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NASA NTRS2005

Step 1: Human System Integration Simulation and Flight Test Progress Report

The Access 5 Human Systems Integration Work Package produced simulation and flight demonstration planning products for use throughout the program. These included: Test Objectives for Command, Control, Communications; Pilot Questionnaire for Command, Control, Communications; Air Traffic Controller Questionnaire for Command, Control, Communications; Test Objectives for Collision Avoidance; Pilot Questionnaire for Collision Avoidance; Plans for Unmanned Aircraft Systems Control Station Simulations Flight Requirements for the Airspace Operations Demonstration

Source record↗
NASA NTRS2009

The International Space Station and the Space Debris Environment: 10 Years On

For just over a decade the International Space Station (ISS), the most heavily protected vehicle in Earth orbit, has weathered the space debris environment well. Numerous hypervelocity impact features on the surface of ISS caused by small orbital debris and meteoroids have been observed. In addition to typical impacts seen on the large solar arrays, craters have been discovered on windows, hand rails, thermal blankets, radiators, and even a visiting logistics module. None of these impacts have resulted in any degradation of the operation or mission of the ISS. Validating the rate of small particle impacts on the ISS as predicted by space debris environment models is extremely complex. First, the ISS has been an evolving structure, from its original 20 metric tons to nearly 300 metric tons (excluding logistics vehicles) ten years later. Hence, the anticipated space debris impact rate has grown with the increasing size of ISS. Secondly, a comprehensive visual or photographic examination of the complete exterior of ISS has never been accomplished. In fact, most impact features have been discovered serendipitously. Further complications include the estimation of the size of an impacting particle without knowing its mass, velocity, and angle of impact and the effect of shadowing by some ISS components. Inadvertently and deliberately, the ISS has also been the source of space debris. The U.S. Space Surveillance Network officially cataloged 65 debris from ISS from November 1998 to November 2008: from lost cameras, sockets, and tool bags to intentionally discarded equipment and an old space suit. Fortunately, the majority of these objects fall back to Earth quickly with an average orbital lifetime of less than two months and a maximum orbital lifetime of a little more than 15 months. The cumulative total number of debris object-years is almost exactly 10, the equivalent of one piece of debris remaining in orbit for 10 years. An unknown number of debris too small to be tracked and cataloged have also been generated, but normally with even shorter orbital lifetimes. Finally, eight collision avoidance maneuvers have been performed to avoid potential collisions between ISS and large, tracked space debris. The most recent such maneuver was accomplished by ESA's Automated Transfer Vehicle, the Jules Verne, just three months before the 10th anniversary of the launch of ISS's first element.

Johnson, Nicholas↗
NASA NTRS2005

Magnetically Attached Multifunction Maintenance Rover

A versatile mobile telerobot, denoted the magnetically attached multifunction maintenance rover (MAGMER), has been proposed for use in the inspection and maintenance of the surfaces of ships, tanks containing petrochemicals, and other large ferromagnetic structures. As its name suggests, this robot would utilize magnetic attraction to adhere to a structure. As it moved along the surface of the structure, the MAGMER would perform tasks that could include close-up visual inspection by use of video cameras, various sensors, and/or removal of paint by water-jet blasting, laser heating, or induction heating. The water-jet nozzles would be mounted coaxially within compressed-air-powered venturi nozzles that would collect the paint debris dislodged by the jets. The MAGMER would be deployed, powered, and controlled from a truck, to which it would be connected by hoses for water, compressed air, and collection of debris and by cables for electric power and communication (see Figure 1). The operation of the MAGMER on a typical large structure would necessitate the use of long cables and hoses, which can be heavy. To reduce the load of the hoses and cables on the MAGMER and thereby ensure its ability to adhere to vertical and overhanging surfaces, the hoses and cables would be paid out through telescopic booms that would be parts of a MAGMER support system. The MAGMER would move by use of four motorized, steerable wheels, each of which would be mounted in an assembly that would include permanent magnets and four pole pieces (see Figure 2). The wheels would protrude from between the pole pieces by only about 3 mm, so that the gap between the pole pieces and the ferromagnetic surface would be just large enough to permit motion along the surface but not so large as to reduce the magnetic attraction excessively. In addition to the wheel assemblies, the MAGMER would include magnetic adherence enhancement fixtures, which would comprise arrays of permanent magnets and pole pieces that could be adjusted to maximize or minimize the overall attractive magnetic force. Even with a paint thickness of 2 mm, a preliminary design provides a safety factor of 5 in the magnetic force in the upside- down, water-jets-operating condition, in which the total load (including the weight of the MAGMER and cables and the water-jet force) would be about 260 lb (the weight of 118 kg). Optionally, the MAGMER could carry magnetic shielding and/or could be equipped with a demagnetizing module to remove residual magnetism from the structure. The MAGMER would carry four charge-coupled-device cameras for visual inspection, monitoring of operation, navigation, and avoidance of collisions with obstacles. The control system of the MAGMER would include navigation and collision-avoidance subsystems that would utilize surface features as landmarks, in addition to direct images of obstacles.

