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Metastable Walking Machines
, 2008
"... Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Due to limited energy budgets and limited control authority, these “disturbances” cannot always be canceled out with high-gain feedback. Minimally-actuated walkin ..."
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Cited by 42 (11 self)
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Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Due to limited energy budgets and limited control authority, these “disturbances” cannot always be canceled out with high-gain feedback. Minimally-actuated walking machines subject to stochastic disturbances no longer satisfy strict conditions for limit-cycle stability; however, they can still demonstrate impressively long-living periods of continuous walking. Here, we employ tools from stochastic processes to examine the “stochastic stability” of idealized rimless-wheel and compass-gait walking on randomly generated uneven terrain. Furthermore, we employ tools from numerical stochastic optimal control to design a controller for an actuated compass gait model which maximizes a measure of stochastic stability- the mean first-passage-time- and compare its performance to a deterministic counterpart. Our results demonstrate that walking is well-characterized as a metastable process, and that the stochastic dynamics of walking should be accounted for during control design in order to improve the stability of our machines.
3D bipedal robotic walking: Models, feedback control, and open problems
- PROCEEDINGS OF THE IFAC SYMPOSIUM ON NONLINEAR CONTROL SYSTEMS
, 2010
"... The fields of control and robotics are contributing to the development of bipedal robots that can realize walking motions with the stability and agility of a human being. Dynamic models for bipeds are hybrid in nature. They contain both continuous and discrete elements, with switching events that ..."
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Cited by 25 (16 self)
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The fields of control and robotics are contributing to the development of bipedal robots that can realize walking motions with the stability and agility of a human being. Dynamic models for bipeds are hybrid in nature. They contain both continuous and discrete elements, with switching events that are spatially driven by unilateral constraints at ground contact and impulse-like forces that occur at foot touchdown. Control laws for these machines must be hybrid as well. The goals of this paper are threefold: highlight certain properties of the models which greatly influence the control law design; present two control design approaches; and indicate some of the many open problems.
Reduction-based control of threedimensional bipedal walking robots,”
- Int. J. of Robotics Research,
, 2010
"... Abstract This paper develops the concept of reduction-based control, which is founded on a controlled form of geometric reduction known as functional Routhian reduction. We prove a geometric property of general serial-chain robots termed recursive cyclicity, identifying the inherent robot symmetrie ..."
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Cited by 16 (4 self)
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Abstract This paper develops the concept of reduction-based control, which is founded on a controlled form of geometric reduction known as functional Routhian reduction. We prove a geometric property of general serial-chain robots termed recursive cyclicity, identifying the inherent robot symmetries that we exploit with the Subrobot Theorem. This shows that any serial-chain robot can be decomposed for arbitrarily lower-dimensional analysis and control. We apply this method to construct stable directional 3-D walking gaits for a 4-DOF hipped bipedal robot. The controlled reduction decouples the biped's sagittal-plane motion from the yaw and lean modes, and on the sagittal subsystem we use passivity-based control to produce known planar limit cycles on flat ground. The unstable yaw and lean modes are separately controlled to 2-periodic orbits through their shaped momenta. We numerically verify the existence of stable 2-periodic straight-walking limit cycles and demonstrate turning capabilities for the controlled biped.
Metastable Legged-Robot Locomotion
, 2008
"... A variety of impressive approaches to legged locomotion exist; however, the science of legged robotics is still far from demonstrating a solution which performs with a level of flexibility, reliability and careful foot placement that would enable practical locomotion on the variety of rough and inte ..."
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Cited by 15 (9 self)
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A variety of impressive approaches to legged locomotion exist; however, the science of legged robotics is still far from demonstrating a solution which performs with a level of flexibility, reliability and careful foot placement that would enable practical locomotion on the variety of rough and intermittent terrain humans negotiate with ease on a regular basis. In this thesis, we strive toward this particular goal by developing a methodology for designing control algorithms for moving a legged robot across such terrain in a qualitatively satisfying manner, without falling down very often. We feel the definition of a meaningful metric for legged locomotion is a useful goal in and of itself. Specifically, the mean first-passage time (MFPT), also called the mean time to failure (MTTF), is an intuitively practical cost function to optimize for a legged robot, and we present the reader with a systematic, mathematical process for obtaining estimates of this MFPT metric. Of
Nonparametric representation of an approximated Poincaré map for learning biped locomotion
, 2009
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Minimalistic control of biped walking in rough terrain
, 2010
"... Toward our comprehensive understanding of legged locomotion in animals and machines, the compass gait model has been intensively studied for a systematic investigation of complex biped locomotion dynamics. While most of the previous studies focused only on the locomotion on flat surfaces, in this ar ..."
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Cited by 7 (0 self)
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Toward our comprehensive understanding of legged locomotion in animals and machines, the compass gait model has been intensively studied for a systematic investigation of complex biped locomotion dynamics. While most of the previous studies focused only on the locomotion on flat surfaces, in this article, we tackle with the problem of bipedal locomotion in rough terrains by using a minimalistic control architecture for the compass gait walking model. This controller utilizes an open-loop sinusoidal oscillation of hip motor, which induces basic walking stability without sensory feedback. A set of simulation analyses show that the underlying mechanism lies in the “phase locking ” mechanism that compensates phase delays between mechanical dynamics and the open-loop motor oscillation resulting in a relatively large basin of attraction in dynamic bipedal walking. By exploiting this mechanism, we also explain how the basin of attraction can be controlled by manipulating the parameters of oscillator not only on a flat terrain but also in various inclined slopes. Based on the simulation analysis, the proposed controller is implemented in a real-world robotic platform to confirm the plausibility of the approach. In addition, by using these basic principles of self-stability and
Models, Feedback Control, and Open Problems of 3D Bipedal Robot Walking
, 2014
"... The fields of control and robotics are working toward the development of bipedal robots that can realize walking motions with the stability and agility of a human being. Dynamic models for bipeds are hybrid in nature. They contain both continuous and discrete elements, with switching events that are ..."
