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Limitations to the study of man in space in the U.S. space program

Research on humans conducted during spaceflight is fraught both with great opportunities and great obstacles. The purpose of this paper is to review some of the limitations to research in space in the United States with hope that an informed scientific community may lead to more rapid and efficient solution of these problems. Limitations arise because opportunities to study the same astronauts in well-controlled situations on repeated spaceflights are practically non-existent. Human research opportunities are further limited by the necessity of avoiding simultaneous mutually-interfering experiments. Environmental factors, including diet and other physiological perturbations concomitant with spaceflight, also complicate research design and interpretation. Technical limitations to research methods and opportunities further restrict the development of the knowledge base. Finally, Earth analogues of space travel all suffer from inadequacies. Though all of these obstacles will eventually be overcome, creativity, diligence, and persistence are required to further our knowledge of humans in space.

Bishop, Phillip A.↗

Limitations to the study of man in the United States space program

Research on humans conducted during space flight is fraught both with great opportunities and great obstacles. The purpose of this paper is to review some of the limitations to United States research in space in the hope that an informed scientific community may lead to more rapid and efficient solution of these problems. Limitations arise because opportunities to study the same astronauts in well-controlled situations on repeated space flights are practically non-existent. Human research opportunities are further limited by the necessity of avoiding simultaneous mutually-interfereing experiments. Environmental factors including diet and other physiological perturbations concomitant with space flight also complicates research design and interpretation. Technical limitations to research methods and opportunities further restrict the development of the knowledge base. Finally, earth analogues of space travel all suffer from inadequacies. Though all of these obstacles will eventually be overcome; creativity, diligence, and persistence are required to further our knowledge of humans in space.

Bishop, Phillip A.↗

Time-dependent viscous incompressible Navier-Stokes equations - The finite difference Galerkin formulation and streamfunction algorithms

Numerical techniques are developed to solve the Navier-Stokes equations for unsteady incompressible flow. The extension of the finite-difference Galerkin (FDG) method of Stephens et al. (1984) to the continuous-time case in two or three space dimensions is explained, and the numerical implementation of the method is discussed with particular attention to the staggered-MAC-grid primitive-variable discretization, the application of discrete mass balance to avoid problems inherent in FDG schemes, the direct interpretation of the FDG expansion variables as a discrete streamfunction, and a mass-balance approach to two-dimensional problems with throughflow or obstacles. Numerical results are presented graphically for the evolution of asymptotic steady flow in a driven cavity at Reynolds number 400, 1000, or 3200; good agreement with published experimental data is demonstrated, with accurate predictions of secondary-vortex formation from wall bubble recirculations at Reynolds number 1000.

Goodrich, John W.↗

Insect-Inspired Flight Control for Unmanned Aerial Vehicles

Flight-control and navigation systems inspired by the structure and function of the visual system and brain of insects have been proposed for a class of developmental miniature robotic aircraft called "biomorphic flyers" described earlier in "Development of Biomorphic Flyers" (NPO-30554), NASA Tech Briefs, Vol. 28, No. 11 (November 2004), page 54. These form a subset of biomorphic explorers, which, as reported in several articles in past issues of NASA Tech Briefs ["Biomorphic Explorers" (NPO-20142), Vol. 22, No. 9 (September 1998), page 71; "Bio-Inspired Engineering of Exploration Systems" (NPO-21142), Vol. 27, No. 5 (May 2003), page 54; and "Cooperative Lander-Surface/Aerial Microflyer Missions for Mars Exploration" (NPO-30286), Vol. 28, No. 5 (May 2004), page 36], are proposed small robots, equipped with microsensors and communication systems, that would incorporate crucial functions of mobility, adaptability, and even cooperative behavior. These functions are inherent to biological organisms but are challenging frontiers for technical systems. Biomorphic flyers could be used on Earth or remote planets to explore otherwise difficult or impossible to reach sites. An example of an exploratory task of search/surveillance functions currently being tested is to obtain high-resolution aerial imagery, using a variety of miniaturized electronic cameras. The control functions to be implemented by the systems in development include holding altitude, avoiding hazards, following terrain, navigation by reference to recognizable terrain features, stabilization of flight, and smooth landing. Flying insects perform these and other functions remarkably well, even though insect brains contains fewer than 10(exp -4) as many neurons as does the human brain. Although most insects have immobile, fixed-focus eyes and lack stereoscopy (and hence cannot perceive depth directly), they utilize a number of ingenious strategies for perceiving, and navigating in, three dimensions. Despite their lack of stereoscopy, insects infer distances to potential obstacles and other objects from image motion cues that result from their own motions in the environment. The concept of motion of texture in images as a source of motion cues is denoted generally as the concept of optic or optical flow. Computationally, a strategy based on optical flow is simpler than is stereoscopy for avoiding hazards and following terrain. Hence, this strategy offers the potential to design vision-based control computing subsystems that would be more compact, would weigh less, and would demand less power than would subsystems of equivalent capability based on a conventional stereoscopic approach.