Bar-Cohen, Yoseph↗
NASA NTRS2014

Analytical Assessment of Simultaneous Parallel Approach Feasibility from Total System Error

In a simultaneous paired approach to closely-spaced parallel runways, a pair of aircraft flies in close proximity on parallel approach paths. The aircraft pair must maintain a longitudinal separation within a range that avoids wake encounters and, if one of the aircraft blunders, avoids collision. Wake avoidance defines the rear gate of the longitudinal separation. The lead aircraft generates a wake vortex that, with the aid of crosswinds, can travel laterally onto the path of the trail aircraft. As runway separation decreases, the wake has less distance to traverse to reach the path of the trail aircraft. The total system error of each aircraft further reduces this distance. The total system error is often modeled as a probability distribution function. Therefore, Monte-Carlo simulations are a favored tool for assessing a "safe" rear-gate. However, safety for paired approaches typically requires that a catastrophic wake encounter be a rare one-in-a-billion event during normal operation. Using a Monte-Carlo simulation to assert this event rarity with confidence requires a massive number of runs. Such large runs do not lend themselves to rapid turn-around during the early stages of investigation when the goal is to eliminate the infeasible regions of the solution space and to perform trades among the independent variables in the operational concept. One can employ statistical analysis using simplified models more efficiently to narrow the solution space and identify promising trades for more in-depth investigation using Monte-Carlo simulations. These simple, analytical models not only have to address the uncertainty of the total system error but also the uncertainty in navigation sources used to alert an abort of the procedure. This paper presents a method for integrating total system error, procedure abort rates, avionics failures, and surveillance errors into a statistical analysis that identifies the likely feasible runway separations for simultaneous paired approaches.

Madden, Michael M.↗
NASA NTRS2016

Airport Traffic Conflict Detection and Resolution Algorithm Evaluation

Two conflict detection and resolution (CD&R) algorithms for the terminal maneuvering area (TMA) were evaluated in a fast-time batch simulation study at the National Aeronautics and Space Administration (NASA) Langley Research Center. One CD&R algorithm, developed at NASA, was designed to enhance surface situation awareness and provide cockpit alerts of potential conflicts during runway, taxi, and low altitude air-to-air operations. The second algorithm, Enhanced Traffic Situation Awareness on the Airport Surface with Indications and Alerts (SURF IA), was designed to increase flight crew awareness of the runway environment and facilitate an appropriate and timely response to potential conflict situations. The purpose of the study was to evaluate the performance of the aircraft-based CD&R algorithms during various runway, taxiway, and low altitude scenarios, multiple levels of CD&R system equipage, and various levels of horizontal position accuracy. Algorithm performance was assessed through various metrics including the collision rate, nuisance and missed alert rate, and alert toggling rate. The data suggests that, in general, alert toggling, nuisance and missed alerts, and unnecessary maneuvering occurred more frequently as the position accuracy was reduced. Collision avoidance was more effective when all of the aircraft were equipped with CD&R and maneuvered to avoid a collision after an alert was issued. In order to reduce the number of unwanted (nuisance) alerts when taxiing across a runway, a buffer is needed between the hold line and the alerting zone so alerts are not generated when an aircraft is behind the hold line. All of the results support RTCA horizontal position accuracy requirements for performing a CD&R function to reduce the likelihood and severity of runway incursions and collisions.

