Autopilot

Autopilot panel of an older Boeing 747 aircraft,.

An autopilot is a mechanical, electrical, or hydraulic system used to guide a vehicle without assistance from a human being. An autopilot can refer specifically to aircraft, self-steering gear for boats, or auto guidance of space craft and missiles. The autopilot of an aircraft is sometimes referred to as "George".

First autopilots

In the early days of aviation, aircraft required the continuous attention of a pilot in order to fly safely. As aircraft range increased allowing flights of many hours, the constant attention led to serious fatigue. An autopilot is designed to perform some of the tasks of the pilot.

The first aircraft autopilot was developed by Sperry Corporation in 1912. The autopilot connected a gyroscopic Heading indicator and attitude indicator to hydraulically operated elevators and rudder (ailerons were not connected as wing dihedral was counted upon to produce the necessary roll stability.) It permitted the aircraft to fly straight and level on a compass course without a pilot's attention, greatly reducing the pilot's workload.

Lawrence Sperry (the son of famous inventor Elmer Sperry) demonstrated it two years later in 1914 at an aviation safety contest held in Paris. At the contest, Lawrence Sperry demonstrated the credibility of the invention were shown by flying the aircraft with his hands away from the controls and visible to onlookers of the contest. This autopilot system was also capable of performing take-off and landing, and the French military command showed immediate interest in the autopilot system. Wiley Post used a Sperry autopilot system to fly alone around the world in less than eight days in 1933.

Further development of the autopilot were performed, such as improved control algorithms and hydraulic servomechanisms. Also, inclusion of additional instrumentation such as the radio-navigation aids made it possible to fly during night and in bad weather. In 1947 a US Air Force C-53 made a transatlantic flight, including takeoff and landing, completely under the control of an autopilot.

In the early 1920s, the Standard Oil tanker J.A Moffet became the first ship to use an autopilot.

Modern autopilots

Not all of the passenger aircraft flying today have an autopilot system. Older and smaller general aviation aircraft especially are still hand-flown, while small airliners with fewer than twenty seats may also be without an autopilot as they are used on short-duration flights with two pilots. The installation of autopilots in aircraft with more than twenty seats is generally made mandatory by international aviation regulations. There are three levels of control in autopilots for smaller aircraft. A single-axis autopilot controls an aircraft in the roll axis only; such autopilots are also known colloquially as "wing levellers", reflecting their limitations. A two-axis autopilot controls an aircraft in the pitch axis as well as roll, and may be little more than a "wing leveller" with limited pitch-oscillation-correcting ability; or it may receive inputs from on-board radio navigation systems to provide true automatic flight guidance once the aircraft has taken off until shortly before landing; or its capabilities may lie somewhere between these two extremes. A three-axis autopilot adds control in the yaw axis and is not required in many small aircraft.

Autopilots in modern complex aircraft are three-axis and generally divide a flight into taxi, takeoff, ascent, level, descent, approach and landing phases. Autopilots exist that automate all of these flight phases except the taxiing. An autopilot-controlled landing on a runway and controlling the aircraft on rollout (i.e. keeping it on the centre of the runway) is known as a CAT IIIb landing or Autoland, available on many major airports' runways today, especially at airports subject to adverse weather phenomena such as fog. Landing, rollout and taxi control to the aircraft parking position is known as CAT IIIc. This is not used to date but may be used in the future. An autopilot is often an integral component of a Flight Management System.

Modern autopilots use computer software to control the aircraft. The software reads the aircraft's current position, and controls a Flight Control System to guide the aircraft. In such a system, besides classic flight controls, many autopilots incorporate thrust control capabilities that can control throttles to optimize the air-speed, and move fuel to different tanks to balance the aircraft in an optimal attitude in the air. Although autopilots handle new or dangerous situations inflexibly, they generally fly an aircraft with a lower fuel-consumption than a human pilot.

