717 research outputs found

    On the periodic motions of simple hopping robots

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    Discrete dynamical systems theory is applied to the analysis of simplified hopping robot models. A one-dimensional vertical hopping model that captures both the vertical hopping dynamics and nonlinear control algorithm is reviewed. A more complicated two-dimensional model that includes both forward and vertical hopping dynamics and a foot placement algorithm is presented. These systems are analyzed using a Poincare return map and hopping behavior is investigated by constructing the return map bifurcation diagrams with respect to system parameters. The diagrams show period doubling leading to chaotic behavior. Using the vertical model results as a guide, dynamic behaviour of the planar hopping system is interpreted

    Exploring Passive Dynamics in Legged Locomotion

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    A common observation among legged animals is that they move their limbs differently as they change their speed. The observed distinct patterns of limb movement are usually referred to as different gaits. Experiments with humans and mammals have shown that switching between different gaits as locomotion speed changes, enables energetically more economical locomotion. However, it still remains unclear why animals with very different morphologies use similar gaits, where these gaits come from, and how they are related. This dissertation approaches these questions by exploring the natural passive dynamic motions of a range of simplified mechanical models of legged locomotion. Recent research has shown that a simple bipedal model with compliant legs and a single set of parameters can match ground reaction forces of both human walking and running. As first contribution of this dissertation, this concept is extended to quadrupeds. A unified model is developed to reproduce many quadrupedal gaits by only varying the initial states of a motion. In addition, the model parameters are optimized to match the experimental data of real horses, as measured by an instrumented treadmill. It is shown that the proposed model is able to not only create similar kinematic motion trajectories, but can also explain the ground reaction forces of real horses moving with different gaits. In order to reveal the mechanical contribution to gaits, the simplistic bipedal and quadrupedal models are then augmented to have passive swing leg motions by including torsional springs at the hip joints. Through a numerical continuation of periodic motions, this work shows that a wide range of gaits emerges from a simple bouncing-in-place motion starting with different footfall patterns. For both, bipedal and quadrupedal models, these gaits arise along one-dimensional manifolds of solutions with varying total energy. Through breaking temporal and spatial symmetries of the periodic motions, these manifolds bifurcate into distinct branches with various footfall sequences. That is, passive gaits are obtained as different oscillatory motions of a single mechanical system with a single set of parameters. By reproducing a variety of gaits as a manifestation of the passive dynamics of unified models, this work provides insights into the underlying dynamics of legged locomotion and may help design of more economical controllers for legged machines.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147585/1/ganzheny_1.pd

    A robust sagittal plane hexapedal running model with serial elastic actuation and simple periodic feedforward control

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    In this article we present a sagittal plane, sprawled posture hexapedal running model with distributed body inertia, massless legs and serial elastic actuation at the hips as well as along the telescoping legs. We show by simulation that simple, periodic, feedforward controlled actuation is sufficient to obtain steady period 1 running gaits at twice the actuation frequency. We observe a nearly linear relation of average running speed and actuation frequency. The ground reaction profiles of the legs show leg specialization as observed in running insects. Interleg phasing has a strong influence on the foot fall sequence and thus the overall body dynamics. While the single leg ground reaction force profiles show little dependency on interleg actuation phase the total reaction force does. Thus, depending on the interleg actuation phase body motions without flight phase are observed as well as body motions and total ground reaction forces that show similarities to those obtained for the spring loaded inverted pendulum model. Further, we show that including leg damping and a ground friction model the periodic orbits have a large region of attraction with respect to the initial conditions. Additionally, the model quickly rejects step up and step down disturbances as well as force impulses. Finally, we briefly discuss the energetics of the hexapedal running model

    Nonholonomic motion planning: steering using sinusoids

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    Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given

    The Penn Jerboa: A Platform for Exploring Parallel Composition of Templates

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    We have built a 12DOF, passive-compliant legged, tailed biped actuated by four brushless DC motors. We anticipate that this machine will achieve varied modes of quasistatic and dynamic balance, enabling a broad range of locomotion tasks including sitting, standing, walking, hopping, running, turning, leaping, and more. Achieving this diversity of behavior with a single under-actuated body, requires a correspondingly diverse array of controllers, motivating our interest in compositional techniques that promote mixing and reuse of a relatively few base constituents to achieve a combinatorially growing array of available choices. Here we report on the development of one important example of such a behavioral programming method, the construction of a novel monopedal sagittal plane hopping gait through parallel composition of four decoupled 1DOF base controllers. For this example behavior, the legs are locked in phase and the body is fastened to a boom to restrict motion to the sagittal plane. The platform's locomotion is powered by the hip motor that adjusts leg touchdown angle in flight and balance in stance, along with a tail motor that adjusts body shape in flight and drives energy into the passive leg shank spring during stance. The motor control signals arise from the application in parallel of four simple, completely decoupled 1DOF feedback laws that provably stabilize in isolation four corresponding 1DOF abstract reference plants. Each of these abstract 1DOF closed loop dynamics represents some simple but crucial specific component of the locomotion task at hand. We present a partial proof of correctness for this parallel composition of template reference systems along with data from the physical platform suggesting these templates are anchored as evidenced by the correspondence of their characteristic motions with a suitably transformed image of traces from the physical platform.Comment: Technical Report to Accompany: A. De and D. Koditschek, "Parallel composition of templates for tail-energized planar hopping," in 2015 IEEE International Conference on Robotics and Automation (ICRA), May 2015. v2: Used plain latex article, correct gap radius and specific force/torque number
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