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A Highly Compliant Passive Antenna for Touch-Mediated Maneuvering of a Biologically Inspired Hexapedal Robot
by Emily Ma
Abstract
A highly compliant, sensor-lined antenna probe can provide mobile robots with tactile information about immediate surroundings for exploration and localization. Analogous in structure and function to insect antennae, this type of antenna probe can be especially useful for feedback to highly dynamic and complex platforms such as fast running legged robots, providing direct information about the geometry of the environment in a robust manner despite the rapidly changing state of the system. Inspired by the effectiveness of cockroach antennae for feedback during rapid legged locomotion, we have designed and calibrated a passive artificial sensor-lined antenna to provide feedback control in a biologically-inspired, hexapedal running robot. We then suggest the process for designing a simple wall-following controller, based on the sensor calibration and the robot’s running and turning dynamics, and present preliminary results.
Article
Introduction
Insects have absolutely extraordinary sensing abilities. Often behaviorally active in low-light levels, insects commonly rely on non-visual senses for self-orientation and navigation. Specialized mechanoreceptors for detecting contact and strain on filamentous support structures such as animal vibrissae or arthropod antennae (Fig. 1) provide tactile cues from the physical environment to augment poor or nonexistent visual guidance [8].
Figure 1. Close-up of the cockroach Peripla-neta Americanaantenna. The proprioceptive active base is composed of the scape (S) and pedicel (P). The passive flagellum (F) forms the rest of the length of the antenna.
In designing sensors for a robot to gather geometric information about its surroundings, the above biologicallycompelling alternative to traditional sensing methods. Common localization methods such as sonar, capacitive, or inductive proximity sensors are highly dependent on the sensed object’s surface roughness, reflectivity and material properties. Vision-based methods can be computationally-expensive and can fail under low visibility due to low-light conditions or high air-particle content.
In nature, antennae are highly flexible structures that undergo very large deflections that cannot be analyzed with classical beam theory, which assumes that deflections are small given high beam stiffness. More importantly, the antenna is highly responsive in the passive mode. When moving slowly, cockroaches do actively probe their surroundings with their antennae. However, when moving quickly, cockroaches let their antennae stream passively alongside their bodies, holding the base of each antenna at a fixed angle. This behavior is clearly exhibited in the behavior of insects as they move alongside walls. Camhi and Johnson have shown that the cockroach Periplaneta Americana can, in fact, control wall-following maneuvers with high fidelity in response to tactile feedback from their antenna [3]. In this light, our goal is to propose a new biologically inspired tactile sensor system and accompanying model-based controller for a hexapedal robot based on these two themes: high flexibility for robustness and passive feedback sensing for control of a highly dynamic platform.
Tactile Sensing in Mobile Robotics
Two interrelated areas of work to note include the use of antenna-like and whisker probes for sensing in general robotics and tactile sensing solutions on dynamic mobile platforms.
Whisker probes are often used in robotics to actively explore an environment. Such probes are either mounted on a stationary platform and actively actuated at the base or fixed on a slow moving platform with a predetermined path. These probes most often take the form of an insensitive flexible beam made from either a short length of stiff piano wire or hypodermic tubing anchored at the base. When the free end of the cantilevered beam is loaded in contact with an external object, bending occurs and deflection is sensed by a piezoelectric element or simple switch. Russell [9] used a simple whisker and considered only contact at the tip to simplify an analysis of loading. With a controlled slow moving platform, Russell was able to successfully and accurately detect and recognize complex shapes. Kaneko and Ueno [5, 13] then proposed an actively controlled antenna that allowed for the detection of a contact point anywhere along the beam length, using just a joint angular sensor and a torque sensor at the base of an inflexible beam. Given classical beam deflection principles that assume high material stiffness, it was shown that such beam deformation is small enough to justify a linear approximation and that the contact length from the fixed end of the beam is simply proportional to the rotational compliance of the beam in contact with the object. Hence, a series of slow, active motions could resolve the contact point. Though passive sensing without utilizing active motion has been investigated by Brock, Salisbury and Tsujimura [1, 10, 12], again, these methods are slow, and require moving platforms to serve the sensor.
Tactile sensors in fast and mobile robotics have mainly functioned as threshold-binary proximity sensors for simple obstacle avoidance. Antenna-like whisker sensors were also mounted on SRI mobile robot Shakey [7], as well as Rodney Brooks and Shigeo Hirose’s legged robots, for simple contact sensing [2, 4]. Whisker sensor arrays have also been used to control ground contact in legged locomotion [11 ] . Monitoring the separation between the foot and ground of a legged robot allows for foot deceleration before contact. Without a fast-response analog sensor, tactile feedback control of a dynamic mobile platform has not yet been well-documented or well-studied.
