Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models

Koolen, Twan; Boer, Tomas de; Rebula, John R.; Goswami, Ambarish; Pratt, Jerry

doi:10.1177/0278364912452673

Cited by 443 publications

(427 citation statements)

References 58 publications

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“…Although there are clear First, it is important to note that planning multiple steps ahead will yield diminishing returns for each additional step planned. Mechanical simulation studies of bipedal walking based on a linear inverted pendulum model show that planning more than two or three steps ahead yields only negligible increases in control authority (51,52). In addition, due to the inescapable variability of motor behavior, any multistep plan will be subject to accumulating error on each successive step.…”

Section: For a Review)mentioning

confidence: 99%

The critical phase for visual control of human walking over complex terrain

Matthis

Barton

Fajen

2017

Proc. Natl. Acad. Sci. U.S.A.

107

104

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To walk efficiently over complex terrain, humans must use vision to tailor their gait to the upcoming ground surface without interfering with the exploitation of passive mechanical forces. We propose that walkers use visual information to initialize the mechanical state of the body before the beginning of each step so the resulting ballistic trajectory of the walker's center-of-mass will facilitate stepping on target footholds. Using a precision stepping task and synchronizing target visibility to the gait cycle, we empirically validated two predictions derived from this strategy: (1) Walkers must have information about upcoming footholds during the second half of the preceding step, and (2) foot placement is guided by information about the position of the target foothold relative to the preceding base of support. We conclude that active and passive modes of control work synergistically to allow walkers to negotiate complex terrain with efficiency, stability, and precision.H umans and other animals are remarkable in their ability to take advantage of what is freely available in the environment to the benefit of efficiency, stability, and coordination in movement. This opportunism can take on at least two forms, both of which are evident in human locomotion over complex terrain: (i) harnessing external forces to minimize the need for self-generated (i.e., muscular) forces (1), and (ii) taking advantage of passive stability to simplify the control of a complex movement (e.g., ref. 2). In the ensuing section, we explain how walkers exploit external forces and passive stability while walking over flat, obstacle-free terrain.* We then generalize this account to walking over irregular surfaces by explaining how walkers can adapt gait to terrain variations while still reaping the benefits of the available mechanical forces and inherent stability. This account leads to hypotheses about how and when walkers use visual information about the upcoming terrain and where that information is found. We derive several predictions from these hypotheses and then put them to the test in three experiments. Passive Control in Human WalkingThe basic movement pattern of the human gait cycle arises primarily from the phasic activation of flexor and extensor muscle groups by spinal-level central pattern generators, regulated by sensory signals from lower limb proprioceptors and cutaneous feedback from the plantar surface of the foot. This low-level neuromuscular circuitry serves to maintain the rhythmic physical oscillations that define locomotor behavior (see ref. 3 for review). This section will provide an overview of the basic biomechanics of the bipedal gait cycle to show how these inherent physical dynamics contribute to the passive stability and energetic efficiency of human locomotion.During the single support phase of the bipedal gait cycle, when only one foot is in contact with the ground, a walker shares the physical dynamics of an inverted pendulum. The body's center of mass (COM) acts as the bob of the pendulum and is support...

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Section: For a Review)mentioning

confidence: 99%

The critical phase for visual control of human walking over complex terrain

Matthis

Barton

Fajen

2017

Proc. Natl. Acad. Sci. U.S.A.

107

104

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“…Inverted pendulum models are useful for simplifying bipeds in single support phase, aiming at predicting future motion of the robot with lower computational cost compared to using a full model of the system. An example of exploiting such simplification is [9] where the concept of capture points is introduced. Simple linear dynamics of capture points let us predict future motion of CoM and plan the next footstep position which will absorb the energy in the robot.…”

Section: Introductionmentioning

confidence: 99%

“…While bringing the system to the rest conditions after pushes exists in literature over a single step [23] or multiple steps [9], we aim at a more generic scenario, i.e. bringing the system to a desired non-zero velocity (given by a joystick).…”

Section: Introductionmentioning

confidence: 99%

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Robust and Agile 3D Biped Walking With Steering Capability Using a Footstep Predictive Approach

Faraji

Pouya²,

Ijspeert³

2014

Robotics: Science and Systems X

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Abstract-In this paper, we formulate a novel hierarchical controller for walking of torque controlled humanoid robots. Our method uses an online whole body optimization approach which generates joint torques, given Cartesian accelerations of different points on the robot. Over such variable translation, we can plan our desired foot trajectories in Cartesian space between starting and ending positions of the foot on the ground. On top level, we use the simplified Linear Inverted Pendulum Model to predict the future motion of the robot. With LIPM, we derive a formulation where the whole system is described by the state of center of mass and footstep locations serve as discrete inputs to this linear system. We then use model predictive control to plan optimal future footsteps which resemble a reference plan, given desired sagittal and steering velocities determined by the high-end user. Using simulations on a child-size torque controlled humanoid robot, the method tolerates various disturbances such as external pushes, sensor noises, model errors and delayed communication in the control loop. It can perform robust walking over slopes and uneven terrains blindly and turn rapidly at the same time. Our generic dynamics model-based method does not depend on any off-line optimization, being suitable for typical torque controlled humanoid robots.

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“…The group, as well as other researchers, have also presented many extended versions of IP models including springs, dampers, telescopic actuators, additional segments and joints. [12][13][14][15][16] .…”

Section: Introductionmentioning

confidence: 99%

The strengths and weaknesses of inverted pendulum models of human walking

2015

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-An investigation into the kinematic and kinetic predictions of two "inverted pendulum" (IP) models of gait was undertaken. The first model consisted of a single leg, with anthropometrically correct mass and moment of inertia, and a point mass at the hip representing the rest of the body. A second model incorporating the physiological extension of a head-arms-trunk (HAT) segment, held upright by an actuated hip moment, was developed for comparison. Simulations were performed, using both models, and quantitatively compared with empirical gait data. There was little difference between the two models' predictions of kinematics and ground reaction force (GRF). The models agreed well with empirical data through mid-stance (20-40% of the gait cycle) suggesting that IP models adequately simulate this phase (mean error less than one standard deviation). IP models are not cyclic, however, and cannot adequately simulate double support and stepto-step transition. This is because the forces under both legs augment each other during double support to increase the vertical GRF. The incorporation of an actuated hip joint was the most novel change and added a new dimension to the classic IP model. The hip moment curve produced was similar to those measured during experimental walking trials. As a result, it was interpreted that the primary role of the hip musculature in stance is to keep the HAT upright. Careful consideration of the differences between the models throws light on what the different terms within the GRF equation truly represent.

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Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models

Cited by 443 publications

References 58 publications

The critical phase for visual control of human walking over complex terrain

The critical phase for visual control of human walking over complex terrain

Robust and Agile 3D Biped Walking With Steering Capability Using a Footstep Predictive Approach

The strengths and weaknesses of inverted pendulum models of human walking

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