to a wider range of legged systems
    Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on; 11/2006
Show more