Optimal Path Searching through Specified Routes using different Algorithms

To connect different electrical, network and data devices with the minimum cost and shortest path, is a complex job. In huge buildings, where the devices are placed at different locations on different floors and only some specific routes are available to pass the cables and buses, the shortest path search becomes more complex. The aim of this thesis project is, to develop an application which indentifies the best path to connect all objects or devices by following the specific routes.To address the above issue we adopted three algorithms Greedy Algorithm, Simulated Annealing and Exhaustive search and analyzed their results. The given problem is similar to Travelling Salesman Problem. Exhaustive search is a best algorithm to solve this problem as it checks each and every possibility and give the accurate result but it is an impractical solution because of huge time consumption. If no. of objects increased from 12 it takes hours to search the shortest path. Simulated annealing is emerged with some promising results with lower time cost. As of probabilistic nature, Simulated annealing could be non optimal but it gives a near optimal solution in a reasonable duration. Greedy algorithm is not a good choice for this problem. So, simulated annealing is proved best algorithm for this problem. The project has been implemented in C-language which takes input and store output in an Excel Workbook

Production and Delivery (Optimization of production system and reliability)

This thesis is done to solve two issues for Sayid Paper Mill Ltd Pakistan. Section one deals with a practical problem arise in SPM that is cutting a given set of raw paper rolls of known length and width, and a set of product paper rolls of known length (equal to the length of raw paper rolls) and width, practical cutting constraints on a single cutting machine, according to demand orders for all customers. To solve this problem requires to determine an optimal cutting schedule to maximize the overall cutting process profitability while satisfying all demands and cutting constraints. The aim of this part of thesis is to develop a mathematical model which solves this problem.Second section deals with a problem of delivering final product from warehouse to different destinations by finding shortest paths. It is an operational routing problem to decide the daily routes for sending trucks to different destination to deliver their final product. This industrial problem is difficult and includes aspect such as delivery to a single destination and multiple destinations with limited resources. The aim of this part of thesis is to develop a process which helps finding shortest path.

An extension of the flower pattern diagram for roll forming

The initial process design of a roll forming system is often based on the traditional ‘flower pattern diagram’. In this diagram, the cross sections of the strip at each roll stand are superimposed on a single plane; the diagram is a 2D representation of the 3D process. In the present work, the flower pattern is extended into three dimensions. To demonstrate the method, the forming path or trajectory of a point at the edge of the strip during forming a V-section is considered. The forming path is a surface curve that lies on a cylindrical surface having its axis along the machine axis. This surface is unwrapped to give its plane development and important features of the forming process can be determined and are readily interpreted from this plane curve. It is shown that at any stage in the process, the axial strain and the curvature of the sheet adjacent to the point are dependent on the slope of the trajectory in this plane projection. This new diagram, which apparently has not been used previously, provides a useful initial method of examining the roll forming process and optimising the flower pattern. The model is purely geometric, as is the original flower pattern approach, and does not include the effect of material behaviour. The concept is applied to several cases available in the literature. It shows that the lowest level of shape defect in the part is achieved when the trajectory of the strip edge follows the shortest line length between the start and finish of forming, leading to the least longitudinal strain introduced in the flange. This trend is in agreement with previous experimental observations, suggesting that the analytical model proposed may be applied for early process design and optimisation before time-consuming numerical analysis is performed.