Jones, Denise R.↗
NASA NTRS2019

Space Traffic Management with a NASA UAS Traffic Management (UTM) Inspired Architecture

Space is becoming increasingly congested as the number of on-orbit satellites and debris objects continues to grow. Space traffic management (STM) is critical for ensuring that the expanding orbital population operates safely and efficiently, avoiding collisions and radio-frequency interference while still facilitating widespread space operations. Recent events such as the FCC approval of SpaceX’s ~12,000 satellite constellation, the signing of Space Policy Directive 3 (which moves Space Situational Awareness responsibilities away from the Department of Defense and to a civil agency), and the growth in rideshare and small launch vehicles illustrate the rapidly changing nature of this domain. This paper will describe the concept of operations (ConOps) for a civilian STM research initiative, which has been developed from previous NASA work to enable safe operation of small unmanned aircraft systems. The STM ConOps proposes an architecture to enable efficient data sharing and coordination between participants to facilitate safe spaceflight operations. It is designed to utilize and promote the emerging field of commercial STM services, as a complement to existing government-provided STM services. The concept envisions a phased evolution that would gradually integrate additional capabilities, proposing a first phase architecture and tentative plans for a broader system. Work towards developing an STM research and prototyping platform is also discussed.

UTM↗
NASA NTRS2019

The NASA Urban Air Mobility Testbed Flight Research Aircraft

The National Aeronautics and Space Administration (NASA) is leading government, industry and academic research effort known as Urban Air Mobility (UAM). The UAM activity goal is to develop the technology needed to make possible an urban air transportation system that makes use of human-crewed and crewless vehicles using automation, artificial intelligence and other technologies to safely and efficiently air transport people and goods within an urban environment. The NASA Langley Research Center (LaRC) created a UAM Flight Research Testbed Aircraft from a Cessna LC40 general aviation aircraft. The testbed has updated digital avionics and research systems needed to conduct flight research. The aircraft has two separate autopilots; a standard Federal Aviation Ad-ministration (FAA) certified system, and a modified research autopilot. The research autopilot has modifications that allow increased authority and enhancements to allow more automation and artificial intelligence controls. A network of three research computers hosts software to research several activities including automated air traffic sense and avoid, ground collision avoidance and obstacle avoidance. These UAM research activities involve automation and artificial intelligence technologies developed at three NASA centers. The NASA Langley, NASA Armstrong, and NASA Ames Research Centers are working together to develop and test these UAM technologies. This paper provides details of the systems, capabilities and research projects of the UAM Testbed Research Aircraft.

Howell, Charles T.↗
NASA NTRS2005

Sense-and-Avoid Equivalent Level of Safety Definition for Unmanned Aircraft Systems. Revision 9

Since unmanned aircraft do not have a pilot on-board the aircraft, they cannot literally comply with the "see and avoid" requirement beyond a short distance from the location of the unmanned pilot. No performance standards are presently defined for unmanned Sense and Avoid systems, and the FAA has no published approval criteria for a collision avoidance system. Before the FAA can develop the necessary guidance (rules / regulations / policy) regarding the see-and-avoid requirements for Unmanned Aircraft Systems (UAS), a concise understanding of the term "equivalent level of safety" must be attained. Since this term is open to interpretation, the UAS industry and FAA need to come to an agreement on how this term can be defined and applied for a safe and acceptable collision avoidance capability for unmanned aircraft. Defining an equivalent level of safety (ELOS) for sense and avoid is one of the first steps in understanding the requirement and developing a collision avoidance capability. This document provides a functional level definition of see-and-avoid as it applies to unmanned aircraft. The sense and avoid ELOS definition is intended as a bridge between the see and avoid requirement and the system level requirements for unmanned aircraft sense and avoid systems. Sense and avoid ELOS is defined in a rather abstract way, meaning that it is not technology or system specific, and the definition provides key parameters (and a context for those parameters) to focus the development of cooperative and non-cooperative sense and avoid system requirements.

Source record↗
NASA NTRS2020

Adaptive Stress Testing: Finding Likely Failure Events with Reinforcement Learning

Finding the most likely path to a set of failure states is important to the analysis of safety-critical systems that operate over a sequence of time steps, such as aircraft collision avoidance systems and autonomous cars. In many applications such as autonomous driving, failures cannot be completely eliminated due to the complex stochastic environment in which the system operates.As a result, safety validation is not only concerned about whether a failure can occur, but also discovering which failures are most likely to occur. This article presents adaptive stress testing (AST), a framework for finding the most likely path to a failure event in simulation. We consider a general black box setting for partially observable and continuous-valued systems operating in an environment with stochastic disturbances. We formulate the problem as a Markov decision process and use reinforcement learning to optimize it. The approach is simulation-based and does not require internal knowledge of the system, making it suitable for black-box testing of large systems. We present different formulations depending on whether the state is fully observable or partially observable. In the latter case, we present a modified Monte Carlo tree search algorithm that only requires access to the pseudorandom number generator of the simulator to overcome partial observability. We also present an extension of the framework, called differential adaptive stress testing (DAST), that can find failures that occur in one system but not in another. This type of differential analysis is useful in applications such as regression testing, where we are concerned with finding areas of relative weakness compared to a baseline. We demonstrate the effectiveness of the approach on an aircraft collision avoidance application, where a prototype aircraft collision avoidance system is stress tested to find the most likely scenarios of near mid-air collision.

