Methods

3.3.3.1 Robotic platform and prior experiments

Experiments were conducted to understand the effect of fluidic loading on underwater contact with beams and a fin [90] (Figure 25), and data from these experiments was selected and processed for analyzing multiple contact classification techniques herein. The robotic platform was designed to drive flexible beams and fins through fluid and into contact with obstacles in air and underwater (Figure 26). Beams of three flexural rigidity distributions were used – denoted flexible, moderate, and stiff – and were designed with a linear taper from base to tip, as in [17]. Beams were instrumented with strain gages in half-bridge configurations (KFG-5-120, Omega, Stamford, CT) at proximal (x=10mm from base) and distal (x=100mm) locations. The fin consisted of three moderate beams cast into a 1mm thick silicone webbing, and it was instrumented with proximal and distal sensors along each beam (Figure 25). One fin was tested due to the complexity of manufacture and instrumentation. The robotic platform drove the beams and fins at a range of speeds ([0.05,0.4] rotations/s (rot/s) for fins; [0.05,1.5] rot/s for beams) into contact with a flat acrylic plate obstacle (200 x 250 x 6.25 mm). The beams and fin were programmed to accelerate from rest to a constant velocity trajectory and then to come into contact with the obstacle, and to decelerate to rest shortly after contact.

Figure 25. Instrumented beams and fin used in contact experiments. Beams of three stiffnesses instrumented with proximal and distal strain gage sensors (a). A fin, with three embedded beams instrumented with sensors along each beam (b), comes into contact with a complex, stair-step obstacle.

Figure 26. Test environments for beams and fins: beams driven in air (a), fin in air (b), beams in water (c), and fin in water (d).

3.3.3.2 Classification techniques

Multiple contact classification techniques were designed and their performance was compared across experimental conditions (Table 2). Simple contact classification techniques were chosen that have been successful in air, in order to explore the complexity introduced by the structure-fluid-structure-interaction between beams and objects during underwater contact. Contact and No Contact conditions are abbreviated as C and NC, respectively.

Table 2. Summary of contact classification techniques Contact Classification Technique Contact Conditions

A. Strain threshold

( )

{

}

,, 1, ,6

i t i t i

ε

ε

B. Strain rate threshold ( ) ( )

, i i i t t t t t t ε −ε − ∆ _>δε − ∆

C. Strain difference threshold

( )

( )

( )

( )

Strain threshold. The maximum strain prior to the time of contact was stored as the strain threshold, εt. C was classified by this technique when the measured strain εm

exceeded the strain threshold, otherwise NC was classified (Figure 27a). Setting a threshold for sensory data (e.g. motor torque) is commonly used to detect the incidence of contact. This technique was based on work by Solomon and Hartmann [50], who set a

measured torque threshold to determine when a robotic whisker came in contact with a rigid object.

Figure 27. Illustration of three contact classification techniques tested: (a) strain threshold, (b) strain rate threshold, and (c) strain difference threshold. For (c), distal strains are subtracted from proximal strains and the difference is used to compute contact. Colored classification bars are shown beneath each time series example.

Strain rate threshold. The slope of the strain at the time of contact was stored as a rate threshold, δεt. C was classified by this technique when the measured strain rate δεm

exceeded the strain rate threshold, otherwise NC was classified. Since the strain rate was typically close to zero after contact, after 5 successive C classifications the robot was classified in C (Figure 27b). Rate thresholds have also been used to detect contact using

robotic whiskers in air, where a large rate of change of curvature of the whisker was used to determine the incidence of contact [96].

Strain difference threshold. For each ordered pair of sensors (εi, εj) along a

single beam, the difference of those sensors’ data was computed, forming εij. εij was

computed after the instant of contact and the sign of the result was used to determine the conditions for contact. If εij was negative after contact for the given pair, then a positive

difference was classified as C and a negative difference was classified as NC (Figure 27c). This technique was selected based on the observation that the difference between proximal and distal strains often changed sign after contact [90], especially underwater.

3.3.3.3 Performance metrics

Contact discrimination was quantified in order to measure and compare the performance of each technique. Contact discrimination was defined as: (1) estimating the instant of contact, and (2) correctly classifying whether the robot is in contact or not in contact. The estimated instant of contact (1) was evaluated using the error in time between the first predicted instant of contact and the actual instant of contact. Since most techniques had false positives, a standardized method was selected to calculate the estimated instant of contact. The instant of contact tc was estimated by the first classified instance of C

with at least 10 following C classifications. The choice of 10 classifications was selected based on preliminary analysis that suggested that 8-12 classifications resulted in best performance from all techniques.

Classification accuracy (2) was evaluated using a modified confusion matrix (from [97]) that classified the state of the system at each sampling time. For each entry of

the confusion matrix, the accuracy was evaluated at each time step and the average accuracy was reported (c.f. Table 3).

Table 3. Confusion matrix of contact classification accuracy Predicted NC C Actual NC ∑ $%&'(&') ∑ $*+ , C NC| NC k k

∑

∑

∑

∑

The performance of each technique was analyzed using data from distributed strain sensors (2 for beams, 6 for fins; c.f. Figure 25). The best sensors and subsets of sensors were selected for each of the classification techniques. Since it was expected that each contact discrimination technique would have differing results depending on the speed, stiffness, and robot structure (i.e. beams, fin), each technique was analyzed individually for each subset of robot parameters. In order to assess the effects of fluid on contact classification, performance data were compared between contact made in air and contact made underwater. Technique-specific thresholds were calculated on data from one set of trials and techniques were tested on data from randomly selected trials with the same conditions. Beams in air using the strain threshold technique (Table 2A) are generally used as the gold standard for comparisons between techniques.