Design criteria for tactile-based control of fast dynamic platforms
Previous work on tactile-based control, as summarized above, has focused mainly on the use of simple binary contact whiskers or active insensitive beams mounted on static or slowmoving platforms. The issues associated with developing a tactile probe for navigational feedback to a fast dynamic legged robot in an unstructured environment are very different. Clearly, active probing is not possible for a robot running at speeds upwards of five body lengths per second (Fig. 2). Moreover, the antenna must be robust enough to survive large impulsive forces due to collisions with obstacles. Finally, for the purpose of obstacle avoidance and wall-following, copious amounts of data to describe the environment accurately are not necessary—data acquired from the sensor should be minimal to quickly process for rapid control, but enough to respond to the environment accurately.
Figure 2. Sprawlette, a hexapedal running robot guided by a simple tactile sensing artificial antenna.
Such design criteria for this dynamic platform demand a high degree of compliance for robustness, minimal sensing and simple passive control. With current sensor technology, it is possible to make a compliant, robust, sensor-lined antenna. Given this, and a good sensor model, we are able to use a simple proportional-derivative controller manually tuned to the robot’s turning dynamics that enables our robot to successfully wall-follow and avoid simple obstacles in unstructured environments.
Antenna Sensor Design and Calibration
Electromechanical Design
A highly compliant and light Spectrasymbol Flex Sensor serves as our base antenna sensor. The conductive elastomer that lines the length of the sensor changes in electrical resistivity proportional to the strain imposed on the elastomer caused by bending or flexing. Though it is possible to extract from the basic sensor the degree to which it is bent, there is no way to detect the point of greatest strain or to differentiate between different shapes the sensor is bent into which have the same total curvature values. We show that total curvature information is sufficient for basic feedback control and suggest a method for extracting further information from this passive compliant resistive sensor below.
The antenna is fixed from the base at a 45 degree angle to the upper right hand corner of the robot to maximize contact with the environment. The antenna is also extended by a thin strip of transparency film fixed to the distal end to increase the likelihood of detecting obstacles further out from the body. Finally, the entire antenna is plastically deformed into an initial curved state to ensure further elastic deformation in the preferential direction of the sensor when in contact with an obstacle.
Sensor Model
Consider the simplest setting in which we are given only the total resistance along the antenna as shown in Fig. 3. In this model, we assume that the distance y from the robot to the wall is related to the total curvature and hence resistance of the flex sensor according to
where the nominal resistance Ro, nominal distance from the wall yand proportional gain Ky are fixed, known constants. We show that this model is sufficient for simple proportional-derivative control. However, further information can be easily extracted from the passive flex sensor by tapping into the sensor at various points along the length. This provides discrete local curvature information, and thus improved shape information.
Figure 3. A simple model of Sprawlette making contact with the wall using its antenna. We assume that the distance y from the front right corner of the robot to the wall is a monotonic function of the total resistance  of our artificial antenna sensor.
Using five segmental measurements of resistance along the length of the antenna, we determined a strong linear correlation between these sensor inputs and world parameters y and [theta] using a simple least-squares fit as an initial attempt at data-fitting (Fig. 4). The least-squares method provides us with the best linear approximation with the least computation. Not only did these extra sensor inputs improve the accuracy of the distance measurement y from the wall, it is possible to now extract useful, albeit approximate, robot heading information [theta].
System Identification for an improved sensor model
To calibrate the antenna, we placed the robot in several different orientations and positions relative to a planar surface. We collected trials for eleven wall angles ranging from -20 to 30 degrees and seven wall distances ranging from 60 to 120 mm. Each trial yielded a data pair—given a certain position d and orientation [theta] ‘input y,’ we obtained a set of five segmental resistance values representing the ‘output x’(Eq. 2). Assuming that the transformation A from x to y is linear, we use least-squares to approximate this transformation as A.
This simple affine model results in a residual norm or mean-squared error of 4.5 mm for distance (7.5%) and 7.2 o for angle (15%) as shown in Fig. 4. The combination of this increased accuracy of distance fit and a rough heading measurement allows for the development of improved control models based on this larger set of parameters. A closer linear fit of to the antenna sensor measurements arises from the observation that the sensor dependence on is negligible beyond distances of 80 mm from the wall. Thus, simply bounding the data set to a distance range of 60 to 80 mm yields a lower residual of 4.9 o (10%). Though this first least-squares calibration is adequate, the improved results in restrictions of data range suggests that a piecewise holonomic linear model would be better suited for the calibration of this type of sensor.
