planning and navigation

8/2/2019 Planning and Navigation

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ROBOTICSPLANNING AND NAVIGATION



PLANNING AND NAVIGATION

INTRODUCTION

TWO KEY COMPETENCES REQUIRED

FOR MOBILE ROBOT NAVIGATION• Given a map and a goal location, path planning involves identifying a trajectory

that will cause the robot to reach the goallocation when executed.

• Given real-time sensor readings, obstacleavoidance means modulating the trajectory of

the robot in order to avoid collisions.



PLANNING AND NAVIGATION

INTEGRATED PLANNING AND EXECUTION

• Consider Robot R at time i has a map Mi & initial belief sate bi.

• Now robot’s goal position (bg) p has temporal constraintslocg(R) = p ; (g<=n).

• A plan q is one or more trajectories from bi to bg.

• Due to incompleteness in Mi or the real world environment isdynamic other plan executed from world state may notconsistent with both bi and Mi.

• So to reach goal nonetheless concept of planning and conceptof reacting should merge and it is called integrated planningand execution.



COMPLETENESS

• “The robot system is complete if and only if , for all

possible problems (i.e., bi, bg & Mi ), when there exists a

trajectory to the goal belief state, the system will achieve

goal belief state”

• In industrial robots ,the dynamics and not just the kinematics

of their motions are significant, further complicating path

planning and execution.

• In contrast, a number of mobile robots operate at such low

speeds that dynamics are rarely considered during pathplanning, further simplifying the mobile robot instantiation of

the problem.



Holonomicity

• Holonomicity is the relationship between the controllable

degrees of freedom of the robot and the total degrees of

freedom of the robot. If the number of controllable degrees of

freedom is equal to the total degrees of freedom a robot is

said to be holonomic. By using a holonomic robot many

movements are much easier to make and returning to a pastpose is much easier.

EXAMPLE:-A car would be non-holonomic , as it has no way to

move laterally. This makes certain movements, such as parallel

parking, difficult. An example of a holonomic vehicle would be

one using mecanum wheels, such as the new Segway RMP.



PATH PLANNING



PATH PLANNING

• Configuration Space(C) – as shown in fig. below forplanar 2- DOF manipulator Configuration space is shownin (b).

F = C – O

F is Free space & O is Configuration space Obstacle



THREE GENERAL STRATEGIES FOR

DECOMPOSITION OF MAP

PATHPLANNING

ROADMAP

CELLDECOMPOSITION

POTENTIALFILED



ROAD MAP

VISIBILITYGRAPH

• The task of the path planner is tofind the shortest path from theinitial position to the goal positionalong the roads defined by thevisibility graph

• The unobstructed straight lines(roads) joining those vertices areobviously the shortest distances

between them.

VORONOIGRAPH

• A Voronoi diagram is a complete

road map method that tends tomaximize the distance between therobot and obstacles in the map.

• Sharp ridges are formed atequidistant points. The Voronoidiagram consists of the edgesformed by these sharp ridge points.



VISIBILITY GRAPH



VISIBILITY GRAPH

ADVANTAGES:-

• When the environmental representation describes objects in

the environment as polygons in either continuous or discrete

space, the visibility graph search can employ the obstacle

polygon descriptions readily.• Visibility graph planning is optimal in terms of the length of

the solution path.

DISADVANTAGES:-

•

MORE INEFFICIENT IN DENSE ENVIRONMENT• IT TENDS TO TAKE ROBOT AS CLOSE AS POSSIBLE TO

OBSTACLES



VORONOI GRAPH



VORONOI DIAGRAMS

ADVANTAGES:-

• Given a particular planned path via Voronoi diagram

planning, a robot with range sensors, such as a laser

rangefinder or ultrasonics, can follow a Voronoi edge in

the physical world using simple control rules that match

those used to create the Voronoi diagram

DISADVANTAGES:-

• This path-planning algorithm maximizes the distance

between the robot and objects in the environment, any

short-range sensor on the robot will be in danger of

failing to sense its surroundings.



