Joseph H. Solomon

Biomechanics: Robotic whiskers used to sense features

Whiskers mimicking those of seals or rats might be useful for underwater tracking or tactile exploration.Several species of terrestrial and marine mammals with whiskers (vibrissae) use them to sense and navigate in their environment — for example, rats use their whiskers to discern the features of objects, and seals rely on theirs to track the hydrodynamic trails of their prey. Here we show that the bending moment — sometimes referred to as torque — at the whisker base can be used to generate three-dimensional spatial representations of the environment, and we use this principle to construct robotic whisker arrays that extract precise information about object shape and fluid flow. Our results will contribute to the development of versatile tactile-sensing systems for robotic applications, and demonstrate the value of hardware models in understanding how sensing mechanisms and movement control strategies are interlocked.

The morphology of the rat vibrissal array: a model for quantifying spatiotemporal patterns of whisker-object contact.

In all sensory modalities, the data acquired by the nervous system is shaped by the biomechanics, material properties, and the morphology of the peripheral sensory organs. The rat vibrissal (whisker) system is one of the premier models in neuroscience to study the relationship between physical embodiment of the sensor array and the neural circuits underlying perception. To date, however, the three-dimensional morphology of the vibrissal array has not been characterized. Quantifying array morphology is important because it directly constrains the mechanosensory inputs that will be generated during behavior. These inputs in turn shape all subsequent neural processing in the vibrissal-trigeminal system, from the trigeminal ganglion to primary somatosensory (“barrel”) cortex. Here we develop a set of equations for the morphology of the vibrissal array that accurately describes the location of every point on every whisker to within ±5% of the whisker length. Given only a whiskers identity (row and column location within the array), the equations establish the whiskers two-dimensional (2D) shape as well as three-dimensional (3D) position and orientation. The equations were developed via parameterization of 2D and 3D scans of six rat vibrissal arrays, and the parameters were specifically chosen to be consistent with those commonly measured in behavioral studies. The final morphological model was used to simulate the contact patterns that would be generated as a rat uses its whiskers to tactually explore objects with varying curvatures. The simulations demonstrate that altering the morphology of the array changes the relationship between the sensory signals acquired and the curvature of the object. The morphology of the vibrissal array thus directly constrains the nature of the neural computations that can be associated with extraction of a particular object feature. These results illustrate the key role that the physical embodiment of the sensor array plays in the sensing process.

Multifunctional Whisker Arrays for Distance Detection, Terrain Mapping, and Object Feature Extraction

Several species of animals use whiskers to accurately navigate and explore objects in the absence of vision. We have developed inexpensive arrays of artificial whiskers based on strain-gage and Flex Sensor technologies that can be used either in passive (“dragging”) mode, or in active (“whisking”) mode. In the present work we explore the range of functions that whisker arrays can serve on a rover. We demonstrate that when mounted on a rover, whisker arrays can (1) Detect obstacles and determine obstacle distance (2) Map terrain features (3) Determine ground and surface texture (4) Provide an estimate of rover speed (5) Identify “slip” of the rover wheels, and (6) Perform 3-dimensional extraction of object shape. We discuss the potential use of whisker arrays on planetary rovers and as an investigative tool for exploring the encoding of sensory information in the nervous system of animals.

Artificial Whiskers Suitable for Array Implementation: Accounting for Lateral Slip and Surface Friction

The exquisite tactile sensing ability of biological whiskers has recently led to increasing interest in constructing robotic versions with similar capabilities. Tactile extraction of three-dimensional (3-D) object shape poses several unique challenges that have only begun to be addressed. The present study develops a method for estimating the contact location of a robotic whisker rotating against an object based on small changes in moment at the whisker base. Importantly, the method accounts for lateral slip as well as surface friction, making it particularly well suited for implementation on an array of robotic whiskers. Array implementation would permit simultaneous extraction of multiple contact points and enable highly parallel, efficient 3-D object feature extraction. A simple, scalable array design is suggested to fulfill this approach.

