Results 1  10
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428
The simplest walking model: Stability, complexity, and scaling
 ASME Journal of Biomechanical Engineering
, 1998
"... We demonstrate that an irreducibly simple, uncontrolled, 2D, twolink model, vaguely resembling human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special case of the passivedynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged ..."
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Cited by 122 (8 self)
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We demonstrate that an irreducibly simple, uncontrolled, 2D, twolink model, vaguely resembling human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special case of the passivedynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at the hip, a pointmass at the hip, and infinitesimal pointmasses at the feet. The feet have plastic (noslip, nobounce) collisions with the slope surface, except during forward swinging, when geometric interference (foot scuffing) is ignored. After nondimensionalizing the governing equations, the model has only one free parameter, the ramp slope γ. This model shows stable walking modes similar to more elaborate models, but allows some use of analytic methods to study its dynamics. The analytic calculations find initial conditions and stability estimates for periodone gait limit cycles. The model exhibits two periodone gait cycles, one of which is stable when 0 <γ<0.015 rad. With increasing γ, stable cycles of higher periods appear, and the walkinglike motions apparently become chaotic through a sequence of period doublings. Scaling laws for the model predict that walking speed is proportional to stance angle, stance angle is proportional to γ 1/3, and that the gravitational power used is proportional to v 4 where v is the velocity along the slope. 1 1
Limit Cycle Control and its Application to the Animation of Balancing and Walking
, 1996
"... Seemingly simple behaviors such as human walking are difficult to model because of their inherent instability. Kinematic animation techniques can freely ignore such intrinsically dynamic problems, but they therefore also miss modeling important motion characteristics. On the other hand, the effect o ..."
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Cited by 92 (13 self)
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Seemingly simple behaviors such as human walking are difficult to model because of their inherent instability. Kinematic animation techniques can freely ignore such intrinsically dynamic problems, but they therefore also miss modeling important motion characteristics. On the other hand, the effect of balancing can emerge in a physicallybased animation, but it requires computing delicate control strategies. We propose an alternative method that adds closedloop feedback to openloop periodic motions. We then apply our technique to create robust walking gaits for a fullydynamic 19 degree offreedom human model. Important global characteristics such as direction, speed and stride rate can be controlled by changing the openloop behavior alone or through simple control parameters, while continuing to employ the same local stabilization technique. Among other features, our dynamic "human" walking character is thus able to follow desired paths specified by the animator. Keywords: control...
Evolving Complete Agents using Artificial Ontogeny
, 2003
"... In this report we introduce an artificial evolutionary system, Artificial Ontogeny (AO), that uses a developmental encoding scheme to translate a given genotype into a complete agent, which then acts in a physicallyrealistic virtual environment. Evolution is accomplished using a genetic algorithm, ..."
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Cited by 73 (5 self)
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In this report we introduce an artificial evolutionary system, Artificial Ontogeny (AO), that uses a developmental encoding scheme to translate a given genotype into a complete agent, which then acts in a physicallyrealistic virtual environment. Evolution is accomplished using a genetic algorithm, in which the genotypes are treated as genetic regulatory networks. The dynamics of the regulatory network direct the growth of the agent, and lead to the construction of both the morphology and neural control of the agent. We demonstrate that such a model can be used to evolve agents to perform nontrivial tasks, such as directed locomotion and block pushing in a noisy environment. It is shown that mutations expressed earlier in development tend to have a more variable morphological and behavioural effect than mutations expressed later in development, which tend to have a less pronounced effect. These results support the hypothesis that ontogeny provides artificial evolution with beneficial mutat...
Stochastic policy gradient reinforcement learning on a simple 3D biped
 Proc. of the 10th Int. Conf. on Intelligent Robots and Systems
, 2004
"... Abstract — We present a learning system which is able to quickly and reliably acquire a robust feedback control policy for 3D dynamic walking from a blankslate using only trials implemented on our physical robot. The robot begins walking within a minute and learning converges in approximately 20 mi ..."
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Cited by 70 (6 self)
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Abstract — We present a learning system which is able to quickly and reliably acquire a robust feedback control policy for 3D dynamic walking from a blankslate using only trials implemented on our physical robot. The robot begins walking within a minute and learning converges in approximately 20 minutes. This success can be attributed to the mechanics of our robot, which are modeled after a passive dynamic walker, and to a dramatic reduction in the dimensionality of the learning problem. We reduce the dimensionality by designing a robot with only 6 internal degrees of freedom and 4 actuators, by decomposing the control system in the frontal and sagittal planes, and by formulating the learning problem on the discrete return map dynamics. We apply a stochastic policy gradient algorithm to this reduced problem and decrease the variance of the update using a statebased estimate of the expected cost. This optimized learning system works quickly enough that the robot is able to continually adapt to the terrain as it walks. I.
The Geometric Mechanics of Undulatory Robotic Locomotion
 INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 1996
"... This paper uses geometric methods to study basic problems in the mechanics and control of locomotion. We consider in detail the case of "undulatory locomotion," in which net motion is generated by coupling internal shape changes with external nonholonomic constraints. Such locomotion pro ..."
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Cited by 63 (14 self)
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This paper uses geometric methods to study basic problems in the mechanics and control of locomotion. We consider in detail the case of "undulatory locomotion," in which net motion is generated by coupling internal shape changes with external nonholonomic constraints. Such locomotion problems have a natural geometric interpretation as a connection on a principal fiber bundle. The properties of connections lead to simplified results for studying both dynamics and issues of controllability for locomotion systems. We demonstrate the utility of this approach using a novel "Snakeboard" and a multisegmented serpentine robot which is modeled after Hirose's Active Cord Mechanism.