CELL DECOMPOSITION PATH PLANNING

EXACT CELLDECOMPOSITION

APPROXIMATECELL

DECOMPOSITION



EXACT CELL DECOMPOSITION

The first step in this type of cell decomposition is to decompose

the free space, which is bounded both externally and internally

by polygons, into trapezoidal and triangular cells by simply

drawing parallel line segments from each vertex of each interior

polygon in the configuration space to the exteriorboundary. Then each cell is numbered and represented as a

node in the connectivity graph. Nodes that are adjacent in the

configuration space are linked in the connectivity graph. A path

in this graph corresponds to a channel in free space, which is

illustrated by the sequence of striped cells. This channel is thentranslated into a free path by connecting the initial

configuration to the goal configuration through the midpoints

of the intersections of the adjacent cells in the channel.



EXACT CELL DECOMPOSITION



APPROXIMATE CELL DECOMPOSITION.

• This approach to cell decomposition is different because it uses a

recursive method to continue subdividing the cells until one of the

following scenarios occurs:

• Each cell lies either completely in free space or completely in the C-

obstacle region• An arbitrary limit resolution is reached.

Once a cell fulfills one of these criteria, it stops decomposing. This

method is also called a "quadtree" decomposition because a cell is

divided into four smaller cells of the same shape each time it gets

decomposed. After the decomposition step, the free path can then

easily be found by following the adjacent, decomposed cells through

free space. An example of this method is illustrated below



APPROXIMATE CELL DECOMPOSITION



Breadth-first search

initial

B C

initial

B

D goal

C

goal




• It starts with start node and explore all of its neighboringnodes as shown above.

• Then for each of these nodes all their unexplored neighboursare explored and so on. This is called Node – expansion.

• Marking a node “active”, all unexplored nodes as “open” and

parent nodes as “visited”.• Nodes are expanded with proximity defined as the shortest

number of edge transitions. Algorithm terminates when itreaches goal node.

• If we assume c(n, n’) is constant it always returns theminimum cost path. But if c(n, n’) isn’t constant then breadth-first search is not guaranteed to be cost-optimal.

• an example of it is wavefront expansion algorithm alsoknown as NF1 or grassfire, which is as shown in the figure.




Given that the entire array can be

in memory, each cell is only

visited once when looking for the

shortest discrete path from theinitial position to the goal

position. So, the search is linear in

the number of cells only.

Thus, complexity does not depend

on the sparseness and density of

the environment nor on the

complexity of the objects



Depth-first search

initial

B

D goal

C

initial

B

D goal

C

goal



Dijkstra’s search

• Similar to breadth-first search, but edge costs assume any positive value andheuristic is taken zero.

• Expansion takes place as in breadth-first search, except that the neighbours of the expanded node are placed in heap and reordered according to their f(n)values. So cheapest state of heap is extracted and expanded. Solution can beback tracked.

• Here time complexity rises from n+m to nlog(n) + m due to heap reorderoperations.

• In applications Dijkstra's search is computed from robot goal position. So, anylow cost paths from goal to any initial point is computed.

• Thus robot can localize and determine the best route toward goal based on itscurrent position.

• This technique allows the robot to reach the goal without re-planning even inpresence of localization and actuation noise.



A* Algorithm

• It is similar to Dijkstra’s but inclusion h(n) takes place .

• Mostly A* is employed on grid, and heuristic if often chosen asthe distance between any cell and goal cell in absence of any

obstacles.

• The time complexity is largely depends on the chosen h(n).

• Often optimal solution is not necessary to obtain. So, the

solution that costs ε times the (unknown) optimal solutionmay be obtained by setting ε > 1. If heuristic is accurate, farfewer states can be expected to be expanded than for optimalA*.



A* Algorithm



D* Algorithm



D* Algorithm

• The D* algorithm represents an incremental re-planning

of version of A*.

• This comes into play when robot encounters a change in

environment which is not predicted before.

• Instead of generating a new solution from scratch(A*),

only effected states are recomputed.

• Compared to A* , search time decrease by a factor of one

or two orders of magnitude.