The autopilot in a modern large aircraft typically reads its position and the aircraft's attitude from an inertial guidance system. Inertial guidance systems accumulate errors over time. They will incorporate error reduction systems such as the carousel system that rotates once a minute so that any errors are dissipated in different directions and have an overall nulling effect. Error in gyroscopes is known as drift. This is due to physical properties within the system, be it mechanical or laser guided, that corrupt positional data. The disagreements between the two are resolved with digital signal processing, most often a six-dimensional Kalman filter. The six dimensions are usually roll, pitch, yaw, altitude, latitude and longitude. Aircraft may fly routes that have a required performance factor, therefore the amount of error or actual performance factor must be monitored in order to fly those particular routes. The longer the flight the more error accumulates within the system. Radio aids such as DME, DME updates and GPS may be used to correct the aircraft position.

Computer system details

The hardware of an autopilot varies from implementation to implementation, but is generally designed with redundancy and reliability as foremost considerations. For example, the Rockwell Collins AFDS-770 Autopilot Flight Director System used on the Boeing 777, uses triplicated FCP-2002 microprocessors which have been formally verified and are fabricated in a radiation resistant process.

Software and hardware in an autopilot is tightly controlled, and extensive test procedures are put in place.

Some autopilots also use design diversity. In this safety feature, critical software processes will not only run on separate computers and possibly even using different architectures, but each computer will run software created by different engineering teams, often being programmed in different programming languages. It is generally considered unlikely that different engineering teams will make the same mistakes. As the software becomes more expensive and complex, design diversity is becoming less common because fewer engineering companies can afford it. The flight control computers on the Space Shuttle uses this design: there are five computers, four of which redundantly run identical software, and a fifth backup running software that was developed independently. The software on the fifth system provides only the basic functions needed to fly the Shuttle, further reducing any possible commonality with the software running on the four primary systems.

Categories

Instrument-aided landings are defined in categories by the International Civil Aviation Organization. These are dependent upon the required visibility level and the degree to which the landing can be conducted automatically without input by the pilot.

CAT I - This category permits pilots to land with a decision height of 200 ft (61 m) and a forward visibility or Runway Visual Range (RVR) of 550 m. Simplex autopilots are sufficient.

CAT II - This category permits pilots to land with a decision height between 200 ft and 100 ft (≈ 30 m) and a RVR of 300 m. Autopilots have a fail passive requirement.

CAT IIIa -This category permits pilots to land with a decision height as low as 50 ft (15 m) and a RVR of 200 m. It needs a fail-passive autopilot. There must be only a 10−6 probability of landing outside the prescribed area.

CAT IIIb - As IIIa but with the addition of automatic roll out after touchdown incorporated with the pilot taking control some distance along the runway. This category permits pilots to land with a decision height less than 50 feet or no decision height and a forward visibility of 250 ft (76 m, compare this to aircraft size, some of which are now over 70 m long) or 300 ft (91 m) in the United States. For a landing-without-decision aid, a fail-operational autopilot is needed. For this category some form of runway guidance system is needed: at least fail-passive but it needs to be fail-operational for landing without decision height or for RVR below 100 m.

CAT IIIc - As IIIb but without decision height or visibility minimums, also known as "zero-zero".

Fail-passive autopilot: in case of failure, the aircraft stays in a controllable position and the pilot can take control of it to go around or finish landing. It is usually a dual-channel system.

Fail-operational autopilot: in case of a failure below alert height, the approach, flare and landing can still be completed automatically. It is usually a triple-channel system or dual-dual system.

Radio-controlled models

In radio-controlled modelling, and especially RC aircraft and helicopters, an autopilot is usually a set of extra hardware and software that deals with pre-programming the model's flight.

See also

Gyrocompass

Driverless car

(source:wikipedia)

Automobile safety

Automobile safety is the study and practice of vehicle design, construction, and equipment to minimize the occurrence and consequences of automobile accidents. (Road traffic safety more broadly includes roadway design.)