Thakoor, Sarita↗

Robot path planning for space-truss assembly

Construction, repair, and maintenance of space-based structures will require extensive planning of operations in order to effectively carry out these tasks. The path planning algorithm described here is a general approach to generating paths that guarantee collision avoidance for a single chain nonredundant or redundant robot. The algorithm uses a graph search of feasible points in position space, followed by a local potential field method that guarantees collision avoidance among objects, structures, and the robot arm as well as conformance to joint limit constraints. This algorithm is novel in its computation of goal attractive potential fields in Cartesian space, and computation of obstacle repulsive fields in robot joint space. These effects are combined to generate robot motion. Computation is efficiently implemented through the computation of the robot arm Jacobian and not the full inverse arm kinematics. These planning algorithms have been implemented and evaluated using existing space-truss designs, and are being integrated into the RPI-CIRSSE Testbed environment.

Muenger, Rolf↗

A Machine Learning Approach to Improve Air Traffic Management Initiatives

Collaborating closely with commercial air carriers and related organizations, the Federal Aviation Administration(FAA) regulates air traffic and ensures the safety and efficiency of air operations. Air traffic controllers make strategic decisions, such as delaying, rerouting, or canceling flights, partly based on guidance provided by the FAA’s Air TrafficControl System Command Center (ATCSCC). The guidance includes, among other things, control measures known asTraffic Management Initiatives (TMIs) designed to enhance safety and improve operational efficiency. TMIs play a crucial role in managing the demand and capacity within the U.S. National Airspace System (NAS). Two major TMIs that are routinely used (primarily to mitigate the adverse effects of bad weather) are Ground Delay Programs (GDPs) andGround Stops (GSs). In a GDP, flights destined for airports facing thunderstorm activity experience delays at their origin airports. This proactive approach minimizes the risk of routing aircraft through hazardous weather conditions and also replaces (fuel burning) airborne delays with ground delays. In a GS, a temporary restriction is imposed on the departure or arrival of aircraft at a specific airport or within a designated airspace. Although other TMIs (e.g., miles-in-trail) are also implemented as part of (air) traffic flow management in the NAS, the focus of this work is on GDPs and GSs. Since TMIs, by design, lead to flight delays or cancellations, it is crucial to put in place the right set of parameters(e.g., scope and duration of the GDP). For example, when the end time of a GDP extends beyond what is necessary, it imposes unnecessary delays on departing flights. This situation could occur as a result of inaccurate prediction of the(required) duration of the GDP based on the weather forecast. On the other hand, if a GDP ends prematurely before the underlying capacity constraints are resolved at the destination airport, it may result in airborne holding. The delicate balance lies in matching the termination of the GDP precisely with the resolution of capacity constraints, avoiding both the imposition of unnecessary ground delays and the need for airborne holding due to premature program termination.Failing to specify the right parameters for TMIs also leads to flight delays, creating a significant obstacle in managing the increasing traffic volumes causing increased work load for the controllers. To address this issue, we propose the integration of Machine Learning (ML) models in the traffic flow management(TFM) pipeline. In current operations, decisions are made by human experts based on extensive training, historical patterns, available traffic and weather data. Since we have an abundance of data from past events that tell us the likely impact of various TMIs, by ingesting historical data, properly trained ML models can offer valuable insights and aid human decision-making. With the FAA increasingly exploring advanced analytics, ML emerges as a focal point for enhancing TFM within the National Airspace System (NAS). As a first step, this study aims to provide traffic controllers with decision-making support for the issuance and adjustment of TMIs. Data analytics and machine learning have been previously employed to address some of the challenges associated with TMIs. Numerous studies have concentrated on various facets of TMI issuance, exploring factors influencing TMI parameters, including arrival rate, airport capacity, and delay prediction. For example, using weather forecasts, several statistical methods were used to produce probabilistic capacity profiles which in conjunction with deterministic models provided insights into the GDP planning process [1–4]. The downside of using deterministic models is that they rely on fixed inputs and predetermined rules, which lack the ability to account for the inherent uncertainty and variability present in real-world scenarios. In a separate series of studies, researchers aimed to predict the occurrences of GDPs and GSs. The majority of these studies utilized various supervised learning methods, including Decision Trees, Naive Bayes, Support VectorMachines, and Random Forests to analyze the influence of weather conditions and arrival demand on TMI incidents[5–8]. However, these studies primarily focused on predicting the incidence of TMIs without explicitly addressing the scope of TMIs, including their duration and their geographical coverage. Furthermore, the emphasis of these studies was largely on GDPs, given their higher frequency and longer duration when compared to GSs. A limited number of studies focused on predicting the parameters of TMIs, specifically addressing their duration and extent. In one such study focusing on optimizing the TMI parameters at San Francisco International Airport (SFO),the authors utilized a probabilistic forecast of fog [9]. They simulated various capacity scenarios based on the (fog)burn-off forecasts, selecting GDP parameters