We propose a predictive runtime monitoring framework that forecasts the distribution of future positions of mobile robots in order to detect and avoid impending property violations such as collisions with obstacles or other agents. Our approach uses a restricted class of temporal logic formulas to represent the likely intentions of the agents along with a combination of temporal logic-based optimal cost path planning and Bayesian inference to compute the probability of these intents given the current trajectory of the robot. First, we construct a large but finite hypothesis space of possible intents represented as temporal logic formulas whose atomic propositions are derived from a detailed map of the robot’s workspace. Next, our approach uses real-time observations of the robot’s position to update a distribution over temporal logic formulae that represent its likely intent. This is performed by using a combination of optimal cost path planning and a Boltzmann noisy rationality model. In this manner, we construct a Bayesian approach to evaluating the posterior probability of various hypotheses given the observed states and actions of the robot. Finally, we predict the future position of the robot by drawing posterior predictive samples using a Monte-Carlo method. We evaluate our framework using two different trajectory datasets that contain multiple scenarios implementing various tasks. The results show that our method can predict future positions precisely and efficiently, so that the computation time for generating a prediction is a tiny fraction of the overall time horizon.
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Predictive Runtime Monitoring of Vehicle Models Using Bayesian Estimation and Reachability Analysis
We present a predictive runtime monitoring technique for estimating future vehicle positions and the probability of collisions with obstacles. Vehicle dynamics model how the position and velocity change over time as a function of external inputs. They are commonly described by discrete-time stochastic models. Whereas positions and velocities can be measured, the inputs (steering and throttle) are not directly measurable in these models. In our paper, we apply Bayesian inference techniques for real-time estimation, given prior distribution over the unknowns and noisy state measurements. Next, we pre-compute the set-valued reachability analysis to approximate future positions of a vehicle. The pre-computed reachability sets are combined with the posterior probabilities computed through Bayesian estimation to provided a predictive verification framework that can be used to detect impending collisions with obstacles. Our approach is evaluated using the coordinated-turn vehicle model for a UAV using on-board measurement data obtained from a flight test of a Talon UAV. We also compare the results with sampling-based approaches. We find that precomputed reachability analysis can provide accurate warnings up to 6 seconds in advance and the accuracy of the warnings improve as the time horizon is narrowed from 6 to 2 seconds. The approach also outperforms sampling in terms of on-board computation cost and accuracy measures.
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- NSF-PAR ID:
- 10233203
- Date Published:
- Journal Name:
- 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- Page Range / eLocation ID:
- 2111 to 2118
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Site description. This data package consists of data obtained from sampling surface soil (the 0-7.6 cm depth profile) in black mangrove (Avicennia germinans) dominated forest and black needlerush (Juncus roemerianus) saltmarsh along the Gulf of Mexico coastline in peninsular west-central Florida, USA. This location has a subtropical climate with mean daily temperatures ranging from 15.4 °C in January to 27.8 °C in August, and annual precipitation of 1336 mm. Precipitation falls as rain primarily between June and September. Tides are semi-diurnal, with 0.57 m median amplitudes during the year preceding sampling (U.S. NOAA National Ocean Service, Clearwater Beach, Florida, station 8726724). Sea-level rise is 4.0 ± 0.6 mm per year (1973-2020 trend, mean ± 95 % confidence interval, NOAA NOS Clearwater Beach station). The A. germinans mangrove zone is either adjacent to water or fringed on the seaward side by a narrow band of red mangrove (Rhizophora mangle). A near-monoculture of J. roemerianus is often adjacent to and immediately landward of the A. germinans zone. The transition from the mangrove to the J. roemerianus zone is variable in our study area. An abrupt edge between closed-canopy mangrove and J. roemerianus monoculture may extend for up to several hundred meters in some locations, while other stretches of ecotone present a gradual transition where smaller, widely spaced trees are interspersed into the herbaceous marsh. Juncus roemerianus then extends landward to a high marsh