MODELING AND PROTOCOL DESIGN FOR EMERGING WIRELESS SYSTEMS

Mobile Mesh Network based In-Transit Visibility (MMN-ITV) system facilitates global real-time tracking capability for the logistics system. In-transit containers form a multi-hop mesh network to forward the tracking information to the nearby sinks, which further deliver the information to the remote control center via satellite. The fundamental challenge to the MMN-ITV system is the energy constraint of the battery-operated containers. Coupled with the unique mobility pattern, cross-MMN behavior, and the large-spanned area, it is necessary to investigate the energy-efficient communication of the MMN-ITV system thoroughly. First of all, this dissertation models the energy-efficient routing under the unique pattern of the cross-MMN behavior. A new modeling approach, pseudo-dynamic modeling approach, is proposed to measure the energy-efficiency of the routing methods in the presence of the cross-MMN behavior. With this approach, it could be identified that the shortest-path routing and the load-balanced routing is energy-efficient in mobile networks and static networks respectively. For the MMN-ITV system with both mobile and static MMNs, an energy-efficient routing method, energy-threshold routing, is proposed to achieve the best tradeoff between them. Secondly, due to the cross-MMN behavior, neighbor discovery is executed frequently to help the new containers join the MMN, hence, consumes similar amount of energy as that of the data communication. By exploiting the unique pattern of the cross-MMN behavior, this dissertation proposes energy-efficient neighbor discovery wakeup schedules to save up to 60% of the energy for neighbor discovery. Vehicular Ad Hoc Networks (VANETs)-based inter-vehicle communications is by now growingly believed to enhance traffic safety and transportation management with low cost. The end-to-end delay is critical for the time-sensitive safety applications in VANETs, and can be a decisive performance metric for VANETs. This dissertation presents a complete analytical model to evaluate the end-to-end delay against the transmission range and the packet arrival rate. This model illustrates a significant end-to-end delay increase from non-saturated networks to saturated networks. It hence suggests that the distributed power control and admission control protocols for VANETs should aim at improving the real-time capacity (the maximum packet generation rate without causing saturation), instead of the delay itself. Based on the above model, it could be determined that adopting uniform transmission range for every vehicle may hinder the delay performance improvement, since it does not allow the coexistence of the short path length and the low interference. Clusters are proposed to configure non-uniform transmission range for the vehicles. Analysis and simulation confirm that such configuration can enhance the real-time capacity. In addition, it provides an improved trade off between the end-to-end delay and the network capacity. A distributed clustering protocol with minimum message overhead is proposed, which achieves low convergence time.

Improving shortest paths in the Delaunay triangulation

We study a problem about shortest paths in Delaunay triangulations. Given two nodes s; t in the Delaunay triangulation of a point set P, we look for a new point p that can be added, such that the shortest path from s to t in the Delaunay triangulation of P u{p} improves as much as possible. We study properties of the problem and give efficient algorithms to find such a point when the graph-distance used is Euclidean and for the link-distance. Several other variations of the problem are also discussed.

On multiple-path sonic anemometer measurement theory

In this paper, a model of the measuring process of sonic anemometers with more than one measuring path is presented. The main hypothesis of the work is that the time variation of the turbulent speed field during the sequence of pulses that produces a measure of the wind speed vector affects the measurement. Therefore, the previously considered frozen flow, or instantaneous averaging, condition is relaxed. This time variation, quantified by the mean Mach number of the flow and the time delay between consecutive pulses firings, in combination with both the full geometry of sensors (acoustic path location and orientation) and the incidence angles of the mean with speed vector, give rise to significant errors in the measurement of turbulence which are not considered by models based on the hypothesis of instantaneous line averaging. The additional corrections (relative to the ones proposed by instantaneous line-averaging models) are strongly dependent on the wave number component parallel to the mean wind speed, the time delay between consecutive pulses, the Mach number of the flow, the geometry of the sensor and the incidence angles of mean wind speed vector. Kaimal´s limit k W1=1/l (where k W1 is the wave number component parallel to mean wind speed and l is the path length) for the maximum wave numbers from which the sonic process affects the measurement of turbulence is here generalized as k W1=C l /l, where C l is usually lesser than unity and depends on all the new parameters taken into account by the present model.

Vestibular navigation directed by the slope of terrain.

Slope of terrain is an important orienting gradient affecting the goal-directed locomotion of animals. Its significance was assessed in experiment 1 by training rats to find in darkness a feeder on the top of a low cone (80-cm base, 0- to 4-cm high). A computerized infrared tracking system monitoring the rat's position in darkness showed that the path length on the cone surface was inversely proportional to cone height. A device allowing continuous generation of slope-guided locomotion was used in experiment 2. This device consists of a 1-m arena, the floor of which can be supported at a point corresponding to the position of one of three equidistant feeders located 17 cm from its center. The arena is inclined by the locomotion of the rat to a plane passing through the elevated (2- or 4-cm) feeder, the rat's center of gravity, and a point at the edge of the arena resting on the floor. The multitude of such planes generated by the rat's locomotion forms the surface of a virtual cone, the top of which is formed by the feeder. Additional path (difference between distance traveled and shortest distance of the animal from the goal at the onset of inclination) is inversely related to the incline of the arena and is a sensitive measure of performance in this type of vestibular navigation.