Figure 4. Left: Calibrated distance values vs. actual distance values for 60 to 120 mm range. Right: Calibrated angle values vs. actual angle values for -20 to 30 degree range.
Horizontal-Plane Dynamics of Sprawlette
Sprawlette is a highly compliant robot with six legs, and two actuators per leg: a low-power shape actuator that changes the orientation of that leg’s pneumatic power actuator (Fig. 5). Although a detailed 36-state, 12-degree of freedom (DOF) dynamic model has been developed for accurate simulation, we hypothesize that that a low dimensional, horizontal-plane template model will suffice for many sensor-based maneuvering tasks. An abstracted template model, when used appropriately, affords a deeper analytical understand of overall systems dynamics. In straight-ahead running, Sprawlette can operate using no sensory feedback by fixing the pneumatic valve timing to generate an alternating tripod gait, and holding the six shape variables to a constant posture. Then for turning behavior, by varying the phase and duty factor of each valve together with the angle of each servo motor, an 18 dimensional control space, U, is generated, which McClung [6] have yoked into a virtual control parameter called the turning factor, u. In short, the turning factor uparameter allows us to simply actuate a maneuver, given sensor determined parameters of the robot with respect to the wall.
Figure. 5. Pneumatic leg actuation and sagittal plane joint compliance of the bio-inspired hexapedal robot Sprawlette.
Antenna-Mediated Wall Following
Controller Design and Results
For the purposes of an initial proof of concept, we have used only total curvature information for control. Basic wall-following behavior was selected to validate the concept of robust feedback control using our passive compliant sensor.Asimple proportional controller was implemented to demonstrate that given sensor measurements and the ability to actuate rotation, Sprawlette could maintain a specified distance from the wall. Although simple proportional feedback had been implemented such that
where the proportional gain Kp is manually tuned, large expected oscillations persist. The robot tended towards the wall but would respond much too quickly, moving too close to the wall, which in turn, drove it to move quickly away from the wall. This unstable or non-convergent response is clear in trials 1 and 5 (Table 1).
Table 1. Resulting behavior from trial runs of Sprawlette given independently tunable gains Kp and Kd.
Such oscillatory behavior was tuned out by adding a derivative term such that
where Kp and Kd are tuned gains and d is the velocity of the robot moving towards the wall. This proportionalderivative controller was then manually tuned to show significant improvement in damping the oscillatory nature of the proportional controller. Results show that the best controller (Trials 3 and 4) requires a high Kp coupled with a nonzero Kd.
Notes on Implementation
The above proportional and proportional-derivative controller were implemented in analog hardware, preprocessing the sensor input before passing the signal to the robot microcontroller 10 kHz ADC ports. T h e unknown resistance of the antenna sensor with respect to a nominal resistance set by balancing a half-bridge circuit of resistors and examining the output signal. Both proportional and derivative gain components of the circuit were built to filter out high frequency noise about 50 Hz since the robot turning bandwidth was approximately 1.5 Hz [6]. This analog circuit allowed us to manually tune our gains Kp and Kd as well as our nominal point with ease.
Conclusions and Future Work
We have demonstrated that highintegrity wall-following behavior of a biologically-inspired hexapedal robot can be driven by a passive compliant tactile antenna sensor and a simple proportional-derivative controller tuned to the steering dynamics of the system. Thus, we conclude that passive and compliant probe sensing for feedback control to a highly dynamic mobile platform is not only practical but effective. Future work will focus on two areas: optimizing and implementing the multi-segmental sensor design and calibration for passive compliant control, and developing a model-based controller to exploit the work done by McClung [6] on system identification of the steering dynamics of the robot. Overall, we hope to develop experimental and theoretical groundwork for the further exploration of passive compliant sensing and control for other task driven behaviors.
Acknowledgements
The author would like to thank Dr. Noah J. Cowan and Professor Mark Cutkosky for their continued support and mentorship, the members of the Stanford Biomimetics Robotics Laboratory and the Berkeley PolyPEDAL Laboratory. This work is supported by the Stanford Mechanical Engineering Summer Underg r a d u a t e Research Institute, by the National Science Foundation under grant MIP9617994 and by the Office of Naval Research under N00014-9810669.
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