The Potential Field Approach

• The potential field method involves modeling the robot as a

particle moving under the influence of a potential field that is

determined by the set of obstacles and the target destination. This

method is usually very efficient because at any moment the motion

of the robot is determined by the potential field at itslocation. Thus, the only computed information has direct relevance

to the robot's motion and no computational power is wasted. It is

also a powerful method because it easily yields itself to

extensions. For example, since potential fields are additive, adding

a new obstacle is easy because the field for that obstacle can besimply added to the old one.




• The method's only major drawback is the existence of local

minima. Because the potential field approach is a local rather

than a global method (it only considers the immediate best

course of action), the robot can get "stuck" in a local minimum

of the potential field function rather than heading towards theglobal minimum, which is the target destination. This is

frequently resolved by coupling the method with techniques

to escape local minima, or by constructing potential field

functions that contain no local minima.




• The potential field method treats the robot as a point underthe influence of an artificial potential field U(q).

• The goal( a minimum in space) acts as a attractive force andobstacles act as peaks, i.e. repulsive.

• So artificial potential field is as

= − = − −

• Attractive potential

Uatt(q) = (0.5). K att . ρ2

goal (q). Where K att ispositive scaling factor

F att (q) = - = - K att . ρgoal (q). ρgoal (q)

= - K att (q – qgoal )

• This converges linearly toward 0 as the robot reaches the goal.




• Repulsive potential

U rep(q) = (.5) . K rep . ((1/ ρ(q) ) – (1/ ρ0 ))2 if ρ(q) <= ρ0.

= 0 if ρ(q) >= ρ0.

repulsive force should be strong when object is near toobstacle and shouldn’t influence its path when far from it. So , defined

as above.

• If object boundary is convex and piecewise differentiable equationturns out to be

• U rep(q) = K rep . ((1/ ρ(q) ) – (1/ ρ0 )) . (1/ ρ2(q)) . (q – qobstacle ) / ρ(q) if ρ(q) <= ρ0. and other part is zero.

•

Under ideal conditions robot’s velocity vector is proportional to fieldforce vector.

• One limitation is local minima occurs according to obstacle shape.

• Other limitation is if object shape concave, several minimaldistances q exist, results oscillation of robot between these points.



Extended Potential field path planning

• Two parameters are introduced.• Rotational potential field –

assumes repulsive force is alsofunction of distance from theobstacle and orientation of robot. This reduces repulsiveforce when robot is parallel to

object.• Task potential field - Filters out

the obstacles that should notinfluence the robotsmovements , i.e. only theobstacles in the sector in frontof the robot are considered.

•

When these two parametersare also introduced thedifference in path planning isshown in fig.



Extended Potential field path planning

Using harmonic potentials

• Hydrodynamics analogy , i.e. robot is moving similar to a fluid

particle following its stream .

• Ensures that there are no local minima .

• Boundary Conditions:

Neuman

-Equipotential lines orthogonal on object boundaries .

-Short but dangerous paths.

Dirichlet

- Equipotential lines parallel to object boundaries

- Long but safe paths



OBSTACLE AVOIDANCE

• During path execution the robot’s actual sensor values

may disagree with the expected values due to map

inaccuracy or other.

• Therefore it is critical that the robot modify its path in

real time based on actual sensor values.

• This is where obstacle avoidance comes in play.

• There are lot of algorithms for obstacle avoidance



OBSTACLE AVOIDANCE

BUG 1 ALGORITHM

• Bug algorithms are simplestalgorithms.

• Following along the obstacle toavoid collision.

• Each encountered obstacle is oncefully circled before it is left at thepoint closest to the goal.

• Advantages-No global map required.

-Completeness guaranteed.

•

Disadvantages - Solutions are oftenhighly suboptimal.



OBSTACLE AVOIDANCE

BUG 2 ALGORITHM

• Following the obstacle alwayson the left or right side .

• Leaving the obstacle if thedirect connection between

start and goal is crossed.• But it is non-optimal, as

inefficient paths can also beconstructed.

•Local Tangent Graph(LTG) isone extension to it, so thatrobot can go along shortcutswhen contouring obstaclesand switch back to goalseeking earlier. In simpler

environments it approachesglobally optimal paths.