patchwork of succulent halophytes (including Salicornia bigellovi, Sesuvium sp., and Batis maritima), scattered dwarf mangrove, and salt pans, followed in turn by upland vegetation that includes Pinus sp. and Serenoa repens. Field design and sample collection. We established three study sites spaced at approximately 5 km intervals along the western coastline of the central Florida peninsula. The sites consisted of the Salt Springs (28.3298°, -82.7274°), Energy Marine Center (28.2903°, -82.7278°), and Green Key (28.2530°, -82.7496°) sites on the Gulf of Mexico coastline in Pasco County, Florida, USA. At each site, we established three plot pairs, each consisting of one saltmarsh plot and one mangrove plot. Plots were 50 m^2 in size. Plots pairs within a site were separated by 230-1070 m, and the mangrove and saltmarsh plots composing a pair were 70-170 m apart. All plot pairs consisted of directly adjacent patches of mangrove forest and J. roemerianus saltmarsh, with the mangrove forests exhibiting a closed canopy and a tree architecture (height 4-6 m, crown width 1.5-3 m). Mangrove plots were located at approximately the midpoint between the seaward edge (water-mangrove interface) and landward edge (mangrove-marsh interface) of the mangrove zone. Saltmarsh plots were located 20-25 m away from any mangrove trees and into the J. roemerianus zone (i.e., landward from the mangrove-marsh interface). Plot pairs were coarsely similar in geomorphic setting, as all were located on the Gulf of Mexico coastline, rather than within major sheltering formations like Tampa Bay, and all plot pairs fit the tide-dominated domain of the Woodroffe classification (Woodroffe, 2002, "Coasts: Form, Process and Evolution", Cambridge University Press), given their conspicuous semi-diurnal tides. There was nevertheless some geomorphic variation, as some plot pairs were directly open to the Gulf of Mexico while others sat behind keys and spits or along small tidal creeks. Our use of a plot-pair approach is intended to control for this geomorphic variation. Plot center elevations (cm above mean sea level, NAVD 88) were estimated by overlaying the plot locations determined with a global positioning system (Garmin GPS 60, Olathe, KS, USA) on a LiDAR-derived bare-earth digital elevation model (Dewberry, Inc., 2019). The digital elevation model had a vertical accuracy of ± 10 cm (95 % CI) and a horizontal accuracy of ± 116 cm (95 % CI). Soil samples were collected via coring at low tide in June 2011. From each plot, we collected a composite soil sample consisting of three discrete 5.1 cm diameter soil cores taken at equidistant points to 7.6 cm depth. Cores were taken by tapping a sleeve into the soil until its top was flush with the soil surface, sliding a hand under the core, and lifting it up. Cores were then capped and transferred on ice to our laboratory at the University of South Florida (Tampa, Florida, USA), where they were combined in plastic zipper bags, and homogenized by hand into plot-level composite samples on the day they were collected. A damp soil subsample was immediately taken from each composite sample to initiate 1 y incubations for determination of active C and N (see below). The remainder of each composite sample was then placed in a drying oven (60 °C) for 1 week with frequent mixing of the soil to prevent aggregation and liberate water. Organic wetland soils are sometimes dried at 70 °C, however high drying temperatures can volatilize non-water liquids and oxidize and decompose organic matter, so 50 °C is also a common drying temperature for organic soils (Gardner 1986, "Methods of Soil Analysis: Part 1", Soil Science Society of America); we accordingly chose 60 °C as a compromise between sufficient water removal and avoidance of non-water mass loss. Bulk density was determined as soil dry mass per core volume (adding back the dry mass equivalent of the damp subsample removed prior to drying). Dried subsamples were obtained for determination of soil organic matter (SOM), mineral texture composition, and extractable and total carbon (C) and nitrogen (N) within the following week. Sample analyses. A dried subsample was apportioned from each composite sample to determine SOM as mass loss on ignition at 550 °C for 4 h. After organic matter was removed from soil via ignition, mineral particle size composition was determined using a combination of wet sieving and density separation in 49 mM (3 %) sodium hexametaphosphate ((NaPO_3)_6) following procedures in Kettler et al. (2001, Soil Science Society of America Journal 65, 849-852). The percentage of dry soil mass composed of silt and clay particles (hereafter, fines) was calculated as the mass lost from dispersed mineral soil after sieving (0.053 mm mesh sieve). Fines could have been slightly underestimated if any clay particles were burned off during the preceding ignition of soil. An additional subsample was taken from each composite sample to