Verification and Validation↗
NASA NTRSDate not supplied

Conjunction Assessment(CA) Support Overview for the EOS Satellites

When a satellite is placed into its desired orbit, to achieve its designed mission objectives, it is imperative to maintain orbit requirements as well as the overall health and safety of the vehicle. One integral part of this process is ensuring that the satellite does not collide with any other vehicle or object in space, which can cause a detrimental consequence to the mission as well as to other satellites within the same orbit regime. To prevent such an occurrence, a thorough collision avoidance process must be followed. This process includes constantly monitoring potential conjunctions and performing collision avoidance maneuvers when necessary, while remaining within the limitations of the mission’s orbit maintenance requirements. This presentation will describe the Earth Observing System (EOS) Aqua, Aura and Terra satellite’s operational collision a! voidance process. It will highlight the routine conjunction assessment screening and data evaluation process performed by the NASA/GSFC EOS Collision Avoidance Engineers. The presentation will include background information, a summary of operational activities and duties, internal tools used for support, EOS High Interest Event statistics, and potential challenges expected in the future.

Syed Hasan↗
NASA NTRS2002

Regaining Lost Separation in a Piloted Simulation of Autonomous Aircraft Operations

NASA is currently investigating a new concept of operations for the National Airspace System, designed to improve capacity while maintaining or improving current levels of safety. This concept, known as Distributed Air/Ground Traffic Management (DAG-TM), allows appropriately equipped autonomous aircraft to maneuver freely for flight optimization while resolving conflicts with other traffic and staying out of special use airspace and hazardous weather. While Airborne Separation Assurance System (ASAS) tools would normally allow pilots to resolve conflicts before they become hazardous, evaluation of system performance in sudden, near-term conflicts is needed in order to determine concept feasibility. If an acceptable safety level can be demonstrated in these situations, then operations may be conducted with lower separation minimums. An experiment was conducted in NASA Langley s Air Traffic Operations Lab to address issues associated with resolving near-term conflicts and the potential use of lower separation minimums. Sixteen commercial airline pilots flew a total of 32 traffic scenarios that required them to use prototype ASAS tools to resolve close range pop-up conflicts. Required separation standards were set at either 3 or 5 NM lateral spacing, with 1000 ft vertical separation being used for both cases. Reducing the lateral separation from 5 to 3 NM did not appear to increase operational risk, as indicated by the proximity to the intruder aircraft. Pilots performed better when they followed tactical guidance cues provided by ASAS than when they didn't follow the guidance. As air-air separation concepts are evolved, further studies will consider integration issues between ASAS and existing Airborne Collision Avoidance Systems (ACAS).These types of non-normal events will require the ASAS to provide effective alerts and resolutions prior to the time that an Airborne Collision Avoidance System (ACAS) would give a Resolution Advisory (RA). When an RA is issued, a pilot must take immediate action in order to avoid a potential near miss. The Traffic Alert and Collision Avoidance System (TCAS) II currently functions as an ACAS aboard commercial aircraft. Depending on the own aircraft s altitude, TCAS only issues RA s 15-35 seconds prior to the Closest Point of Approach (CPA). Prior to an RA, DAG-TM pilots operating autonomous aircraft must rely solely on ASAS for resolution guidance. An additional area of DAG-TM concept feasibility relates to a potential reduction in separation standards. Lower separation standards are likely needed in order to improve NAS efficiency and capacity. Current separation minimums are based in large part on the capabilities of older radar systems. Safety assessments are needed to determine the feasibility of reduced separation minimums. They will give strong consideration to surveillance system performance, including accuracy, integrity, and availability. Candidate surveillance systems include Automatic Dependent Surveillance-Broadcast (ADS-B) and multi-lateration systems. Considering studies done for Reduced Vertical Separation Minimums (RVSM) operations, it is likely that flight technical errors will also be considered. In addition to a thorough evaluation of surveillance system performance, a potential decision to lower the separation standards should also take operational considerations into account. An ASAS Safety Assessment study identified improper maneuvering in response to a conflict (due to ambiguous or improper resolution commands or a pilot s failure to comply with the resolution) as a potential safety risk. If near-term conflicts with lower separation minimums were determined to be more challenging for pilots, the severity of these risks could be even greater.