Effective web service discovery using a combination of a semantic model and a data mining technique

With the advent of Service Oriented Architecture, Web Services have gained tremendous popularity. Due to the availability of a large number of Web services, finding an appropriate Web service according to the requirement of the user is a challenge. This warrants the need to establish an effective and reliable process of Web service discovery. A considerable body of research has emerged to develop methods to improve the accuracy of Web service discovery to match the best service. The process of Web service discovery results in suggesting many individual services that partially fulfil the user’s interest. By considering the semantic relationships of words used in describing the services as well as the use of input and output parameters can lead to accurate Web service discovery. Appropriate linking of individual matched services should fully satisfy the requirements which the user is looking for. This research proposes to integrate a semantic model and a data mining technique to enhance the accuracy of Web service discovery. A novel three-phase Web service discovery methodology has been proposed. The first phase performs match-making to find semantically similar Web services for a user query. In order to perform semantic analysis on the content present in the Web service description language document, the support-based latent semantic kernel is constructed using an innovative concept of binning and merging on the large quantity of text documents covering diverse areas of domain of knowledge. The use of a generic latent semantic kernel constructed with a large number of terms helps to find the hidden meaning of the query terms which otherwise could not be found. Sometimes a single Web service is unable to fully satisfy the requirement of the user. In such cases, a composition of multiple inter-related Web services is presented to the user. The task of checking the possibility of linking multiple Web services is done in the second phase. Once the feasibility of linking Web services is checked, the objective is to provide the user with the best composition of Web services. In the link analysis phase, the Web services are modelled as nodes of a graph and an allpair shortest-path algorithm is applied to find the optimum path at the minimum cost for traversal. The third phase which is the system integration, integrates the results from the preceding two phases by using an original fusion algorithm in the fusion engine. Finally, the recommendation engine which is an integral part of the system integration phase makes the final recommendations including individual and composite Web services to the user. In order to evaluate the performance of the proposed method, extensive experimentation has been performed. Results of the proposed support-based semantic kernel method of Web service discovery are compared with the results of the standard keyword-based information-retrieval method and a clustering-based machine-learning method of Web service discovery. The proposed method outperforms both information-retrieval and machine-learning based methods. Experimental results and statistical analysis also show that the best Web services compositions are obtained by considering 10 to 15 Web services that are found in phase-I for linking. Empirical results also ascertain that the fusion engine boosts the accuracy of Web service discovery by combining the inputs from both the semantic analysis (phase-I) and the link analysis (phase-II) in a systematic fashion. Overall, the accuracy of Web service discovery with the proposed method shows a significant improvement over traditional discovery methods.

Influence of presbyopic corrections on driving-related eye and head movements

Purpose: To investigate whether wearing different presbyopic vision corrections alters the pattern of eye and head movements when viewing and responding to driving-related traffic scenes. Methods: Participants included 20 presbyopes (mean age: 56.1 ± 5.7 years) who had no experience of wearing presbyopic vision corrections, apart from single vision (SV) reading spectacles. Each participant wore five different vision corrections: distance SV lenses, progressive addition spectacle lenses (PAL), bifocal spectacle lenses (BIF), monovision (MV) and multifocal contact lenses (MTF CL). For each visual condition, participants were required to view videotape recordings of traffic scenes, track a reference vehicle, and identify a series of peripherally presented targets. Digital numerical display panels were also included as near visual stimuli (simulating the visual displays of a vehicle speedometer and radio). Eye and head movements were measured, and the accuracy of target recognition was also recorded. Results: The path length of eye movements while viewing and responding to driving-related traffic scenes was significantly longer when wearing BIF and PAL than MV and MTF CL (both p ≤ 0.013). The path length of head movements was greater with SV, BIF, and PAL than MV and MTF CL (all p < 0.001). Target recognition and brake response times were not significantly affected by vision correction, whereas target recognition was less accurate when the near stimulus was located at eccentricities inferiorly and to the left, rather than directly below the primary position of gaze (p = 0.008), regardless of vision correction. Conclusions: Different presbyopic vision corrections alter eye and head movement patterns. The longer path length of eye and head movements and greater number of saccades associated with the spectacle presbyopic corrections may affect some aspects of driving performance.