that minimized airborne and overall ground delays. However, this approach exclusively emphasizes stratus (fog) burn-off as the primary determinant of GDP and GS, neglecting other influential factors like severe weather events, runway closures, lower capacity than traffic demand, and other important variables. Given the complexity of predicting the TMI and determining its scope, we seek a more holistic approach. We aim to consider all significant factors that could impact TMIs and their parameters. What sets this research apart is the fusion of all data sources relevant to the issuance and adjustment of TMIs and it represents the first comprehensive attempt to optimize TMIs in this manner. Since this comprehensive solution involves various aspects, we break down the problem into smaller components and input all parameters into a unified model called the “TMI Adjuster”. Figure 1 shows the overall framework and the list of datasets used in each model. The objective of the TMI Adjuster module is to deliver reliable, consistent and expedited recommendations for the progression, adjustment, and termination of TMIs. The ML solution entails developing a pipeline capable of predicting the necessity of a TMI (e.g., GS or GDP) along with its various parameters. For example, in the case of a GS, this includes the scope of the GS either in terms of distance from the destination airport or based on pre-defined airspace sectors. Here, scope refers to those regions and departing airports that are subject to the GS. In this paper, we concentrate on the issuance of GSs in the three major airports in the New York area — LaGuardia(LGA), John F. Kennedy International (JFK), and Newark Liberty International (EWR). We fuse traffic, weather and other relevant aviation data from years 2017 to 2019 to train and validate the ML models. In particular, we use the following datasets: •Terminal Aerodrome Forecast (TAF): meteorological forecasts specific to each airport, issued four times a day, covering predefined time periods. •TMI data: includes all GSs and GDPs along with their respective parameters. •Aviation System Performance Metrics (ASPM): includes traffic related data such as aircraft delays, arrival, and departure rates. •Notices to Airmen (NOTAMs): utilized to extract runway closure data and manage interdependencies between terminals in close proximity. •Flight cancellation data •Airspace Flow Programs (AFP): includes information on flight airborne holdings caused by TMIs. The data preprocessing entails transforming ASPM, TMI, AFP, NOTAMs, and weather data into an hourly format and consolidating all datasets by merging them based on date and time as the primary key. The TMI Adjuster framework comprises two parallel models: one dedicated to GS and a second model focused on GDP. As previously mentioned, our specific focus is on the GS model as a multi-classification problem. In this framework, each data point of the GS model input summarizes ten hours of data. Specifically, the data loader for the GS model generates the input and output of the model as follows: at a given time step, the input includes the actual traffic, weather, and TMI data from the two-hour window before the time step, alongside the weather forecast and scheduled traffic for the next 8 hours starting from the time step. Based on this information, the output of the GS model for each time interval consists of three dimensions. The first dimension represents a binary decision on whether there should be a GS in place for the next hour or not. The second dimension is related to the scope of the GS in the United States, and the third dimension is related to the scope of the GS in Canada (i.e., to determine if the GS impacts airports in Canada).One of the challenges with TMI modeling is the sparsity of TMI events, particularly regarding its scope. To address this challenge in the scope of the GS model output, we implement grouping. The GS scope for the US region is defined based on a list of centers that should be included when the GS is in place. With 20 centers in the US, we utilized historical data to group them into 4 categories. In particular, we summarized our historical data in a graph format where nodes represent centers, and link weights are defined based on the co-occurrence of centers in the scope parameter ofTMIs. By identified strongly connected components in this graph, we were able to partition the centers into four groups. We consider two model structures for the GS Model. Firstly, a hierarchical classification model [10], where the human decision-making for a GS is of hierarchical nature. The decision-maker first decides whether there is a need fora GS, and if the answer is yes, determines the scope. A hierarchical classification model organizes the problem into a class hierarchy, typically a tree or a Directed Acyclic Graph (DAG) structure, and considers the dependency of the decision in the previous step to the next component [10]. Here, we employ the local classifier per level approach, which involves training one multi-class classifier for each level of the class hierarchy. The second structure is the independent structure. In this setting, as the name suggests, we do not consider the dependency of the decisions in the different dimensions of the output of the model. Instead, for each dimension, we train a multi-class classifier independently. Table 1 summarizes GS model statistics for training, validation and testing. The table documents the effect of limiting data to the time steps when there was actually a TMI in place or when a TMI had just terminated. This resulted in a more balanced distribution of the GS class(GS positive class)versus “No GS”(GS negative class), which might help the training process. While JFK and LGA follow very similar distributions, with 40% and 42% GS positive class respectively, EWR has proportionally fewer GS incidents at 28%. Our subsequent phase involves evaluating the performance of both hierarchical structure and independent structure using different state-of-the-art multi-class classifier models such as Random Forest, Decision Trees, K-nearest Neighbors, and Logistic Regression and forecast the duration and scope of the GSs.