determine extractable N and organic C concentrations via 0.5 M potassium sulfate (K_2SO_4) extractions. We combined soil and extractant (ratio of 1 g dry soil:5 mL extractant) in plastic bottles, reciprocally shook the slurry for 1 h at 120 rpm, and then gravity filtered it through Fisher G6 (1.6 μm pore size) glass fiber filters, followed by colorimetric detection of nitrite (NO_2^-) + nitrate (NO_3^-) and ammonium (NH_4^+) in the filtrate (Hood Nowotny et al., 2010,Soil Science Society of America Journal 74, 1018-1027) using a microplate spectrophotometer (Biotek Epoch, Winooski, VT, USA). Filtrate was also analyzed for dissolved organic C (referred to hereafter as extractable organic C) and total dissolved N via combustion and oxidation followed by detection of the evolved CO_2 and N oxide gases on a Formacs HT TOC/TN analyzer (Skalar, Breda, The Netherlands). Extractable organic N was then computed as total dissolved N in filtrate minus extractable mineral N (itself the sum of extractable NH_4-N and NO_2-N + NO_3-N). We determined soil total C and N from dried, milled subsamples subjected to elemental analysis (ECS 4010, Costech, Inc., Valencia, CA, USA) at the University of South Florida Stable Isotope Laboratory. Median concentration of inorganic C in unvegetated surface soil at our sites is 0.5 % of soil mass (Anderson, 2019, Univ. of South Florida M.S. thesis via methods in Wang et al., 2011, Environmental Monitoring and Assessment 174, 241-257). Inorganic C concentrations are likely even lower in our samples from under vegetation, where organic matter would dilute the contribution of inorganic C to soil mass. Nevertheless, the presence of a small inorganic C pool in our soils may be counted in the total C values we report. Extractable organic C is necessarily of organic C origin given the method (sparging with HCl) used in detection. Active C and N represent the fractions of organic C and N that are mineralizable by soil microorganisms under aerobic conditions in long-term soil incubations. To quantify active C and N, 60 g of field-moist soil were apportioned from each composite sample, placed in a filtration apparatus, and incubated in the dark at 25 °C and field capacity moisture for 365 d (as in Lewis et al., 2014, Ecosphere 5, art59). Moisture levels were maintained by frequently weighing incubated soil and wetting them up to target mass. Daily CO_2 flux was quantified on 29 occasions at 0.5-3 week intervals during the incubation period (with shorter intervals earlier in the incubation), and these per day flux rates were integrated over the 365 d period to compute an estimate of active C. Observations of per day flux were made by sealing samples overnight in airtight chambers fitted with septa and quantifying headspace CO_2 accumulation by injecting headspace samples (obtained through the septa via needle and syringe) into an infrared gas analyzer (PP Systems EGM 4, Amesbury, MA, USA). To estimate active N, each incubated sample was leached with a C and N free, 35 psu solution containing micronutrients (Nadelhoffer, 1990, Soil Science Society of America Journal 54, 411-415) on 19 occasions at increasing 1-6 week intervals during the 365 d incubation, and then extracted in 0.5 M K_2SO_4 at the end of the incubation in order to remove any residual mineral N. Active N was then quantified as the total mass of mineral N leached and extracted. Mineral N in leached and extracted solutions was detected as NH_4-N and NO_2-N + NO_3-N via colorimetry as above. This incubation technique precludes new C and N inputs and persistently leaches mineral N, forcing microorganisms to meet demand by mineralizing existing pools, and thereby directly assays the potential activity of soil organic C and N pools present at the time of soil sampling. Because this analysis commences with disrupting soil physical structure, it is biased toward higher estimates of active fractions. Calculations. Non-mobile C and N fractions were computed as total C and N concentrations minus the extractable and active fractions of each element. This data package reports surface-soil constituents (moisture, fines, SOM, and C and N pools and fractions) in both gravimetric units (mass constituent / mass soil) and areal units (mass constituent / soil surface area integrated through 7.6 cm soil depth, the depth of sampling). Areal concentrations were computed as X × D × 7.6, where X is the gravimetric concentration of a soil constituent, D is soil bulk density (g dry soil / cm^3), and 7.6 is the sampling depth in cm.more » « less