The effect of monocular and binocular cataract blur on postural stability among older adults

Purpose: First-eye cataract surgery can reduce the rate of falls among older adults, yet the effect of second-eye surgery on the rate of falling remains unclear. The present study investigated the effect of monocular and binocular simulated cataract blur on postural stability among older adults. Methods: Postural stability was assessed on 34 healthy older adults (mean 68.2 years, SD 3.5) with normal vision, using a portable force platform (BT4, HUR Labs, Finland) which collected data on centre of pressure (COP) displacement. Stability was assessed on firm and foam surfaces under four binocular viewing conditions using Vistech filters to simulate cataract blur: [1] best-corrected vision both eyes; [2] blur over non-dominant eye, [3] blur over dominant eye and [4] blur over both eyes. Binocular logMAR visual acuity, Pelli-Robson contrast sensitivity and stereoacuity were also measured under these viewing conditions and ocular dominance measured using the hole-in-card test. Generalized estimating equations with an exchangeable correlation structure examined the effect of the surface and vision conditions on postural stability. Results: Visual acuity and contrast sensitivity were significantly reduced under monocular and binocular cataract blur compared to normal viewing. All blur conditions resulted in loss of stereoacuity. Binocular cataract blur significantly reduced postural stability compared to normal vision on the firm (COP path length; p=0.013) and foam surface (anterior-posterior COP RMS, COP path length and COP area; p<0.01). However, no significant differences in postural stability were found between the monocular blur conditions compared to normal vision, or between the dominant and non-dominant monocular blur conditions on either the firm or foam surfaces. Conclusions: Findings indicate that binocular blur significantly impairs postural stability, and suggests that improvements in postural stability may justify first-eye cataract surgery, particularly during somatosensory disruption. Postural stability was not significantly impaired in the monocular cataract blur conditions compared to the normal vision condition, nor was there any effect of ocular dominance on postural stability in the presence of monocular cataract blur.

Dynamics of transformation and fragmentation of composite liquid nano-particles

Recent research on particle size distributions and particle concentrations near a busy road cannot be explained by the conventional mechanisms for particle evolution of combustion aerosols. Specifically they appear to be inadequate to explain the experimental observations of particle transformation and the evolution of the total number concentration. This resulted in the development of a new mechanism based on their thermal fragmentation, for the evolution of combustion aerosol nano-particles. A complex and comprehensive pattern of evolution of combustion aerosols, involving particle fragmentation, was then proposed and justified. In that model it was suggested that thermal fragmentation occurs in aggregates of primary particles each of which contains a solid graphite/carbon core surrounded by volatile molecules bonded to the core by strong covalent bonds. Due to the presence of strong covalent bonds between the core and the volatile (frill) molecules, such primary composite particles can be regarded as solid, despite the presence of significant (possibly, dominant) volatile component. Fragmentation occurs when weak van der Waals forces between such primary particles are overcome by their thermal (Brownian) motion. In this work, the accepted concept of thermal fragmentation is advanced to determine whether fragmentation is likely in liquid composite nano-particles. It has been demonstrated that at least at some stages of evolution, combustion aerosols contain a large number of composite liquid particles containing presumably several components such as water, oil, volatile compounds, and minerals. It is possible that such composite liquid particles may also experience thermal fragmentation and thus contribute to, for example, the evolution of the total number concentration as a function of distance from the source. Therefore, the aim of this project is to examine theoretically the possibility of thermal fragmentation of composite liquid nano-particles consisting of immiscible liquid v components. The specific focus is on ternary systems which include two immiscible liquid droplets surrounded by another medium (e.g., air). The analysis shows that three different structures are possible, the complete encapsulation of one liquid by the other, partial encapsulation of the two liquids in a composite particle, and the two droplets separated from each other. The probability of thermal fragmentation of two coagulated liquid droplets is discussed and examined for different volumes of the immiscible fluids in a composite liquid particle and their surface and interfacial tensions through the determination of the Gibbs free energy difference between the coagulated and fragmented states, and comparison of this energy difference with the typical thermal energy kT. The analysis reveals that fragmentation was found to be much more likely for a partially encapsulated particle than a completely encapsulated particle. In particular, it was found that thermal fragmentation was much more likely when the volume ratio of the two liquid droplets that constitute the composite particle are very different. Conversely, when the two liquid droplets are of similar volumes, the probability of thermal fragmentation is small. It is also demonstrated that the Gibbs free energy difference between the coagulated and fragmented states is not the only important factor determining the probability of thermal fragmentation of composite liquid particles. The second essential factor is the actual structure of the composite particle. It is shown that the probability of thermal fragmentation is also strongly dependent on the distance that each of the liquid droplets should travel to reach the fragmented state. In particular, if this distance is larger than the mean free path for the considered droplets in the air, the probability of thermal fragmentation should be negligible. In particular, it follows form here that fragmentation of the composite particle in the state with complete encapsulation is highly unlikely because of the larger distance that the two droplets must travel in order to separate. The analysis of composite liquid particles with the interfacial parameters that are expected in combustion aerosols demonstrates that thermal fragmentation of these vi particles may occur, and this mechanism may play a role in the evolution of combustion aerosols. Conditions for thermal fragmentation to play a significant role (for aerosol particles other than those from motor vehicle exhaust) are determined and examined theoretically. Conditions for spontaneous transformation between the states of composite particles with complete and partial encapsulation are also examined, demonstrating the possibility of such transformation in combustion aerosols. Indeed it was shown that for some typical components found in aerosols that transformation could take place on time scales less than 20 s. The analysis showed that factors that influenced surface and interfacial tension played an important role in this transformation process. It is suggested that such transformation may, for example, result in a delayed evaporation of composite particles with significant water component, leading to observable effects in evolution of combustion aerosols (including possible local humidity maximums near a source, such as a busy road). The obtained results will be important for further development and understanding of aerosol physics and technologies, including combustion aerosols and their evolution near a source.