Obstacle AvoidanceVector Field Histogram (VFH)

• Environment represented in a grid (2 DOF) and cell values

equivalent to the probability that there is an obstacle.

• Reduction in different steps to a 1 DOF histogram and the

steering direction is computed in two steps:•all openings for the robot to pass are found.

•the one with lowest cost function G is selected.

Target direction = alignment of the robot path with the goal .Wheel orientation = difference between the new direction and

the current wheel orientation previous direction = difference

between the previously selected direction and the new direction



Obstacle AvoidanceVector Field Histogram (VFH+)

• It’s an extension to VFH.

• Accounts also in a very simplified way for vehicle

kinematics

- robot moving on arcs or straight lines

-obstacles blocking a given direction also

blocks all the trajectories (arcs) going through this direction

- obstacles are enlarged so that all kinematically blocked

trajectories are properly taken into account



Obstacle AvoidanceVector Field Histogram (VFH)

Limitations:

• Limitation if narrow areas (e.g. doors) have to be passed.

•

Local minima might not be avoided.

• Reaching of the goal can not be guaranteed.

• Dynamics of the robot not really considered.



OBSTACLE AVOIDANCE

VECTOR FIELD HISTOGRAM



Obstacle Avoidance

Bubble Band Technique

• A bubble is defined as the maximum local subset of the freespace around a given configuration of the robot that which canbe traveled in any direction without collision.

• So, robot geometry is taken into account.

• Computing bubble band require global map and global pathplanner.

• The bubble band takes into account forces from modeled objectand internal forces. The internal forces try to minimize the“slack” (energy) between adjacent bubbles.

•

The bubble band model is used to deflect the robot from itsoriginally intended path in a way that minimizes bubble bandtension.

• Advantage is one can account robot dimensions. But themethod is mostly applicable when environmental condition isknown ahead of time, just as with offline path-planning

techniques



Obstacle Avoidance

Curvature velocity techniques

Basic Curvature Velocity Approach(CVM)

• CVM begins by adding physical constraints from the robot and theenvironmental to a velocity space.

• Velocity space consists of rotational velocity ω and translational

velocity v, thus assuming that the robot travels only along arcs of circles with curvature c = ω / v.

• Two constraints are identified: one is due robot kinematics i.e., - v max < v < v max and - ωmax < ω < ωmax . And other is due to obstaclesblocking certain v and ω values due to their positions.

• Obstacles are approximated as circular and divided into few intervals.

The distance from an end point of an interval to robot is calculatedand in between end points distance function is assumed to beconstant.

• CVM takes dynamics of vehicle into consideration, but seriouslimitation is circular simplification of objects which is highlyunacceptable in some environments.

•

It can suffer from local minima



Obstacle Avoidance

Curvature velocity techniques

Lane Curvature Method(LCM)

• Designed to overcome difficulties in CVM. In LCM problem isstemmed from the approximation that the robot moves onlyalong fixed arcs, but robot can change direction before going togoal.

• LCM calculates a set of desired lanes, trading off lane lengthand lane width to the closest obstacle. The lane with best

properties is chosen using objective function. The local headingis chosen in such a way that the robot will transition to the bestlane if it is not in that lane already.

• One caveat in this is that the parameters in the objective

function must be chosen wisely to optimize system behaviour.



Obstacle AvoidanceDynamic Window approach:-

Local dynamic window approach

• The kinematics of the robot are considered via search invelocity space:

• Circular trajectories : The dynamic window approachconsiders only circular trajectories uniquely determinedby pairs (v , ω) of translational and rotational velocities.

•

Dynamic window : The dynamic window restricts theadmissible velocities to those that can be reached withina short time interval given the limited accelerations of the robot.



Obstacle AvoidanceDynamic Window approach

The rectangular window shows the possible speeds (v , ω)

and the overlap with obstacles in configuration space




Maximizing the objective function

- In order to incorporate the criteria target heading,

and velocity, the maximum of the objective function, G(v ,

ω ), is computed over V r .