Improvements in roadway and automobile designs have steadily reduced injury and death rates in all first world countries. Nevertheless, auto collisions are the leading cause of injury-related deaths, an estimated total of 1.2 million in 2004, or 25% of the total from all causes. Risk compensation limits the improvement that can be made, often leading to reduced safety where one might expect the opposite.

Occupational driving

Work-related roadway crashes are the leading cause of death from traumatic injuries in the U.S. workplace. They accounted for nearly 12,000 deaths between 1992 and 2000. Deaths and injuries from these roadway crashes result in increased costs to employers and lost productivity in addition to their toll in human suffering. Truck drivers tend to endure higher fatality rates than workers in other occupations, but concerns about motor vehicle safety in the workplace are not limited to those surrounding the operation of large trucks. Workers outside the motor carrier industry routinely operate company-owned vehicles for deliveries, sales and repair calls, client visits etc. In these instances, the employer providing the vehicle generally plays a major role in setting safety, maintenance, and training policy. As in non-occupational driving, young drivers are especially at risk. In the workplace, 45% of all fatal injuries to workers under age 18 between 1992 and 2000 in the United States resulted from transportation incidents.

Active and passive safety

The terms "active" and "passive" are simple but important terms in the world of automotive safety. "Active safety" is used to refer to technology assisting in the prevention of a crash and "passive safety" to components of the vehicle (primarily airbags, seatbelts and the physical structure of the vehicle) that help to protect occupants during a crash .

Crash avoidance

Crash avoidance systems and devices help the driver — and, increasingly, help the vehicle itself — to avoid a collision. This category includes:

The vehicle's headlamps, reflectors, and other lights and signals

The vehicle's mirrors

The vehicle's brakes, steering, and suspension systems

Driver assistance

A subset of crash avoidance is driver assistance systems, which help the driver to detect ordinarily-hidden obstacles and to control the vehicle. Driver assistance systems include:

Automatic Braking systems to prevent or reduce the severity of collision.

Infrared night vision systems to increase seeing distance beyond headlamp range

Adaptive highbeam which automatically and continuously adapts the headlamp range to the distance of vehicles ahead or which are oncoming

Adaptive headlamps swivels headlamps around corners

Reverse backup sensors, which alert drivers to difficult-to-see objects in their path when reversing

Backup camera

Adaptive cruise control which maintains a safe distance from the vehicle in front

Lane departure warning systems to alert the driver of an unintended departure from the intended lane of travel

Tire pressure monitoring systems or Deflation Detection Systems

Traction control systems which restore traction if driven wheels begin to spin

Electronic Stability Control, which intervenes to avert an impending loss of control

Anti-lock braking systems

Electronic brakeforce distribution systems

Emergency brake assist systems

Cornering Brake Control systems

Precrash system

Automated parking system

Crashworthiness

Crashworthy systems and devices prevent or reduce the severity of injuries when a crash is imminent or actually happening. Much research is carried out using anthropomorphic crash test dummies.

Seatbelts limit the forward motion of an occupant, stretch to slow down the occupant's deceleration in a crash, and prevent occupants being ejected from the vehicle.

Airbags inflate to cushion the impact of a vehicle occupant with various parts of the vehicle's interior.

Laminated windshields remain in one piece when impacted, preventing penetration of unbelted occupants' heads and maintaining a minimal but adequate transparency for control of the car immediately following a collision. Tempered glass side and rear windows break into granules with minimally sharp edges, rather than splintering into jagged fragments as ordinary glass does.

Crumple zones absorb and dissipate the force of a collision, displacing and diverting it away from the passenger compartment and reducing the impact force on the vehicle occupants. Vehicles will include a front, rear and maybe side crumple zones (like Volvo SIPS) too.

Side impact protection beams.

Collapsible universally jointed steering columns, (with the steering system mounted behind the front axle - not in the front crumple zone), reduce the risk and severity of driver impalement on the column in a frontal crash.