The impact of presbyopic spectacles and contact lenses on driving performance

Presbyopia affects individuals from the age of 45 years onwards, resulting in difficulty in accurately focusing on near objects. There are many optical corrections available including spectacles or contact lenses that are designed to enable presbyopes to see clearly at both far and near distances. However, presbyopic vision corrections also disturb aspects of visual function under certain circumstances. The impact of these changes on activities of daily living such as driving are, however, poorly understood. Therefore, the aim of this study was to determine which aspects of driving performance might be affected by wearing different types of presbyopic vision corrections. In order to achieve this aim, three experiments were undertaken. The first experiment involved administration of a questionnaire to compare the subjective driving difficulties experienced when wearing a range of common presbyopic contact lens and spectacle corrections. The questionnaire was developed and piloted, and included a series of items regarding difficulties experienced while driving under day and night-time conditions. Two hundred and fifty five presbyopic patients responded to the questionnaire and were categorised into five groups, including those wearing no vision correction for driving (n = 50), bifocal spectacles (BIF, n = 54), progressive addition lenses spectacles (PAL, n = 50), monovision (MV, n = 53) and multifocal contact lenses (MTF CL, n = 48). Overall, ratings of satisfaction during daytime driving were relatively high for all correction types. However, MV and MTF CL wearers were significantly less satisfied with aspects of their vision during night-time than daytime driving, particularly with regard to disturbances from glare and haloes. Progressive addition lens wearers noticed more distortion of peripheral vision, while BIF wearers reported more difficulties with tasks requiring changes in focus and those who wore no vision correction for driving reported problems with intermediate and near tasks. Overall, the mean level of satisfaction for daytime driving was quite high for all of the groups (over 80%), with the BIF wearers being the least satisfied with their vision for driving. Conversely, at night, MTF CL wearers expressed the least satisfaction. Research into eye and head movements has become increasingly of interest in driving research as it provides a means of understanding how the driver responds to visual stimuli in traffic. Previous studies have found that wearing PAL can affect eye and head movement performance resulting in slower eye movement velocities and longer times to stabilize the gaze for fixation. These changes in eye and head movement patterns may have implications for driving safety, given that the visual tasks for driving include a range of dynamic search tasks. Therefore, the second study was designed to investigate the influence of different presbyopic corrections on driving-related eye and head movements under standardized laboratory-based conditions. Twenty presbyopes (mean age: 56.1 ± 5.7 years) who had no experience of wearing presbyopic vision corrections, apart from single vision reading spectacles, were recruited. Each participant wore five different types of vision correction: single vision distance lenses (SV), PAL, BIF, MV and MTF CL. For each visual condition, participants were required to view videotape recordings of traffic scenes, track a reference vehicle and identify a series of peripherally presented targets while their eye and head movements were recorded using the faceLAB® eye and head tracking system. Digital numerical display panels were also included as near visual stimuli (simulating the visual displays of a vehicle speedometer and radio). The results demonstrated that the path length of eye movements while viewing and responding to driving-related traffic scenes was significantly longer when wearing BIF and PAL than MV and MTF CL. The path length of head movements was greater with SV, BIF and PAL than MV and MTF CL. Target recognition was less accurate when the near stimulus was located at eccentricities inferiorly and to the left, rather than directly below the primary position of gaze, regardless of vision correction type. The third experiment aimed to investigate the real world driving performance of presbyopes while wearing different vision corrections measured on a closed-road circuit at night-time. Eye movements were recorded using the ASL Mobile Eye, eye tracking system (as the faceLAB® system proved to be impractical for use outside of the laboratory). Eleven participants (mean age: 57.25 ± 5.78 years) were fitted with four types of prescribed vision corrections (SV, PAL, MV and MTF CL). The measures of driving performance on the closed-road circuit included distance to sign recognition, near target recognition, peripheral light-emitting-diode (LED) recognition, low contrast road hazards recognition and avoidance, recognition of all the road signs, time to complete the course, and driving behaviours such as braking, accelerating, and cornering. The results demonstrated that driving performance at night was most affected by MTF CL compared to PAL, resulting in shorter distances to read signs, slower driving speeds, and longer times spent fixating road signs. Monovision resulted in worse performance in the task of distance to read a signs compared to SV and PAL. The SV condition resulted in significantly more errors made in interpreting information from in-vehicle devices, despite spending longer time fixating on these devices. Progressive addition lenses were ranked as the most preferred vision correction, while MTF CL were the least preferred vision correction for night-time driving. This thesis addressed the research question of how presbyopic vision corrections affect driving performance and the results of the three experiments demonstrated that the different types of presbyopic vision corrections (e.g. BIF, PAL, MV and MTF CL) can affect driving performance in different ways. Distance-related driving tasks showed reduced performance with MV and MTF CL, while tasks which involved viewing in-vehicle devices were significantly hampered by wearing SV corrections. Wearing spectacles such as SV, BIF and PAL induced greater eye and head movements in the simulated driving condition, however this did not directly translate to impaired performance on the closed- road circuit tasks. These findings are important for understanding the influence of presbyopic vision corrections on vision under real world driving conditions. They will also assist the eye care practitioner to understand and convey to patients the potential driving difficulties associated with wearing certain types of presbyopic vision corrections and accordingly to support them in the process of matching patients to optical corrections which meet their visual needs.

