Results 1 - 10
of
107
The dynamics of legged locomotion: Models, analyses, and challenges
- SIAM Review
, 2006
"... Cheetahs and beetles run, dolphins and salmon swim, and bees and birds fly with grace and economy surpassing our technology. Evolution has shaped the breathtaking abilities of animals, leaving us the challenge of reconstructing their targets of control and mechanisms of dexterity. In this review we ..."
Abstract
-
Cited by 115 (22 self)
- Add to MetaCart
(Show Context)
Cheetahs and beetles run, dolphins and salmon swim, and bees and birds fly with grace and economy surpassing our technology. Evolution has shaped the breathtaking abilities of animals, leaving us the challenge of reconstructing their targets of control and mechanisms of dexterity. In this review we explore a corner of this fascinating world. We describe mathematical models for legged animal locomotion, focusing on rapidly running insects, and highlighting achievements and challenges that remain. Newtonian body-limb dynamics are most naturally formulated as piecewise-holonomic rigid body mechanical systems, whose constraints change as legs touch down or lift off. Central pattern generators and proprioceptive sensing require models of spiking neurons, and simplified phase oscillator descriptions of ensembles of them. A full neuro-mechanical model of a running animal requires integration of these elements, along with proprioceptive feedback and models of goal-oriented sensing, planning and learning. We outline relevant background material from neurobiology and biomechanics, explain key properties of the hybrid dynamical systems that 1 underlie legged locomotion models, and provide numerous examples of such models, from the simplest, completely soluble ‘peg-leg walker ’ to complex neuro-muscular subsystems that are yet to be assembled into models of behaving animals. 1
A simply stabilized running model
- SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
, 2003
"... The spring-loaded inverted pendulum (SLIP), or monopedal hopper, is an archetypal model for running in numerous animal species. Although locomotion is generally considered a complex task requiring sophisticated control strategies to account for coordination and stability, we show that stable gaits ..."
Abstract
-
Cited by 72 (17 self)
- Add to MetaCart
(Show Context)
The spring-loaded inverted pendulum (SLIP), or monopedal hopper, is an archetypal model for running in numerous animal species. Although locomotion is generally considered a complex task requiring sophisticated control strategies to account for coordination and stability, we show that stable gaits can be found in the SLIP with both linear and “air ” springs, controlled by a simple fixed-leg reset policy. We first derive touchdown-to-touchdown Poincaré maps under the common assumption of negligible gravitational effects during the stance phase. We subsequently include and assess these effects and briefly consider coupling to pitching motions. We investigate the domains of attraction of symmetric periodic gaits and bifurcations from the branches of stable gaits in terms of nondimensional parameters.
A muscle-reflex model that encodes principles of legged mechanics predicts human walking dynamics and muscle activities
- IEEE Trans. Neural Syst. Rehabil. Eng
"... Abstract — While neuroscientists identify increasingly complex neural circuits that control animal and human gait, biomechanists find that locomotion requires little control if principles of legged mechanics are heeded that shape and exploit the dynamics of legged systems. Here we show that muscle r ..."
Abstract
-
Cited by 44 (11 self)
- Add to MetaCart
Abstract — While neuroscientists identify increasingly complex neural circuits that control animal and human gait, biomechanists find that locomotion requires little control if principles of legged mechanics are heeded that shape and exploit the dynamics of legged systems. Here we show that muscle reflexes could be vital to link these two observations. We develop a model of human locomotion that is controlled by muscle reflexes which encode principles of legged mechanics. Equipped with this reflex control, we find this model to stabilize into a walking gait from its dynamic interplay with the ground, reproduce human walking dynamics and leg kinematics, tolerate ground disturbances, and adapt to slopes without parameter interventions. In addition, we find this model to predict some individual muscle activation patterns known from walking experiments. The results suggest not only that the interplay between mechanics and motor control is essential to human locomotion, but also that human motor output could for some muscles be dominated by neural circuits that encode principles of legged mechanics. Index Terms — legged locomotion, feedback control, balance. I.
Fast biped walking with a sensor-driven neuronal controller and real-time online learning
, 2006
"... In this paper, we present our design and experiments on a planar biped robot under the control of a pure sensor-driven controller. This design has some special mechanical features, for example small curved feet allowing rolling action and a properly positioned center of mass, that facilitate fast wa ..."