Barhydt, Richard↗
NASA NTRS2006

A Convex Guidance Algorithm for Formation Reconfiguration

In this paper, a reconfiguration guidance algorithm for formation flying spacecraft is presented. The formation reconfiguration guidance problem is first formulated as a continuous-time minimum-fuel or minimum-energy optimal control problem with collision avoidance and control constraints. The optimal control problem is then discretized to obtain a finite dimensional parameter optimization problem. In this formulation, the collision avoidance constraints are imposed via separating planes between each pair of spacecraft. A heuristic is introduced to choose these separating planes that leads to the convexification of the collision avoidance constraints. Additionally, convex constraints are imposed to guarantee that no collisions occur between discrete time samples. The resulting finite dimensional optimization problem is a second order cone program, for which standard algorithms can compute the global optimum with deterministic convergence and a prescribed level of accuracy. Consequently, the formation reconfiguration algorithm can be implemented onboard a spacecraft for real-time operations.

formation reconfiguration↗
NASA NTRS1983

Conflict resolution maneuvers during near miss encounters with cockpit traffic displays

The benefits and liabilities associated with pilots' use of a cockpit traffic display to assess the threat posed by air traffic and to make small maneuvers to avoid situations which would result in collision avoidance advisories are experimentally studied. The crew's task was to fly a simulated wide-body aircraft along a straight course at constant altitude while intruder aircraft appeared on a variety of converging trajectories. The main experimental variables were the amount and quality of the information displayed on the intruder aircraft's estimated future position. Pilots were to maintain a horizontal separation of at least 1.5 nautical miles or a vertical separation of 500 ft, so that collision avoidance advisories would not be triggered. The results show that pilots could usually maneuver to provide the specified separation but often made course deviations greater than 1.5 nm or 500 ft.

Palmer, E.↗
NASA NTRS2015

Implementation of an Open-Scenario, Long-Term Space Debris Simulation Approach

This paper provides a status update on the implementation of a flexible, long-term space debris simulation approach. The motivation is to build a tool that can assess the long-term impact of various options for debris-remediation, including the LightForce space debris collision avoidance concept that diverts objects using photon pressure [9]. State-of-the-art simulation approaches that assess the long-term development of the debris environment use either completely statistical approaches, or they rely on large time steps on the order of several days if they simulate the positions of single objects over time. They cannot be easily adapted to investigate the impact of specific collision avoidance schemes or de-orbit schemes, because the efficiency of a collision avoidance maneuver can depend on various input parameters, including ground station positions and orbital and physical parameters of the objects involved in close encounters (conjunctions). Furthermore, maneuvers take place on timescales much smaller than days. For example, LightForce only changes the orbit of a certain object (aiming to reduce the probability of collision), but it does not remove entire objects or groups of objects. In the same sense, it is also not straightforward to compare specific de-orbit methods in regard to potential collision risks during a de-orbit maneuver. To gain flexibility in assessing interactions with objects, we implement a simulation that includes every tracked space object in Low Earth Orbit (LEO) and propagates all objects with high precision and variable time-steps as small as one second. It allows the assessment of the (potential) impact of physical or orbital changes to any object. The final goal is to employ a Monte Carlo approach to assess the debris evolution during the simulation time-frame of 100 years and to compare a baseline scenario to debris remediation scenarios or other scenarios of interest. To populate the initial simulation, we use the entire space-track object catalog in LEO. We then use a high precision propagator to propagate all objects over the entire simulation duration. If collisions are detected, the appropriate number of debris objects are created and inserted into the simulation framework. Depending on the scenario, further objects, e.g. due to new launches, can be added. At the end of the simulation, the total number of objects above a cut-off size and the number of detected collisions provide benchmark parameters for the comparison between scenarios. The simulation approach is computationally intensive as it involves tens of thousands of objects; hence we use a highly parallel approach employing up to a thousand cores on the NASA Pleiades supercomputer for a single run. This paper describes our simulation approach, the status of its implementation, the approach to developing scenarios and examples of first test runs.

laser↗
NASA NTRS2019

Unmanned Aircraft Systems (UAS) Integration in the National Airspace System (NAS) Project: ACAS Xu Engineering Analysis Results