G = a. heading (v , ω) + b. velocity (v , ω) + c. dist (v , ω)

heading = measure of progress toward the goaldist = Distance to the closest obstacle in trajectory

velocity = Forward velocity of the robot, encouraging fast

movements




Global dynamic window approach

• It adds NF1 to local dynamic approach.

• Global dynamic window approach calculates NF1 only onselected rectangular region that is directed towards goal. Thewidth of the grid is enlarged and recalculated if goal can’t bereached within constraints of the chosen region.

• If the NF1 cannot be calculated because is robot is surroundedby obstacles, the method degrades to local dynamic approach.This keeps robot moving so that a possible way out may befound and resume NF1.

• Occupancy grid is updated from range measurements as therobot moves in environment.

• Advantage is without priori knowledge some of theadvantages of global path planning are achieved.



Obstacle Avoidance

• Some more algorithms are also used like Nearness Diagram,

Gradient Method , Schlegel approach to obstacle avoidance(

this also assumes circular arc paths, real time performance is

achieved), by adding dynamic constraints, Tzafestas and

Tzafestas( provides fuzzy and neurofuzzy approaches),

biological approach……..



NAVIGATION ARCHITECTURES



NAVIGATION ARCHITECTURES

The study of navigation architectures is the study of principled designsfor the software modules that constitute a mobile robot navigationsystem.It combines techniques for path planning, obstacle avoidance,localization, and perceptual interpretation etc.

Modularity for code reuse and sharing:

Modularity is great importance in mobile robotics because in the

course project the mobile robot hardware or its physicalenvironmental characteristics can change.We will be able to changepart of the robot’s competence without causing a string of side effectsthat force us to revisit the functioning of other robot competences.

Control localization:

Robot architecture includes multiple types of control functionality.By

localizing each functionality to a specific unit in the architecture, weenable individual testing as well as a principled strategy for controlcomposition.Localization of control can enable a specific learningalgorithm to be applied to just one aspect of a mobile robot’s overallcontrol system.



Techniques for decomposition

• Decompositions identify axes along which we can justify

discrimination of robot software into distinct modules and

also helps classify various mobile robots into a more

quantitative taxonomy.

Temporal decompositionControl Decomposition



TEMPORAL DECOMPOSITION

• Four important interrelated trends correlate with temporal decompositionSensor response time: A particular module’s sensor response time can be definedas the amount of time between acquisition of a sensor-based event and acorresponding change in the output of the module.It increases as one moves upthe stack in figure shown.

Temporal depth: Temporal depth applies to the temporal window that affects themodule’s output, both backward and forward in time. Temporal horizon describes

the amount of look ahead used by the module during the process of choosing anoutput. Temporal memory describes the historical time span of sensor input that isused by the module to determine the next output.

Spatial locality: The spatial impact of layers increases dramatically as one movesfrom low-level modules to high-level modules. Real-time modules tend to controlwheel speed and orientation, controlling spatially localized behavior.

Context specificity :A module makes decisions as a function not only of its

immediate inputs but also as a function of the robot’s context as captured by othervariables, such as the robot’s representation of the environment. Lowest-levelmodules tend to produce outputs directly using little context and being relativelycontext insensitive. Highest-level modules tend to exhibit very high contextspecificity.



CONTROL DECOMPOSITION

• Control decomposition identifies the way in which each module’s

output contributes to the overall robot control outputs.Consider the

robot algorithm and the physical robot instantiation to be members

of an overall system whose connectivity we wish to examine.

• This overall system S is comprised of a set M of modules, each

module 'm' connected to other modules via inputs and outputs. Thesystem is closed,meaning that the input of every module 'm' is the

output of one or more modules in M . Each module has precisely

one output and one or more inputs.

• The one output can be connected to any number of other modules

inputs.

• Control decomposition discriminates between different types of

control pathways through the portion of this system comprising the

robot algorithm



Research @

• Approximate dynamic programming using trajectory libraries

is being explored as one means of achieving (near) optimal

motion control (Atkeson).

• Other researchers (Likhachev, Stentz) are developing graphrepresentations and heuristic graph search algorithms for

motion and path planning that can search high dimensional

graphs in real-time and deal well with uncertainty.