Abstract
-
Cited by 36 (3 self)
- Add to MetaCart
In this paper, we present our design and experiments on a planar biped robot under the control of a pure sensor-driven controller. This design has some special mechanical features, for example small curved feet allowing rolling action and a properly positioned center of mass, that facilitate fast walking through exploitation of the robot’s natural dynamics. Our sensor-driven controller is built with biologically inspired sensor- and motor-neuron models, and does not employ any kind of position or trajectory tracking control algorithm. Instead, it allows our biped robot to exploit its own natural dynamics during critical stages of its walking gait cycle. Due to the interaction between the sensor-driven neuronal controller and the properly designed mechanics of the robot, the biped robot can realize stable dynamic walking gaits in a large domain of the neuronal parameters. In addition, this structure allows the use of a policy
Adaptive dynamic walking of a quadruped robot on natural ground based on biological concepts
- The International Journal of Robotics Research
, 2007
"... The paper reports on a project to make a quadruped robot walk with medium forward speed on irregular terrain in an outdoor environ-ment using a neural system model. The necessary conditions for sta-ble dynamic walking on irregular terrain in general are proposed, and the neural system is designed by ..."
Abstract
-
Cited by 32 (2 self)
- Add to MetaCart
(Show Context)
The paper reports on a project to make a quadruped robot walk with medium forward speed on irregular terrain in an outdoor environ-ment using a neural system model. The necessary conditions for sta-ble dynamic walking on irregular terrain in general are proposed, and the neural system is designed by comparing biological concepts with those necessary conditions described in physical terms. A PD-controller is used at joints to construct a virtual spring–damper sys-tem as the visco-elasticity model of a muscle. The neural system model consists of a CPG (central pattern generator), responses and reflexes. A response directly and quickly modulates the CPG phase, and a reflex directly generates joint torque. The state of the virtual spring–damper system is switched, based on the CPG phase. In or-der to make a self-contained quadruped (called Tekken2) walk on natural ground, several new reflexes and responses are developed in addition to those developed in previous studies. A flexor reflex pre-vents a leg from stumbling on small bumps and pebbles. A sideways stepping reflex stabilizes rolling motion on a sideways inclined slope. A corrective stepping reflex/response prevents the robot from falling down in the case of loss of ground contact. A crossed flexor reflex helps a swinging leg keep enough clearance between the toe and the ground. The effectiveness of the proposed neural system model con-trol and especially the newly developed reflexes and responses are validated by indoor and outdoor experiments using Tekken2. A CPG
Stability analysis of legged locomotion models by symmetry-factored return maps
- International Journal of Robotics Research
, 2004
"... We present a new stability analysis for hybrid legged locomotion systems based on the “symmetric” factorization of return maps. We apply this analysis to 2 and 3 degree of freedom (DOF) models of the Spring Loaded Inverted Pendulum (SLIP) with different leg recirculation strategies. Despite the non- ..."
Abstract
-
Cited by 32 (8 self)
- Add to MetaCart
(Show Context)
We present a new stability analysis for hybrid legged locomotion systems based on the “symmetric” factorization of return maps. We apply this analysis to 2 and 3 degree of freedom (DOF) models of the Spring Loaded Inverted Pendulum (SLIP) with different leg recirculation strategies. Despite the non-integrability of the SLIP dynamics, we obtain a necessary condition for asymptotic stability (and a sufficient condition for instability) at a fixed point, formulated as an exact algebraic expression in the physical parameters. We use this expression to study a variety of 2 DOF SLIP models that have previously been posited as low dimensional representations of running, focusing on the sensory “cost” required to achieve “fast ” transients as measured by the degree of singularity of the linearized dynamics. We introduce a new 3 DOF SLIP model with pitching dynamics whose stability properties, revealed by this analysis, provide for the first time the beginnings of a formal explanation for the surprisingly stable gaits of the open loop controlled robot, RHex.
The Role and Implementation of Compliance in Legged Locomotion
, 2008
"... Many robots excel at precise positioning and trajectory tracking using software control, and most successful robotic applications utilize this ability—examples include CNC machining, robotic welding, painting, and pick-and-place circuit board assembly. The mechanical design of these robots focuses o ..."