Pedestrian protection systems.

Padding of the instrument panel and other interior parts of the vehicle likely to be struck by the occupants during a crash.

Post-crash survivability

Post-crash survivability is the chance that you can survive a crash after it occurs, these devices are often miscellaneous, and are not heavily produced as it is very difficult for them to function.

Pedestrian safety

1974 Mini Clubman Experimental Safety Vehicle featuring a "pedestrian-friendly" front end.

Since at least the early 1970s, attention has also been given to vehicle design regarding the safety of pedestrians in car-pedestrian collisions. Proposals in Europe would require cars sold there to have a minimum/maximum hood (bonnet) height. From 2006 the use of "bull bars", a fashion on 4x4s and SUVs, became illegal.

Conspicuity

A Swedish study found that pink cars are involved in the fewest accidents, with black cars being most often involved in crashes (Land transport NZ 2005).

In Auckland New Zealand, a study found that there was a significantly lower rate of serious injury in silver cars; with higher rates in brown, black, and green cars. (Furness et al., 2003)

The Vehicle Color Study, conducted by Monash University Accident Research Centre (MUARC) and published in 2007, analysed 855,258 accidents occurring between 1987 and 2004 in the Australian states of Victoria and Western Australia that resulted in injury or in a vehicle being towed away. The study analysed risk by light condition. It found that in daylight black cars were 12% more likely than white to be involved in an accident, followed by grey cars at 11%, silver cars at 10%, and red and blue cars at 7%, with no other colors found to be significantly more or less risky than white. At dawn or dusk the risk ratio for black cars jumped to 47% more likely than white, and that for silver cars to 15%. In the hours of darkness only red and silver cars were found to be significantly more risky than white, by 10% and 8% respectively.

Daytime running lamp that have been standard on Swedish cars since the 1970s, are soon to be mandatory across the entire EU.

History

Automobile safety may have become an issue almost from the beginning of mechanised road vehicle development. The second steam-powered "Fardier" (artillery tractor), created by Nicolas-Joseph Cugnot in 1771, is reported by some to have crashed into a wall during its demonstration run. However according to Georges Ageon, the earliest mention of this occurrence dates from 1801 and it does not feature in contemporary accounts.

One of the earliest recorded automobile fatalities was Mary Ward, on August 31, 1869 in Parsonstown, Ireland.

In the 1930s, plastic surgeon Claire L. Straith and physician C. J. Strickland advocated the use of seat belts and padded dashboards. Strickland founded the Automobile Safety League of America.

In 1934, GM performed the first barrier crash test.

In 1942, Hugh De Haven published the classic Mechanical analysis of survival in falls from heights of fifty to one hundred and fifty feet.

In 1949 SAAB incorporated aircraft safety thinking into automobiles making the Saab 92 the first production SAAB car with a safety cage, and the American Tucker was built with the world's first padded dashboard.

In 1956, Ford tried unsuccessfully to interest Americans in purchasing safer cars with their Lifeguard safety package. (Its attempt nevertheless earns Ford Motor Trend's "Car of the Year" award for 1956.)

In 1958, the United Nations established the World Forum for Harmonization of Vehicle Regulations, an international standards body advancing auto safety. Many of the most life saving safety innovations, like seat belts and roll cage construction were brought to market under its auspices. That same year, Volvo engineer Nils Bohlin invented and patented the three-point lap and shoulder seat belt, which became standard equipment on all Volvo cars in 1959. Over the next several decades, three-point safety belts were gradually mandated in all vehicles by regulators throughout the industrialised world.

In 1966, the U.S. established the United States Department of Transportation (DOT) with automobile safety one of its purposes. The National Transportation Safety Board (NTSB) was created as an independent organization on April 1, 1967, but was reliant on the DOT for administration and funding. However, in 1975 the organization was made completely independent by the Independent Safety Board Act (in P.L. 93-633; 49 U.S.C. 1901).