Farzan Masrour Shalmani↗

Procedures for the interpretation and use of elevation scanning laser/multi-sensor data for short range hazard detection and avoidance for an autonomous planetary rover

An autonomous roving science vehicle that relies on terrain data acquired by a hierarchy of sensors for navigation was one method of carrying out such a mission. The hierarchy of sensors included a short range sensor with sufficient resolution to detect every possible obstacle and with the ability to make fast and reliable terrain characterizations. A multilaser, multidetector triangulation system was proposed as a short range sensor. The general system was studied to determine its perception capabilities and limitations. A specific rover and low resolution sensor system was then considered. After studying the data obtained, a hazard detection algorithm was developed that accounts for all possible terrains given the sensor resolution. Computer simulation of the rover on various terrains was used to test the entire hazard detection system.

Troiani, N.↗

An Obstacle Alerting System for Agricultural Application

Wire strikes are a significant cause of helicopter accidents. The aircraft most at risk are aerial applicators. The present study examines the effectiveness of a wire alert delivered by way of the lightbar, a GPS-based guidance system for aerial application. The alert lead-time needed to avoid an invisible wire is compared with that to avoid a visible wire. A flight simulator was configured to simulate an agricultural application helicopter. Two pilots flew simulated spray runs in fields with visible wires, invisible wires, and no wires. The wire alert was effective in reducing wire strikes. A lead-time of 3.5 sec was required for the alert to be effective. The lead- time required was the same whether the pilot could see the wire or not.

DeMaio, Joe↗

An Obstacle Alerting System for Agricultural Application

Wire strikes are a significant cause of helicopter accidents. The aircraft most at risk are aerial applicators. The present study examines the effectiveness of a wire alert delivered by way of the lightbar, a GPS-based guidance system for aerial application. The alert lead-time needed to avoid an invisible wire is compared with that to avoid a visible wire. A flight simulator was configured to simulate an agricultural application helicopter. Two pilots flew simulated spray runs in fields with visible wires, invisible wires, and no wires. The wire alert was effective in reducing wire strikes. A lead-time of 3.5 sec was required for the alert to be effective. The lead-time required was the same whether the pilot could see the wire or not.

DeMaio, Joe↗

Collision Avoidance Approach Using Deep Reinforcement Learning

A method to enable autonomous robots moving in a 2D space collision free motivates the purposed approach for collision avoidance for autonomous UAM vehicles. Challenges of autonomous collision free navigation for both problems are similar. Agents in each environment do not know the intent, or goal, of the other. Finding the time efficient paths require some level of anticipation with neighboring agents which is computationally expensive. In the original work, these obstacles were overcome with a novel application of deep reinforcement learning which offloads the online computation to an offline learning algorithm. A value network that encodes the estimated time to the goal given the agent’s state and the observable portion of the other agent’s state is trained on a baseline policy and further refined with reinforcement learning to promote time efficient collision free navigation. Online, the value network efficiently informs the agent’s decision making in the face of uncertainty of the other agent’s next move. In this paper, challenges extending this methodology to the 3D environment of autonomous UAM vehicles with kinematic constraints are discussed and initial results shown.