Abstract
-
Cited by 29 (2 self)
- Add to MetaCart
(Show Context)
Many robots excel at precise positioning and trajectory tracking using software control, and most successful robotic applications utilize this ability—examples include CNC machining, robotic welding, painting, and pick-and-place circuit board assembly. The mechanical design of these robots focuses on rigid transmissions and minimizing compliance in the structure, so the software controller can accurately track a desired position as a function of time, regardless of any disturbance forces. However, there is a class of tasks for which rigid actuation is not ideal: physical interaction with the world, especially interaction that involves an impact or kinetic energy transfer. Animals tend to excel at these tasks, and far outperform the best robots. Examples include walking, running, catching a ball, gripping a piece of fruit firmly but without causing damage, and many types of assembly tasks. For dynamic behaviors such as running, the performance limitations of a robot are often due to limitations of the mechanical design. A robot is an integrated system of electronics, software, and mechanism, and each part of the system limits or enables the behavior of the whole. While some behaviors can easily be implemented through simple actuators and direct software control, a running machine requires mechanical design that is specialized for the task. Among other things,
Cheap rapid locomotion of a quadruped robot: Self-stabilization of bounding gait
- In: Proceedings of the International Conference on Intelligent Autonomous Systems
, 2004
"... Abstract. The legged animals are capable of rapid, energy efficient, and adaptive lo-comotion in a complex environment. Toward a comprehensive understanding of the nature of such ecologically balanced legged locomotion, in this paper, we propose a novel method to achieve a form of bounding gait for ..."
Abstract
-
Cited by 26 (10 self)
- Add to MetaCart
(Show Context)
Abstract. The legged animals are capable of rapid, energy efficient, and adaptive lo-comotion in a complex environment. Toward a comprehensive understanding of the nature of such ecologically balanced legged locomotion, in this paper, we propose a novel method to achieve a form of bounding gait for a quadruped robot by using a minimalistic approach. Although this method uses a simple sinusoidal position con-trol with no global sensory feedback, it is shown that the rapid bounding is possible in a relatively robust manner by properly exploiting the intrinsic dynamics and the interaction with the environment. The behavioral analyses with the robot experiments show that this relatively complicated dynamic locomotion is achieved even with a simple controller mainly because of a self-stabilization mechanism. Moreover, by ex-ploiting this mechanism of self-stabilization, we propose a unique approach to control the forward velocity of the locomotion. 1
The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper
- SUBMITTED TO THE IEEE TRANSACTIONS ON AUTOMATIC CONTROL AS A REGULAR PAPER
, 2007
"... A hybrid controller that induces provably stable running gaits on an Asymmetric Spring Loaded Inverted Pendulum (ASLIP) is developed. The controller acts on two levels. On the first level, continuous within-stride control asymptotically imposes a (virtual) holonomic constraint corresponding to a de ..."
Abstract
-
Cited by 25 (7 self)
- Add to MetaCart
A hybrid controller that induces provably stable running gaits on an Asymmetric Spring Loaded Inverted Pendulum (ASLIP) is developed. The controller acts on two levels. On the first level, continuous within-stride control asymptotically imposes a (virtual) holonomic constraint corresponding to a desired torso posture, and creates an invariant surface on which the two-degree-of-freedom restriction dynamics of the closed-loop system (i.e., the hybrid zero dynamics) is diffeomorphic to the center-of-mass dynamics of a Spring Loaded Inverted Pendulum (SLIP). On the second level, event-based control stabilizes the closed-loop hybrid system along a periodic orbit of the SLIP dynamics. The controller’s performance is discussed through comparison with a second control law that creates a one-degreeof-freedom non-compliant hybrid zero dynamics. Both controllers induce identical steady-state behaviors (i.e. periodic solutions). Under transient conditions, however, the controller inducing a compliant hybrid zero dynamics based on the SLIP accommodates significantly larger disturbances, with less actuator effort, and without violation of the unilateral ground force constraints.
Exploiting body dynamics for controlling a running quadruped robot
- Proceedings of International Conference on Advanced Robotics (ICAR 2005
, 2005
"... Abstract — Exploiting the body dynamics to control the behav-ior of robots is one of the most challenging issues, because the use of body dynamics has a significant potential in order to enhance both complexity of the robot design and the speed of movement. In this paper, we explore the control stra ..."
Abstract
-
Cited by 22 (6 self)
- Add to MetaCart
(Show Context)
Abstract — Exploiting the body dynamics to control the behav-ior of robots is one of the most challenging issues, because the use of body dynamics has a significant potential in order to enhance both complexity of the robot design and the speed of movement. In this paper, we explore the control strategy of rapid four-legged locomotion by exploiting the intrinsic body dynamics. Based on the fact that a simple model of four-legged robot is known to exhibit interesting locomotion behavior, this paper analyzes the characteristics of the dynamic locomotion for the purpose of the locomotion control. The results from a series of running experiments with a robot show that, by exploiting the unique characteristics induced by the body dynamics, the forward velocity can be controlled by using a very simple method, in which only one control parameter is required. Furthermore it is also shown that a few of such different control parameters exist, each of them can control the forward velocity. Interestingly, with these parameters, the robot exhibits qualitatively different behavior during the locomotion, which could lead to our comprehensive understanding toward the behavioral diversity of adaptive robotic systems. I.