Volvo developed the first rear-facing child seat in 1964 and introduced its own booster seat in 1978.

Consumer information label for a vehicle with at least one US NCAP star rating

In 1979, NHTSA began crash-testing popular cars and publishing the results, to inform consumers and encourage manufacturers to improve the safety of their vehicles. Initially, the US NCAP crash tests examined compliance with the occupant-protection provisions of FMVSS 208. Over the subsequent years, this NHTSA program was gradually expanded in scope. In 1997, the European New Car Assessment Programme (Euro NCAP) was established to test new vehicles' safety performance and publish the results for vehicle shoppers' information. The NHTSA crash tests are presently operated and published as the U.S. branch of the international NCAP programme.

In 1984, New York State passed the first US law requiring seat belt use in passenger cars. Seat belt laws have since been adopted by all 50 states, except for New Hampshire. and NHTSA estimates increased seat belt use as a result save 10,000 per year in the USA.

In 1986, the central 3rd brake light was mandated in North America. Over the next 15 years, most of the world's other jurisdictions mandated the 3rd brake lamp as well.

In 1995, the IIHS begins frontal offset crash tests.

In 1997, EuroNCAP is founded.

In 2003, the IIHS begins conducting side impact crash tests.

In 2004, NHTSA released new tests designed to test the rollover risk of new cars and SUVs. Only the Mazda RX-8 got a 5-star rating.

In 2009, Citroën become the first manufacturer to feature "Snowmotion", an Intelligent Anti Skid system developed in conjunction with Bosch, which gives drivers a level of control in extreme ice or snow conditions similar to a 4x4 

Safety trends

Despite technological advances, about 40,000 people die every year in the U.S. Although the fatality rates per vehicle registered and per vehicle distance travelled have steadily decreased since the advent of significant vehicle and driver regulation, the raw number of fatalities generally increases as a function of rising population and more vehicles on the road. However, sharp rises in the price of fuel and related driver behavioural changes are reducing 2007-8 highway fatalities in the U.S. to below the 1961 fatality count. Litigation has been central in the struggle to mandate safer cars.

International comparison

In 1996, the U.S. had about 2 deaths per 10,000 motor vehicles, compared to 1.9 in Germany, 2.6 in France, and 1.5 in the UK. In 1998, there were 3,421 fatal accidents in the UK, the fewest since 1926.

The sizable traffic safety lead enjoyed by the USA since the 1960s had narrowed significantly by 2002, with the US improvement percentages lagging in 16th place behind those of Australia, Austria, Canada, Denmark, Finland, Germany, Great Britain, Iceland, Japan, Luxembourg, the Netherlands, New Zealand, Norway, Sweden, and Switzerland in terms of deaths per thousand vehicles, while in terms of deaths per 100 million vehicle miles travelled, the USA had dropped from first place to tenth place.

Government-collected data, such as that from the U.S. Fatality Analysis Reporting System, show other countries achieving safety performance improvements over time greater than those achieved in the U.S.:

1979 Fatalities 2002 Fatalities Percent Change

United States 51,093 42,815 -16.2%

Great Britain 6,352 3,431 -46.0%

Canada 5,863 2,936 -49.9%

Australia 3,508 1,715 -51.1%

Data From Table above showing data from the U.S. Fatality Analysis Reporting System

Research on the trends in use of heavy vehicles indicate that a significant difference between the U.S. and other countries is the relatively high prevalence of pickup trucks and SUVs in the U.S. A 2003 study by the U.S. Transportation Research Board found that SUVs and pickup trucks are significantly less safe than passenger cars, that imported-brand vehicles tend to be safer than American-brand vehicles, and that the size and weight of a vehicle has a significantly smaller effect on safety than the quality of the vehicle's engineering.The level of large commercial truck traffic has substantially increased since the 1960s, while highway capacity has not kept pace with the increase in large commercial truck traffic on U.S. highways. However, other factors exert significant influence; Canada has lower roadway death and injury rates despite a vehicle mix comparable to that of the U.S.Nevertheless, the widespread use of truck-based vehicles as passenger carriers is correlated with roadway deaths and injuries not only directly by dint of vehicular safety performance per se, but also indirectly through the relatively low fuel costs that facilitate the use of such vehicles in North America; motor vehicle fatalities decline as fuel prices increase.