Virtual Model Control of a Bipedal Walking Robot
 IEEE Conference on Robotics and Automation
, 1997
"... The transformation from high level task specification to low level motion control is a fundamental issue in sensorimotor control in animals and robots. This paper describes a control scheme called Virtual Model Control that addresses this issue. Virtual Model Control is a motion control language tha ..."
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Cited by 62 (9 self)
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The transformation from high level task specification to low level motion control is a fundamental issue in sensorimotor control in animals and robots. This paper describes a control scheme called Virtual Model Control that addresses this issue. Virtual Model Control is a motion control language that uses simulations of imagined mechanical components to create forces, which are applied through real joint torques, thereby creating the illusion that the virtual components are connected to the robot. Due to the intuitive nature of this technique, designing a Virtual Model Controller requires the same skills as designing the mechanism itself. A high level control system can be cascaded with the low level Virtual Model Controller to modulate the parameters of the virtual mechanisms. Discrete commands from the high level controller would then result in fluid motion. Virtual Model Control has been applied to a physical bipedal walking robot. A simple algorithm utilizing a simple set of virtua...
Intuitive Control of a Planar Bipedal Walking Robot
 Proceedings of the IEEE International Conference on Robotics and Automation
, 1998
"... Bipedal robots are difficult to analyze mathematically. However, successful control strategies can be discovered using simple physical intuition and can be described in simple terms. Five things have to happen for a planar bipedal robot to walk. Height has to be stabilized. Pitch has to be stabilize ..."
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Cited by 61 (6 self)
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Bipedal robots are difficult to analyze mathematically. However, successful control strategies can be discovered using simple physical intuition and can be described in simple terms. Five things have to happen for a planar bipedal robot to walk. Height has to be stabilized. Pitch has to be stabilized. Speed has to be stabilized. The swing leg has to move so that the feet are in locations which allow for the stability of height, pitch, and speed. Finally, transitions from support leg to support leg must occur at appropriate times. If these five objectives are achieved, the robot will walk. A number of different intuitive control strategies can be used to achieve each of these five objectives. Further, each strategy can be implemented in a variety of ways. We present several strategies for each objective which we have implemented on a bipedal walking robot. Using these simple intuitive strategies, we have compelled a seven link planar bipedal robot, called Spring Flamingo, to walk. The r...
Exploiting Inherent Robustness and Natural Dynamics in the Control of Bipedal Walking Robots
, 2000
"... Walking is an easy task for most humans and animals. Two characteristics which make it easy are the inherent robustness (tolerance to variation) of the walking problem and the natural dynamics of the walking mechanism. In this thesis we show how understanding and exploiting these two characteristics ..."
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Cited by 57 (5 self)
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Walking is an easy task for most humans and animals. Two characteristics which make it easy are the inherent robustness (tolerance to variation) of the walking problem and the natural dynamics of the walking mechanism. In this thesis we show how understanding and exploiting these two characteristics can aid in the control of bipedal robots. Inherent robustness allows for the use of simple, low impedance controllers. Natural dynamics reduces the requirements of the controller. We present a series of simple physical models of bipedal walking. The insight gained from these models is used in the development of three planar (motion only in the sagittal plane) control algorithms. The first uses simple strategies to control the robot to walk. The second exploits the natural dynamics of a kneecap, compliant ankle, and passive swingleg. The third achieves fast swing of the swingleg in order to enable the robot to walk quickly (1.25 m s ). These algorithms are implemented on Spring Flamingo...
Limit Cycles and Their Stability in a Passive Bipedal Gait
 INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... It is wellknown that a suitably designed unpowered mechanical biped robot can "walk" down an inclined plane with a steady gait. The characteristics of the gait (e.g., velocity, time period, step length) depend on the geometry and the inertial properties of the robot and the slope of the p ..."
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Cited by 55 (2 self)
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It is wellknown that a suitably designed unpowered mechanical biped robot can "walk" down an inclined plane with a steady gait. The characteristics of the gait (e.g., velocity, time period, step length) depend on the geometry and the inertial properties of the robot and the slope of the plane. A passive
Controlled symmetries and passive walking
 In IFAC Triennial World Congress
, 2002
"... Abstract: It was shown in Spong [1999b] that the passive gaits for a planar 2DOF biped walking on a shallow slope can be made slope invariant by a passivity based control that compensates only the gravitational torques acting on the biped. In this paper we extend these results to the general case o ..."
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Cited by 50 (0 self)
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Abstract: It was shown in Spong [1999b] that the passive gaits for a planar 2DOF biped walking on a shallow slope can be made slope invariant by a passivity based control that compensates only the gravitational torques acting on the biped. In this paper we extend these results to the general case of a 3D, nDOF robot. We show that if there exists a passive walking gait, i.e. a stable limit cycle, then there exists a passivitybased nonlinear control law that renders the limit cycle slope invariant. The result is constructive in the sense that we generate the resulting control law and initial conditions from the initial conditions of the passive biped and the ground slope. This intuitively simple result relies on some wellknown symmetries in the dynamics of mechanical systems with respect to the group action of SO(3) on solution trajectories of the system. We also discuss the design of an additional passivity based control term designed to increase the basin of attraction of the passive limit cycle.