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We propose a predictive runtime monitoring approach for linear systems with stochastic disturbances. The goal of the monitor is to decide if there exists a possible sequence of control inputs over a given time horizon to ensure that a safety property is maintained with a sufficiently high probability. We derive an efficient algorithm for performing the predictive monitoring in real time, specifically for linear time invariant (LTI) systems driven by stochastic disturbances. The algorithm implicitly defines a control envelope set such that if the current control input to the system lies in this set, there exists a future strategy over a time horizon consisting of the next N steps to guarantee the safety property of interest. As a result, the proposed monitor is oblivious of the actual controller, and therefore, applicable even in the presence of complex control systems including highly adaptive controllers. Furthermore, we apply our proposed approach to monitor whether a UAV will respect a “geofence” defined by a geographical region over which the vehicle may operate. To achieve this, we construct a data-driven linear model of the UAVs dynamics, while carefully modeling the uncertainties due to wind, GPS errors and modeling errors as time-varying disturbances. Using realistic data obtained from flight tests, we demonstrate the advantages and drawbacks of the predictive monitoring approach.more » « less
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null (Ed.)Abstract Neural state classification (NSC) is a recently proposed method for runtime predictive monitoring of hybrid automata (HA) using deep neural networks (DNNs). NSC trains a DNN as an approximate reachability predictor that labels an HA state x as positive if an unsafe state is reachable from x within a given time bound, and labels x as negative otherwise. NSC predictors have very high accuracy, yet are prone to prediction errors that can negatively impact reliability. To overcome this limitation, we present neural predictive monitoring (NPM), a technique that complements NSC predictions with estimates of the predictive uncertainty. These measures yield principled criteria for the rejection of predictions likely to be incorrect, without knowing the true reachability values. We also present an active learning method that significantly reduces the NSC predictor’s error rate and the percentage of rejected predictions. We develop two versions of NPM based, respectively, on the use of frequentist and Bayesian techniques to learn the predictor and the rejection rule. Both versions are highly efficient, with computation times on the order of milliseconds, and effective, managing in our experimental evaluation to successfully reject almost all incorrect predictions. In our experiments on a benchmark suite of six hybrid systems, we found that the frequentist approach consistently outperforms the Bayesian one. We also observed that the Bayesian approach is less practical, requiring a careful and problem-specific choice of hyperparameters.more » « less
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Abstract The majority of bird and bat species are incapable of carrying tags that transmit their position to satellites. Given fundamental power requirements for such communication, burdened mass guidelines and battery technology, this constraint necessitates the continued use of very high frequency (VHF) radio beacons. As such, efforts should be made to mitigate their primary deficiencies: detection range, localization time and localization accuracy.
The integration of a radiotelemetry system with an unmanned aerial vehicle (UAV) could significantly improve the capacity for data collection from VHF tags. We present a UAV‐integrated radiotelemetry system that relies on open source hardware and software. Localization methods, including signal processing, bearing estimation based on principal component analysis, localization techniques and test results, are discussed.
Using a low‐power beacon applicable for bats and small birds, testing showed that the improved vantage of the UAV‐radiotelemetry system (UAV‐RT) provided significantly higher received signal power compared to the low‐level flights (maximum range beyond 1.4 km). Flight testing of localization methods showed median bearing errors between 2.3° and 6.8°, with localization errors of between 5% and 14% of the distance to the tag. In a direct comparison to an experienced radiotelemetry user, the UAV‐RT system provided bearing and localization estimates with 53% less error.
This paper introduces the core functionality and use methods of the UAV‐RT system, while presenting baseline localization performance metrics. An associated website hosts plans for assembly and software installation. The methods of UAV‐RT use for tag detection will be further developed in future works. For both the detection and localization problems, the mobility of a flying asset drastically reduces tracker time requirements. A 7‐min flight would be sufficient to collect five equally spaced bearing estimates over a 1‐km transect. The use of a software‐defined radio on the UAV‐RT system will allow for the simultaneous detection and localization of multiple tags.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IROS45743.2020.9340755