NHTSA has issued relatively few regulations since the mid 1980s; most of the vehicle-based reduction in vehicle fatality rates in the U.S. during the last third of the 20th Century were gained by the initial NHTSA safety standards issued from 1968 to 1984 and subsequent voluntary changes in vehicle design and construction by vehicle manufacturers. 

Pregnant women

When pregnant, women should continue to use seatbelts and airbags properly. A University of Michigan study found that "unrestrained or improperly restrained pregnant women are 5.7 times more likely to have an adverse fetal outcome than properly restrained pregnant women". If seatbelts are not long enough, extensions are available from the car manufacturer or an aftermarket supplier.

Infants and children

Children present significant challenges in engineering and producing safe vehicles, because most children are significantly smaller and lighter than most adults. Safety devices and systems designed and optimised to protect adults — particularly calibration-sensitive devices like airbags and active seat belts — can be ineffective or hazardous to children. In recognition of this, many medical professionals and jurisdictions recommend or require that children under a particular age, height, and/or weight ride in a child seat and/or in the back seat, as applicable. In Sweden, for instance, a child or an adult shorter than 140 cm is legally forbidden to ride in a place with an active airbag in front of it.

Child safety locks and driver-controlled power window lockout controls prevent children from opening doors and windows from inside the vehicle.

Infants left in cars

Very young children can perish from heat or cold if left unattended in a parked car, whether deliberately or through absentmindedness. In June 2009, a 1 year old girl was accidentally forgotten in a car in Denmark on an extremely hot day and died from heat exhaustion.

Teenage Drivers

In the UK, a full driving licence can be had at age 17, and most areas in the United States will issue a full driver's license at the age of 16, and all within a range between 14 and 18. In addition to being relatively inexperienced, teen drivers are also cognitively immature, compared to other drivers. This combination leads to a relatively high crash rate among this demographic.

In some areas, new drivers' vehicles must bear a warning sign to alert other drivers that the vehicle is being driven by an inexperienced and learning driver, giving them opportunity to be more cautious and to encourage other drivers to give novices more leeway. In the US New Jersey has Kyleigh's Law citing that teen drivers must have a decal on their vehicle. Commercial services also exist to that provide a notification phone number to report unsafe driving such as IsmyKidDrivingSafe.com  and CarefulTeenDriver.com.

Some countries, such as Australia, the United States, Canada and New Zealand, have graduated levels of driver's licence, with special rules. In Italy, the maximum speed and power of vehicles driven by new drivers is restricted. In Romania, the maximum speed of vehicles driven by new drivers (less than one year in experience) is 20 km/h lower than the national standard (except villages, towns and cities).

(source:wikipedia)

Motion planning

Real-Time Scalable Motion Planning for Crowds

Motion planning (a.k.a., the "navigation problem", the "piano mover's problem") is a term used in robotics for the process of detailing a task into discrete motions.

For example, consider navigating a mobile robot inside a building to a distant waypoint. It should execute this task while avoiding walls and not falling down stairs. A motion planning algorithm would take a description of these tasks as input, and produce the speed and turning commands sent to the robot's wheels. Motion planning algorithms might address robots with a larger number of joints (e.g., industrial manipulators), more complex tasks (e.g. manipulation of objects), different constraints (e.g., a car that can only drive forward), and uncertainty (e.g. imperfect models of the environment or robot).

Motion planning has several robotics applications, such as autonomy, automation, and robot design in CAD software, as well as applications in other fields, such as animating digital characters, architectural design, robotic surgery, and the study of biological molecules.