Radial distance determination in the rat vibrissal system and the effects of Weber's law

Rats rhythmically tap and brush their vibrissae (whiskers) against objects to tactually explore the environment. To extract a complex feature such as the contour of an object, the rat must at least implicitly estimate radial object distance, that is, the distance from the base of the vibrissa to the point of object contact. Radial object distance cannot be directly measured, however, because there are no mechanoreceptors along the vibrissa. Instead, the mechanical signals generated by the vibrissas interaction with the environment must be transmitted to mechanoreceptors near the vibrissa base. The first part of this paper surveys the different mechanical methods by which the rat could determine radial object distance. Two novel methods are highlighted: one based on measurement of bending moment and axial force at the vibrissa base, and a second based on measurement of how far the vibrissa rotates beyond initial contact. The second part of the paper discusses the application of Webers law to two methods for radial distance determination. In both cases, Webers law predicts that the rat will have greatest sensing resolution close to the vibrissa tip. These predictions could be tested with behavioural experiments that measure the perceptual acuity of the rat.

Extracting Object Contours with the Sweep of a Robotic Whisker Using Torque Information

Several recent studies have investigated the problem of object feature extraction with artificial whiskers. Many of these studies have used an approach in which the whisker is rotated against the object through a small angle. Each small-angle “tap” of the whisker provides information about the radial distance between the base of the whisker and the object. By tapping at various points on the object, a full representation of the surface can be gradually constructed in three-dimensional space. It is clear, however, that this tapping method does not exploit useful information about object contours that could be extracted by “sweeping” the whisker against the object. Rotating the whisker against the object through a large angle permits the collection of a sequence of contact points as the whisker slips along the surface. The present paper derives an algorithm based on a numerical cantilever beam model of the whisker to measure object profile shape over a single large-angle whisker rotation using only information about torque and angle at the whisker base. The algorithm is validated experimentally using three different object shapes. As the method does not require measurement of force, it is well suited for implementation on an array of robotic whiskers to accomplish quick and precise object feature extraction.

Fully interconnected, linear control for limit cycle walking

Limit cycle walkers are a class of bipeds that achieve stable locomotion without enforcing full controllability throughout the gait cycle. Although limit cycle walkers produce more natural-looking and efficient gaits than bipeds that are based on other control principles such as zero moment point walking, they cannot yet achieve the stability and versatility of human locomotion. One open question is the degree of complexity required in the control algorithm to ensure reliable terrain adaptation and disturbance rejection. The present study applies a fully interconnected, linear controller to a two-dimensional, five-link walking model, achieving stable and efficient locomotion over unpredictable terrain (slopes varying between 2° and 7° and step-downs varying between 0 and 25% leg length). The results indicate that elaborate control principles are not necessarily required for stable bipedal walking.

Linear reactive control for efficient 2D and 3D bipedal walking over rough terrain

The kinematics of human walking are largely driven by passive dynamics, but adaptation to varying terrain conditions and responses to perturbations require some form of active control. The basis for this control is often thought to take the form of entrainment between a neural oscillator (i.e., a central pattern generator and/or distributed counterparts) and the mechanical system. Here we use techniques in evolutionary robotics to explore the potential of a purely reactive, linear controller to control bipedal locomotion over rough terrain. In these simulation studies, joint torques are computed as weighted linear sums of sensor states, and the weights are optimized using an evolutionary algorithm. We show that linear reactive control can enable a seven-link 2D biped and a nine-link 3D biped to walk over rough terrain (steps of ∼5% leg length or more in the 2D case). In other words, the simulated walker gradually learns the appropriate weights to achieve stable locomotion. The results indicate that oscillatory neural structures are not necessarily a requirement for robust bipedal walking. The study of purely reactive control through linear feedback may help to reveal some basic control principles of stable walking.

Linear reactive control of three-dimensional bipedal walking in the presence of noise and uncertainty

Walking control of biped robots is a challenging problem, and improving robustness to noise and uncertainty remains difficult. We recently developed a novel control framework for 3D bipedal walking that we call “linear reactive control.” It is linear because control torques are computed as simple weighted sums of sensor states. It is reactive because it depends only on the model’s current state. The present simulation study shows that this controller performs reliably in the presence of realistic models of joint actuation, sensor noise, and uncertainty in model and contact parameters. The controller is able to maintain a stable gait in the presence of noisy sensor inputs and low-impedance actuation. It also performs reliably on models with high uncertainty (up to 20%) in measurements of their dynamic parameters and widely varying ground contact parameters. The robustness of this controller to realistic conditions validates this method as a promising avenue for bipedal control.

Erratum: Extracting object contours with the sweep of a robotic whisker using torque information (International Journal of Robotics Research (2009) doi: 10.1177/0278364908104468)

[This corrects the article on p. 298 in vol. 105.].