Collision Avoidance↗

Collision Avoidance Approach Using Deep Reinforcement Learning

A method to enable autonomous robots moving in a 2D space collision free motivates the purposed approach for collision avoidance for autonomous UAM vehicles. Challenges of autonomous collision free navigation for both problems are similar. Agents in each environment do not know the intent, or goal, of the other. Finding the time efficient paths require some level of anticipation with neighboring agents which is computationally expensive. In the original work, these obstacles were overcome with a novel application of deep reinforcement learning which offloads the online computation to an offline learning algorithm. A value network that encodes the estimated time to the goal given the agent’s state and the observable portion of the other agent’s state is trained on a baseline policy and further refined with reinforcement learning to promote time efficient collision free navigation. Online, the value network efficiently informs the agent’s decision making in the face of uncertainty of the other agent’s next move. In this paper, challenges extending this methodology to the 3D environment of autonomous UAM vehicles with kinematic constraints are discussed and initial results shown.

Collision Avoidance↗

Proportional proximity sensing for telerobots using Coherent Laser Radar

The ability of a telerobotic manipulator to operate in confined spaces while avoiding unwanted collisions is enhanced by the accurate sensing of its proximate environment. To achieve the fidelity required for precise manipulator control, a proportional proximity sensor system with a sufficiently large measurement envelope is required. Current proximity sensors provide a binary indication of the presence of obstacles within a small envelope with coarse or no proportional measurement of their location. A proportional proximity sensor system configured as a Frequency Modulated Continuous Wave (FMCW) Coherent Laser Radar (CLR) using a semiconductor laser as the energy source is described and analyzed. The source and reflected energies mix coherently to generate a radio frequency (RF) signal whose frequency is proportional to the range. The system is tested for accuracy, range, depth of range, speed, and sensitivity and the results are presented. Techniques to derive orientation information and an application to telerobotic control are also described.

Vazquez, Sixto L.↗

Turbulent Concentration of MM-Size Particles in the Protoplanetary Nebula: Scaled-Dependent Multiplier Functions

The initial accretion of primitive bodies (asteroids and TNOs) from freely-floating nebula particles remains problematic. Here we focus on the asteroids where constituent particle (read "chondrule") sizes are observationally known; similar arguments will hold for TNOs, but the constituent particles in those regions will be smaller, or will be fluffy aggregates, and are unobserved. Traditional growth-bysticking models encounter a formidable "meter-size barrier" [1] (or even a mm-cm-size barrier [2]) in turbulent nebulae, while nonturbulent nebulae form large asteroids too quickly to explain long spreads in formation times, or the dearth of melted asteroids [3]. Even if growth by sticking could somehow breach the meter size barrier, other obstacles are encountered through the 1-10km size range [4]. Another clue regarding planetesimal formation is an apparent 100km diameter peak in the pre-depletion, pre-erosion mass distribution of asteroids [5]; scenarios leading directly from independent nebula particulates to this size, which avoid the problematic m-km size range, could be called "leapfrog" scenarios [6-8]. The leapfrog scenario we have studied in detail involves formation of dense clumps of aerodynamically selected, typically mm-size particles in turbulence, which can under certain conditions shrink inexorably on 100-1000 orbit timescales and form 10-100km diameter sandpile planetesimals. The typical sizes of planetesimals and the rate of their formation [7,8] are determined by a statistical model with properties inferred from large numerical simulations of turbulence [9]. Nebula turbulence can be described by its Reynolds number Re = L/eta sup(4/3), where L = ETA alpha sup (1/2) the largest eddy scale, H is the nebula gas vertical scale height, and α the nebula turbulent viscosity parameter, and η is the Kolmogorov or smallest scale in turbulence (typically about 1km), with eddy turnover time tη. In the nebula, Re is far larger than any numerical simulation can handle, so some physical model is needed to extend the results of numerical simulations to nebula conditions.

