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This paper developes a method for mathematically modeling terrain surfaces for use on an unmanned Martian vehicle. The data collected by the vehicle consists of terrain height and two directional slopes at each data point. The parameters for the mathematical terrain model are stochastically determined by using least square approximations.-
Digital terrain models produced by computer correlation of stereo images are likely to contain occasional gross errors in terrain elevation. These errors typically result from having mismatched sub-areas of the two images, a problem which can occur for a variety of image- and terrain-related reasons. Such elevation errors produce undesirable effects when the models are further processed, and should be detected and corrected as early in the processing as possible. Algorithms have been developed to detect and correct errors in digital terrain models. These algorithms focus on the use of constraints on both the allowable slope and the allowable change in slope in local areas around each point. Relaxation-like techniques are employed in the iteration of the detection and correction phases to obtain best results.
A method is developed for modeling terrain surfaces for use on an unmanned Martian roving vehicle. The modeling procedure employs a two-step process which uses gradient as well as height data in order to improve the accuracy of the model's gradient. Least square approximation is used in order to stochastically determine the parameters which describe the modeled surface. A complete error analysis of the modeling procedure is included which determines the effect of instrumental measurement errors on the model's accuracy. Computer simulation is used as a means of testing the entire modeling process which includes the acquisition of data points, the two-step modeling process and the error analysis. Finally, to illustrate the procedure, a numerical example is included.
The Mars Digital Terrain Model (DTM) is the result of a new project to: (1) digitize the series of 1:2,000,000-scale topographic maps of Mars, which are being derived photogrammetically under a separate project, and (2) reformat the digital contour information into rasters of elevation that can be readily registered with the Digital Image Model (DIM) of Mars. Derivation of DTM's involves interpolation of elevation values into 1/64-degree resolution and transformation of them to a sinusoidal equal-area projection. Digital data are produced in blocks corresponding with the coordinates of the original 1:2,000,000-scale maps, i.e., the dimensions of each block in the equatorial belt are 22.5 deg of longitude and 15 deg of latitude. This DTM is not only compatible with the DIM, but it can also be registered with other data such as geologic units or gravity. It will be the most comprehensive record of topographic information yet compiled for the Martian surface. Once the DTM's are established, any enhancement of Mars topographic information made with updated data, such as data from the planned Mars Observer Mission, will be by mathematical transformation of the DTM's, eliminating the need for recompilation.
It is pointed out that the importance of digital terrain models in the processing, analysis, and interpretation of remote sensing data is increasing. In investigations related to the study of radar images, digital terrain models can have a particular significance, because radar reflection is a function of the terrain characteristics. A procedure for the analysis and interpretation of radar images is discussed. The procedure is based on a utilization of computer simulation which makes it possible to produce simulated radar images on the basis of a digital terrain model. The simulated radar images are used for the geometric and radiometric rectification of real radar images. A description of the employed procedures is provided, and the obtained results are discussed, taking into account a test area in Northern California.
A terrain modeling algorithm that would reconstruct the sensed ground images formed by the triangulation scheme, and classify as unsafe any terrain feature that would pose a hazard to a roving vehicle is described. This modeler greatly reduces quantization errors inherent in a laser/sensing system through the use of a thinning algorithm. Dual filters are employed to separate terrain steps from the general landscape, simplifying the analysis of terrain features. A crosspath analysis is utilized to detect and avoid obstacles that would adversely affect the roll of the vehicle. Computer simulations of the rover on various terrains examine the performance of the modeler.
This paper describes the SIMSCAPE middleware toolkit that has been developed recently to provide a common infrastructure for importing terrain model data from multiple data sources and making them available to simulation applications. The SIMSCAPE infrastructure simplifies the overall simulation design by eliminating the traditional need for custom terrain model interfaces to terrain data sources and simulation users. SIMSCAPE provides a collection of libraries and tools to use and manage terrain environment models within a wide range of simulation applications.
Topographical terrain models are generated by digitally delineating the boundary of the region under investigation from the data obtained from an airborne synthetic aperture radar image and surface elevation data concurrently acquired either from an airborne instrument or at ground level. A set of coregistered boundary maps thus generated are then digitally combined in three dimensional space with the acquired surface elevation data by means of image processing software stored in a digital computer. The method is particularly applicable for generating terrain models of flooded regions covered entirely or in part by foliage.