Transit users' route-choice modelling in transit assignment : a review

This paper reviews the main studies on transit users’ route choice in thecontext of transit assignment. The studies are categorized into three groups: static transit assignment, within-day dynamic transit assignment, and emerging approaches. The motivations and behavioural assumptions of these approaches are re-examined. The first group includes shortest-path heuristics in all-or-nothing assignment, random utility maximization route-choice models in stochastic assignment, and user equilibrium based assignment. The second group covers within-day dynamics in transit users’ route choice, transit network formulations, and dynamic transit assignment. The third group introduces the emerging studies on behavioural complexities, day-to-day dynamics, and real-time dynamics in transit users’ route choice. Future research directions are also discussed.

Intelligent computing and sensing for active safety on construction sites

On obstacle-cluttered construction sites where heavy equipment is in use, safety issues are of major concern. The main objective of this paper is to develop a framework with algorithms for obstacle avoidance and path planning based on real-time three-dimensional job site models to improve safety during equipment operation. These algorithms have the potential to prevent collisions between heavy equipment vehicles and other on-site objects. In this study, algorithms were developed for image data acquisition, real-time 3D spatial modeling, obstacle avoidance, and shortest path finding and were all integrated to construct a comprehensive collision-free path. Preliminary research results show that the proposed approach is feasible and has the potential to be used as an active safety feature for heavy equipment.

Planning most-likely paths from overhead imagery

This paper is about planning paths from overhead imagery, the novelty of which is taking explicit account of uncertainty in terrain classification and spatial variation in terrain cost. The image is first classified using a multi-class Gaussian Process Classifier which provides probabilities of class membership at each location in the image. The probability of class membership at a particular grid location is then combined with a terrain cost evaluated at that location using a spatial Gaussian process. The resulting cost function is, in turn, passed to a planner. This allows both the uncertainty in terrain classification and spatial variations in terrain costs to be incorporated into the planned path. Because the cost of traversing a grid cell is now a probability density rather than a single scalar value, we can produce not only the most-likely shortest path between points on the map, but also sample from the cost map to produce a distribution of paths between the points. Results are shown in the form of planned paths over aerial maps, these paths are shown to vary in response to local variations in terrain cost.