protoplanetary nebula↗

CFIT Prevention Using Synthetic Vision

In commercial aviation, over 30-percent of all fatal accidents worldwide are categorized as Controlled Flight Into Terrain (CFIT) accidents where a fully functioning airplane is inadvertently flown into the ground, water, or an obstacle. An experiment was conducted at NASA Langley Research Center investigating the presentation of a synthetic terrain database scene to the pilot on a Primary Flight Display (PFD). The major hypothesis for the experiment is that a synthetic vision system (SVS) will improve the pilot s ability to detect and avoid a potential CFIT compared to conventional flight instrumentation. All display conditions, including the baseline, contained a Terrain Awareness and Warning System (TAWS) and Vertical Situation Display (VSD) enhanced Navigation Display (ND). Sixteen pilots each flew 22 approach - departure maneuvers in Instrument Meteorological Conditions (IMC) to the terrain challenged Eagle County Regional Airport (EGE) in Colorado. For the final run, the flight guidance cues were altered such that the departure path went into the terrain. All pilots with a SVS enhanced PFD (12 of 16 pilots) noticed and avoided the potential CFIT situation. All of the pilots who flew the anomaly with the baseline display configuration (which included a TAWS and VSD enhanced ND) had a CFIT event.

Arthur, Jarvis J., III↗

Verifying Autonomous Air Traffic Algorithms in the Presence of Sensor Error and Flight Perturbations

We offer a method to verify algorithms for air traffic control in the presence of sensor errors and flight perturbations. Since errors and perturbations are described by stochastic processes, verification by analytical methods is difficult. We turn to Monte Carlo simulation, but there are two major obstacles. Since air traffic algorithms are safety-critical, the algorithm must be established at a very high confidence level which requires an enormous number of trials. Another is that a simulation attempts to show that an algorithm correctly handles a hazard that might appear, but there is a lack of information about the frequency of occurrence of hazards in the airspace. This paper offers a solution to these and other obstacles. It recognizes there may be a number of algorithms that address different hazards, and the results of the different simulations must be combined to satisfy a global reliability requirement at a high confidence level. To demonstrate the feasibility of the approach, we apply it to an example, an initial effort in collision avoidance.

verification↗

High Gain Antenna Pointing on the Mars Exploration Rovers

This paper describes the algorithm used to point the high gain antennae on NASA/JPL's Mars exploration rovers. Each rover's gimballed antenna must track the Earth as it moves across the Martian sky during communication sessions. The pointing algorithm accounts for obstacles to the line-of-sight posed by (1) features on the rover and in the surrounding environment (2) gimbal range limitations, and (3) kinematic singularities in the gimbal mechanism. The algorithm treats all obstacles with a generalized approach that computes the intercept-times to each obstacle. Where possible, the algorithm takes advantage of pairs of joint-space solutions arising from the mechanism design. The algorithm chooses the solution that provides the longest obstruction-free tracking time. Upon encountering an obstacle, the algorithm automatically switches to the other solution if it is not also obstructed. This algorithm has successfully provided obstruction-free pointing for both rovers throughout the mission.

inverse kinematics↗

Distance estimation and collision prediction for on-line robotic motion planning

An efficient method for computing the minimum distance and predicting collisions between moving objects is presented. This problem is incorporated into the framework of an in-line motion-planning algorithm to satisfy collision avoidance between a robot and moving objects modeled as convex polyhedra. In the beginning, the deterministic problem where the information about the objects is assumed to be certain is examined. L(1) or L(infinity) norms are used to represent distance and the problem becomes a linear programming problem. The stochastic problem is formulated where the uncertainty is induced by sensing and the unknown dynamics of the moving obstacles. Two problems are considered: First, filtering of the distance between the robot and the moving object at the present time. Second, prediction of the minimum distance in the future in order to predict the collision time.

Kyriakopoulos, K. J.↗

Distance estimation and collision prediction for on-line robotic motion planning

An efficient method for computing the minimum distance and predicting collisions between moving objects is presented. This problem has been incorporated in the framework of an in-line motion planning algorithm to satisfy collision avoidance between a robot and moving objects modeled as convex polyhedra. In the beginning the deterministic problem, where the information about the objects is assumed to be certain is examined. If instead of the Euclidean norm, L(sub 1) or L(sub infinity) norms are used to represent distance, the problem becomes a linear programming problem. The stochastic problem is formulated, where the uncertainty is induced by sensing and the unknown dynamics of the moving obstacles. Two problems are considered: (1) filtering of the minimum distance between the robot and the moving object, at the present time; and (2) prediction of the minimum distance in the future, in order to predict possible collisions with the moving obstacles and estimate the collision time.

Kyriakopoulos, K. J.↗