Mathematic modeling of terrain for autonomous surface vehicle guidance system
This paper develops a procedure for an autonomous Martian rover to classify objects into obstacles and non-obstacles. These so called 'objects' are actually models generated by the Terrain Modeling and Edge Detection schemes. The classification process is performed using a set of object parameters which distinguish unobstructive objects from obstacles.
The ground-level digital elevation model (DEM) or digital terrain model (DTM) information are invaluable for environmental modeling, such as water dynamics in forests, canopy height, forest biomass, carbon estimation, etc. We propose to extract the DTM over forested areas from the combination of interferometric complex coherence from single-pass TanDEM-X (TDX) data at HH polarization and Digital Surface Model (DSM) derived from high-resolution WorldView (WV) image pair by means of random volume over ground (RVoG) model. The RVoG model is a widely and successfully used model for polarimetric SAR interferometry (Pol-InSAR) technique for vertical forest structure parameter retrieval [1][2][3][4]. The ground-level DEM have been obtained by complex volume decorrelation in the RVoG model with the DSM using stereo-photogrammetric technique. Finally, the airborne lidar data were used to validate the ground-level DEM and forest canopy height results.
The following problem is considered: A point robot is placed in a terrain populated by an unknown number of polyhedral obstacles of varied sizes and locations in two/three dimensions. The robot is equipped with a sensor capable of detecting all the obstacle vertices and edges that are visible from the present location of the robot. The robot is required to autonomously navigate and build the complete terrain model using the sensor information. It is established that the necessary number of scanning operations needed for complete terrain model acquisition by any algorithm that is based on scan from vertices strategy is given by the summation of i = 1 (sup n) N(O sub i)-n and summation of i = 1 (sup n) N(O sub i)-2n in two- and three-dimensional terrains respectively, where O = (O sub 1, O sub 2,....O sub n) set of the obstacles in the terrain, and N(O sub i) is the number of vertices of the obstacle O sub i.
An application for registering and merging multiresolution terrain models is presented and some of the associated tools are discussed.
An application of octrees for registering and merging multiresolution terrain models is presented and some of the associated tools are discussed.
The initial phase of a program to determine the best interpretation strategy and sensor configuration for a radar remote sensing system for geologic applications is discussed. In this phase, terrain modeling and radar image simulation were used to perform parametric sensitivity studies. A relatively simple computer-generated terrain model is presented, and the data base, backscatter file, and transfer function for digital image simulation are described. Sets of images are presented that simulate the results obtained with an X-band radar from an altitude of 800 km and at three different terrain-illumination angles. The simulations include power maps, slant-range images, ground-range images, and ground-range images with statistical noise incorporated. It is concluded that digital image simulation and computer modeling provide cost-effective methods for evaluating terrain variations and sensor parameter changes, for predicting results, and for defining optimum sensor parameters.
A roving vehicle capable of autonomously exploring the surface of an alien world is under development and an advanced terrain modeler to characterize the possible paths of the rover as hazardous or safe is presented. This advanced terrain modeler has several improvements over the Troiani modeler that include: a crosspath analysis, better determination of hazards on slopes, and methods for dealing with missing returns at the extremities of the sensor field. The results from a package of programs to simulate the roving vehicle are then examined and compared to results from the Troiani modeler.
Computer-generated radar simulations and mathematical geologic terrain models were used to establish the optimum radar sensor operating parameters for geologic research. An initial set of mathematical geologic terrain models was created for three basic landforms and families of simulated radar images were prepared from these models for numerous interacting sensor, platform, and terrain variables. The tradeoffs between the various sensor parameters and the quantity and quality of the extractable geologic data were investigated as well as the development of automated techniques of digital SAR image analysis. Initial work on a texture analysis of SEASAT SAR imagery is reported. Computer-generated radar simulations are shown for combinations of two geologic models and three SAR angles of incidence.
Immersive environments are being used to support mission operations at the Jet Propulsion Laboratory. This technology contributed to the Mars Pathfinder Mission in planning sorties for the Sojourner rover and is being used for the Mars Exploration Rover (MER) missions. The stereo imagery captured by the rovers is used to create 3D terrain models, which can be viewed from any angle, to provide a powerful and information rich immersive visualization experience. These technologies contributed heavily to both the mission success and the phenomenal level of public outreach achieved by Mars Pathfinder and MER. This paper will review the utilization of terrain modelling for immersive environments in support of MER.