This presentation provides an overview of the results from a two-part engineering analysis conducted as part of the Unmanned Aircraft Systems (UAS) Integration in the National Airspace System (NAS) Project. Part one of this analysis examined how to present resolution advisories (RAs) issued by Airborne Collision Avoidance System (ACAS) Xu, which can be in the vertical dimension, the horizontal dimension, or both (i.e., "blended"). The study varied the appearance of the alerting and the verbiage used in the aural alerts. Results revealed high acceptability ratings for the appearance of the RA guidance. Part two of the analysis assessed pilot acceptability of varying levels of automation in the collision avoidance (CA) task. Pilots experienced conditions in which ACAS Xu RAs were executed either manually or automatically (i.e., auto-Collision Avoidance). In some conditions the return to a previously filed course was also executed automatically (auto-Return to Course). Results indicated that improvements are needed to how the state of the automation is presented. Implications of these findings are also discussed.

Detect and Avoid↗
NASA NTRS2010

The Monotonic Lagrangian Grid for Fast Air-Traffic Evaluation

This paper describes the continued development of a dynamic air-traffic model, ATMLG, intended for rapid evaluation of rules and methods to control and optimize transport systems. The underlying data structure is based on the Monotonic Lagrangian Grid (MLG), which is used for sorting and ordering positions and other data needed to describe N moving bodies, and their interactions. In ATMLG, the MLG is combined with algorithms for collision avoidance and updating aircraft trajectories. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. In this paper, we use ATMLG to examine how the ability to maintain a required separation between aircraft decreases as the number of aircraft in the volume increases. This requires keeping track of the primary and subsequent collision avoidance maneuvers necessary to maintain a five mile separation distance between all aircraft. Simulation results show that the number of collision avoidance moves increases exponentially with the number of aircraft in the volume.

Alexandrov, Natalia↗
NASA NTRS2017

Distributed Fast Motion Planning for Spacecraft Swarms in Cluttered Environments using Spherical Expansions and Sequence of Convex Optimization Problems

This paper presents a novel guidance algorithm for spacecraft swarms in an environment cluttered with many obstacles like a debris field or the asteroid belt. The objective of this algorithm is to reconfigure the swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with the obstacles. The agents first use a spherical-expansion-based sampling algorithm to cooperatively explore the workspace and find paths to the desired terminal positions. Using a distributed assignment algorithm, the agents converge on an optimal assignment of the target locations in the desired formation. Then each agent generates a locally optimal trajectory from its current location to its terminal position by solving a sequence of convex optimization problems. As the agent moves along this trajectory, it receives the position of other agents and updates its trajectory to avoid collisions with other agents and the obstacles. Thus the swarm achieves the desired formation in a distributed manner while avoiding collisions. Moreover, this algorithm is computationally efficient, therefore it can be implemented onboard resource-constrained spacecraft. Simulations results show that the proposed distributed algorithm can be used by a spacecraft swarm to reconfigure a desired formation around an asteroid in a collision-free manner.

Bandyopadhyay, Saptarshi↗
NASA NTRS1991

Path planning for assembly of strut-based structures

A path planning method with collision avoidance for a general single chain nonredundant or redundant robot is proposed. Joint range boundary overruns are also avoided. The result is a sequence of joint vectors which are passed to a trajectory planner. A potential field algorithm in joint space computes incremental joint vectors delta-q = delta-q(sub a) + delta-q(sub c) + delta-q(sub r). Adding delta-q to the robot's current joint vector leads to the next step in the path. Delta-q(sub a) is obtained by computing the minimum norm solution of the underdetermined linear system J delta-q(sub a) = x(sub a) where x(sub a) is a translational and rotational force vector that attracts the robot to its goal position and orientation. J is the manipulator Jacobian. Delta-q(sub c) is a collision avoidance term encompassing collisions between the robot (links and payload) and obstacles in the environment as well as collisions among links and payload of the robot themselves. It is obtained in joint space directly. Delta-q(sub r) is a function of the current joint vector and avoids joint range overruns. A higher level discrete search over candidate safe positions is used to provide alternatives in case the potential field algorithm encounters a local minimum and thus fails to reach the goal. The best first search algorithm A* is used for graph search. Symmetry properties of the payload and equivalent rotations are exploited to further enlarge the number of alternatives passed to the potential field algorithm.

Muenger, Rolf↗