Concepts

Example of a workspace.

Configuration space of a point-sized robot. White = Cfree, gray = Cobs.

Configuration space for a rectangular translating robot (pictured red). White =Cfree, gray = Cobs, where dark gray = the objects, light gray = configurations where the robot would touch an object or leave the workspace.

Example of a valid path.

Example of an invalid path.

Example of a road map.

A basic motion planning problem is to produce a continuous motion that connects a start configuration S and a goal configuration G, while avoiding collision with known obstacles. The robot and obstacle geometry is described in a 2D or 3D workspace, while the motion is represented as a path in (possibly higher-dimensional) configuration space.

Configuration Space

A configuration describes the pose of the robot, and the configuration space C is the set of all possible configurations. For example:

If the robot is a single point (zero-sized) translating in a 2-dimensional plane (the workspace), C is a plane, and a configuration can be represented using two parameters (x, y).

If the robot is a 2D shape that can translate and rotate, the workspace is still 2-dimensional. However, C is the special Euclidean group SE(2) = R2 SO(2) (where SO(2) is the special orthogonal group of 2D rotations), and a configuration can be represented using 3 parameters (x, y, θ).

If the robot is solid 3D shape that can translate and rotate, the workspace is 3-dimensional, but C is the special Euclidean group SE(3) = R3 SO(3), and a configuration requires 6 parameters: (x, y, z) for translation, and Euler angles (α, β, γ).

If the robot is a fixed-base manipulator with N revolute joints (and no closed-loops), C is N-dimensional.

Free Space

The set of configurations that avoids collision with obstacles is called the free space Cfree. The complement of Cfree in C is called the obstacle or forbidden region.

Often, it is prohibitively difficult to explicitly compute the shape of Cfree. However, testing whether a given configuration is in Cfree is efficient. First, forward kinematics determine the position of the robot's geometry, and collision detection tests if the robot's geometry collides with the environment's geometry.

Algorithms

Low-dimensional problems can be solved with grid-based algorithms that overlay a grid on top of configuration space, or geometric algorithms that compute the shape and connectivity of Cfree.

Exact motion planning for high-dimensional systems under complex constraints is computationally intractable. Potential-field algorithms are efficient, but fall prey to local minima (an exception is the harmonic potential fields). Sampling-based algorithms avoid the problem of local minima, and solve many problems quite quickly. They are unable to determine that no path exists, but they have a probability of failure that decreases to zero as more time is spent.

Sampling-based algorithms are currently considered state-of-the-art for motion planning in high-dimensional spaces, and have been applied to problems which have dozens or even hundreds of dimensions (robotic manipulators, biological molecules, animated digital characters, and legged robots).

Grid-Based Search

Grid-based approaches overlay a grid on configuration space, and assume each configuration is identified with a grid point. At each grid point, the robot is allowed to move to adjacent grid points as long as the line between them is completely contained within Cfree (this is tested with collision detection). This discretizes the set of actions, and search algorithms (like A*) are used to find a path from the start to the goal.

These approaches require setting a grid resolution. Search is faster with coarser grids, but the algorithm will fail to find paths through narrow portions of Cfree. Furthermore, the number of points on the grid grows exponentially in the configuration space dimension, which make them inappropriate for high-dimensional problems.

Traditional grid-based approaches produce paths whose heading changes are constrained to multiples of a given base angle, often resulting in suboptimal paths. Any-angle path planning approaches find shorter paths by propagating information along grid edges (to search fast) without constraining their paths to grid edges (to find short paths).

Grid-based approaches often need to search repeatedly, for example, when the knowledge of the robot about the configuration space changes or the configuration space itself changes during path following. Incremental heuristic search algorithms replan fast by using experience with the previous similar path-planning problems to speed up their search for the current one.