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Cited by 5 (3 self)
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The fields of control and robotics are working toward the development of bipedal robots that can realize walking motions with the stability and agility of a human being. Dynamic models for bipeds are hybrid in nature. They contain both continuous and discrete elements, with switching events that are governed by a combination of unilateral constraints and impulse-like forces that occur at foot touchdown. Control laws for these machines must be hybrid as well. The goals of this paper are fourfold: highlight certain properties of the models which greatly influence the control law design; overview the literature; present two control design approaches in depth; and indicate some of the many open problems.
Metastability for High-Dimensional Walking Systems on Stochastically Rough Terrain
"... Abstract—Biped walking is a complex task, but usually with a natural limit-cycle behavior when walking on an even ground. However, perturbations during walking can make the robot fall. Several works addressed the issue of measuring the robustness to disturbances, and most methods study the effect of ..."
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Cited by 1 (0 self)
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Abstract—Biped walking is a complex task, but usually with a natural limit-cycle behavior when walking on an even ground. However, perturbations during walking can make the robot fall. Several works addressed the issue of measuring the robustness to disturbances, and most methods study the effect of a single perturbation. But when walking, the disturbances can be multiple, such as walking on rough terrains. The metastability is a concept that helps studying the case of multiple disturbances. The performance measure is the expectation of the time during which the robot can keep balance. However, until today, only two methods permit to measure this metrics: the discretization of all the state-space and the Monte-Carlo sampling. The former one cannot address high dimensional state-space and the latter is too much time-consuming when the falls are rare. We propose here a solution for walkers with high-dimensional states, even when falls are very rares. The novelty of this method is to rely on the property that limit-cycle walkers may return to the limit-cycle several times before to fall. This method is even extended to the cases of bifurcations or chaos. We illustrate the performance of the approach with a simulated high-dimensional actuated walking system. I.
Dominant Sources of Variability in Passive Walking
"... Abstract — This paper investigates possible sources of vari-ability in the dynamics of legged locomotion, even in its most idealized form. The rimless wheel model is a seemingly deterministic legged dynamic system, popular within the legged locomotion community for understanding basic collision dy-n ..."
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Cited by 1 (1 self)
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Abstract — This paper investigates possible sources of vari-ability in the dynamics of legged locomotion, even in its most idealized form. The rimless wheel model is a seemingly deterministic legged dynamic system, popular within the legged locomotion community for understanding basic collision dy-namics and energetics during passive phases of walking. Despite the simplicity of this legged model, however, experimental motion capture data recording the passive step-to-step dynamics of a rimless wheel down a constant-slope terrain actually demonstrate significant variability, providing strong evidence that stochasticity is an intrinsic–and thus unavoidable–property of legged locomotion that should be modeled with care when designing reliable walking machines. We present numerical comparisons of several hypotheses as to the dominant source(s) of this variability: 1) the initial distribution of the angular velocity, 2) the uneven profile of the leg lengths and 3) the distribution of the coefficients of friction and restitution across collisions. Our analysis shows that the 3rd hypothesis most accurately predicts the noise characteristics observed in our experimental data while the 1st hypothesis is also valid for certain contexts of terrain friction. These findings suggest that variability due to ground contact dynamics, and not simply due to geometric variations more typically modeled in terrain, is important in determining the stochasticity and resulting stability of walking robots. Although such ground contact variability might be an expected result in field robotics on significantly rough terrain, we again note our experimental data applies seemingly deterministic-looking terrains: our results suggest that stochastic ground collision models should play an important role in the analysis and optimization of dynamic performance and stability in robot walking. I.
Adaptive grip control on an uncertain object
"... Abstract — Maintaining the grip on an artery with a pulsating impedance, holding the steering wheel of a vehicle on a bumpy terrain, or holding a live hamster without excessive squeezing may be trivial tasks to most humans. However, a robot will find it very difficult to maintain the grip of such un ..."
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Cited by 1 (1 self)
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Abstract — Maintaining the grip on an artery with a pulsating impedance, holding the steering wheel of a vehicle on a bumpy terrain, or holding a live hamster without excessive squeezing may be trivial tasks to most humans. However, a robot will find it very difficult to maintain the grip of such uncertain objects based on real-time feedback control. This paper presents a stochastic control law to maintain the grip on an uncertain object while manipulating against external forces. The radial impedance parameters of the soft object is assumed to undergo Gaussian random variations. Here we demonstrate that the proposed model free grip controller can maintain a safe grip at two diagonally opposite points of the object merely based on the statistics of the normal force. It accomplishes this by computing a probability of grip failure to adapt the compression on the soft object. A novel optimal estimation algorithm that can concurrently estimate the unknown impedance parameters of the object and the states of the coupled dynamic system is discussed as a potential tool to be used in predictive optimal impedance control on uncertain objects. Experimental results on adaptive grip control on a cylindrical tube inflated and deflated with a Gaussian random variation has been presented to validate the algorithm. I.