• Some recent significant applications of developed motion and

path planning techniques include maneuver planning in the

winning DARPA Urban Challenge vehicle in 2007 (Likhachev)

and autonomous flight planning in the Boeing Unmanned

Little Bird helicopter (Singh).



Research @

• Current work spans such problems as planning for tightcoordination of heterogeneous robots engaged in complex tasks(e.g., construction of large beam and node structures) that cannotbe completed by a singe robot , multi-robot path planning forcoverage, surveillance, search and large-teamapplications ,collaborative task planning and scheduling of heterogeneous teams in dynamic environments involvingcontinual new task discovery ,robot soccer ,and execution-driven

task scheduling and resource allocation in large-scale, multi-actorsystems .

• Reference :

http://www.ri.cmu.edu/research_guide/planning_scheduling.html















Research @ MIT

• Researchers at the MIT’s Computer Science and ArtificialIntelligence Laboratory (CSAIL)and Laboratory for Informationand Decision Systems (LIDS) came up with a system whichenables robots to move more efficiently, thus saving time andenergy. Since it is more intuitive and efficient, the new

algorithm also provides more predictable movement which iscrucial for robots which interact with humans.

• Graduate student Sertac Karaman and associate professor of aeronautics and astronautics Emilio Frazzoli, both of LIDS,developed a new variation on that algorithm which finds the

paths that are much closer to the optimum. Every time thealgorithm evaluates a new, randomly selected point, itconsiders all the previously evaluated points within a fixedradius of the new one and determines which would offer theshortest path from the starting point.

http://lids.mit.edu/

http://lids.mit.edu/



Research @ MIT

• Shkolnik’s algorithm assumes that every new point it adds to

its map has a sphere of open space around it, so it doesn’t

evaluate any other points within that sphere. As the map

expands, the algorithm discovers new possible sources of

collision and rescales the spheres accordingly. The

researchers’ new system then uses Frazzoli and Karaman’s

algorithm to refine the route.

• Reference :

http://www.robaid.com/robotics/new-algorithm-leads-to-more-

efficient-robots-with-predictable-movement.htm

http://www.robaid.com/robotics/new-algorithm-leads-to-more-efficient-robots-with-predictable-movement.htm































Research @ Stanford university

• The Elastic Strip Framework provides an efficient method for

performing local adjustments to a plan in dynamic

environments while respecting original goals of the plan. The

approach combines advantages of planning and execution

based methods. The initial trajectory is computed by a global

motion planner. For obstacle avoidance the costly search in

high-dimensional configuration space is replaced with a

directed exploration in the neighborhood of the planned

trajectory. To modify a motion in reaction to changes in the

environment, real-time obstacle avoidance is combined withdesired posture behavior. The modification of motion is

performed in a task-consistent manner, leaving task execution

unaffected by obstacle avoidance and posture behavior.



Research @ Stanford university



Research @ Stanford University

• The Elastic Strip is a powerful tool for real-time motion generationand motion execution in free space. To fully complete the set of possible motions however, the framework must allow the robot tocome into contact with the environment, and our goal is to revisethe work to accommodate for the contact. Note that in n-dimensional configuration space, the obstacle boundaries to be

traced still form an (n-1)-dimensional subspace, and with thetransitions between contact and free space the dimensionality of the problem increases and poses many challenges. First, the initialplan must provide a convenient encoding of motion intensions inboth free space and contact space. Notions such as desirableproximity and contacts must be easily extractable from the plan andincorporated into the framework. A new local modification schemeis needed and the final model must be able to cope with theuncertainty and imprecision inherent to real robots andenvironments they live in. This is a topic of ongoing research.



Some more references

• http://web.mit.edu/aeroastro/news/magazine/aeroastro8/aut

onomous-planning.html

• http://cs.stanford.edu/groups/manips/research/control-

architectures

•http://www.kuffner.org/james/plan/

http://web.mit.edu/aeroastro/news/magazine/aeroastro8/autonomous-planning.html


http://cs.stanford.edu/groups/manips/research/control-architectures


http://www.kuffner.org/james/plan/

http://www.kuffner.org/james/plan/










planning and navigation

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