Geometric Algorithms

Point robots among polygonal obstacles

Visibility graph

Cell decomposition

Translating objects among obstacles

Minkowski sum

Potential Fields

One approach is to treat the robot's configuration as a point in a potential field that combines attraction to the goal, and repulsion from obstacles. The resulting trajectory is output as the path. This approach has advantages in that the trajectory is produced with little computation. However, they can become trapped in local minima of the potential field, and fail to find a path.

Sampling-Based Algorithms

Sampling-based algorithms represent the configuration space with a roadmap of sampled configurations. A basic algorithm samples N configurations in C, and retains those in Cfree to use as milestones. A roadmap is then constructed that connects two milestones P and Q if the line segment PQ is completely in Cfree. Again, collision detection is used to test inclusion in Cfree. To find a path that connects S and G, they are added to the roadmap. If a path in the roadmap links S and G , the planner succeeds, and returns that path. If not, the reason is not definitive: either there is no path in Cfree, or the planner did not sample enough milestones.

These algorithms work well for high-dimensional configuration spaces, because unlike combinatorial algorithms, their running time is not (explicitly) exponentially dependent on the dimension of C. They are also (generally) substantially easier to implement. They are probabilistically complete, meaning the probability that they will produce a solution approaches 1 as more time is spent. However, they cannot determine if no solution exists.

Given basic visibility conditions on Cfree, it has been proven that as the number of configurations N grows higher, the probability that the above algorithm finds a solution approaches 1 exponentially . Visibility is not explicitly dependent on the dimension of C; it is possible to have a high-dimensional space with "good" visibility or a low dimensional space with "poor" visibility. The experimental success of sample-based methods suggests that most commonly seen spaces have good visibility.

There are many variants of this basic scheme:

It is typically much faster to only test segments between nearby pairs of milestones, rather than all pairs.

Nonuniform sampling distributions attempt to place more milestones in areas that improve the connectivity of the roadmap.

Quasirandom samples typically produce a better covering of configuration space than pseudorandom ones, though some recent work argues that the effect of the source of randomness is minimal compared to the effect of the sampling distribution.

If only one or a few planning queries are needed, it is not always necessary to construct a roadmap of the entire space. Tree-growing variants are typically faster for this case (single-query planning). Roadmaps are still useful if many queries are to be made on the same space (multi-query planning)

Completeness and Performance

A motion planner is said to be complete if the planner always produces a feasible path, when one exists. Most complete algorithms are geometry-based. The performance of a complete planner is assessed by its computational complexity.

Resolution completeness is the property that the planner is guaranteed to find a path if the resolution of an underlying grid is fine enough. Most resolution complete planners are grid-based. The computational complexity of resolution complete planners is dependent on the number of points in the underlying grid, which is O(1/hd), where h is the resolution (the length of one side of a grid cell) and d is the configuration space dimension.

Probabilistic completeness is the property that as more “work” is performed, the probability that the planner fails to find a path, if one exists, asymptotically approaches zero. Several sample-based methods are probabilistically complete. The performance of a probabilistically complete planner is measured by the rate of convergence.

Incomplete planners do not always produce a feasible path when one exists. Sometimes incomplete planners do work well in practice.

Problem Variants

Many algorithms have been developed to handle variants of this basic problem.

Differential Constraints

Holonomic

Manipulator arms (with dynamics)

Nonholonomic

Cars

Unicycles

Planes

Acceleration bounded systems

Moving obstacles (time cannot go backward)

Bevel-tip steerable needle

Differential Drive Robots

Optimality Constraints

Hybrid Systems

Hybrid systems are those that mix discrete and continuous behavior. Examples of such systems are:

Robotic manipulation

Mechanical assembly

Legged robot locomotion

Reconfigurable robots

Uncertainty

Motion uncertainty

Missing information

Active sensing

Sensorless planning

Applications

Robot navigation

Automation

The driverless car

Robotic surgery

Digital character animation

protein folding

Safety and accessibility in computer-aided architectural design

(source:wikipedia)