Dynamic Path Planning

FOLLOW THE GAP METHOD [FGM] FOR MOBILE ROBOTS

Presented by: Vikrant Kumar M. Tech. MED CIM 133569

Robotics – Control & Intelligence – Path Planning – Dynamic Path Planning

Robotics & Automation

Programming and Intelligence

Control & Intelligence

Controller Design Sensors for Robot Motion Planning and Control

Path Planning

Static Path Planning

Dynamic Path Planning

Mechanical Design

Mobile Robot Navigation

• Global Navigation – from knowledge of goal point• Local Navigation – from knowledge of near by objects

in path• Personal Navigation – continuous updating of current

position

Robot’s ability to safely move towards the Goal using its knowledge and sensorial information of the surrounding environment.

Three terms important in navigation are:

Static Path Planning

• Probabilistic Roadmap (PRM) - Two phase navigation:• Learning phase• Query phase

• Visibility Graph – navigating at the boundary of obstacles, turning at corners only, finding shortest straight line path.

Based on a map and goal location, finding a geometric path.

Methods

Dynamic Path Planning

• Bug Algorithms• Artificial Potential Field (APF) Algorithm• Harmonic Potential Field (HPF) Algorithm• Virtual Force Field (VFF) method• Virtual Field Histogram (VFH) method• Follow the Gap Method (FGM)

Aim is of avoiding unexpected obstacles along the robot’s trajectory to reach the goal.

Methods

Some terms of concern• Point Robot Approach

• Field of view of Robot

• Non-holonomic constraints

Point Robot Approach• Robot and Obstacles are assumed circular.• Radius of robot is added to radius of obstacles• The Robot is reduced to a point, while Obstacles are equally enlarged.

Field of view• The sector region within the range of robot’s sensors to get

information of environment.• Two quantitative measures of field of view:• End angles of the sector on right and left sides.• Radius of the sector.

Nonholonomic Constraints• If the vector space of the possible motion directions of a mechanical

system is restricted • And the restriction can not be converted into an algebraic relation

between configuration variables.• Can be visualized as, inability of a car like vehicle to move sideways, it

is bound to follow an arc to reach a lateral co-ordinate.

Nonholonomic Constraints and Field of View of Robot

Nonholonomic Constraint

Field of View

Rmin

Bug Algorithms

• Common sense approach of moving directly to goal.

• Contour the obstacle when found, until moving straight to goal is possible again.• Path chosen – often too long• Robot prone to move close to obstacles

Possible paths with Bug Algorithm

Artificial Potential Field (APF)• Presently very popular• Obstacles represent “repulsive potential”• Goal represent “attractive Potential”

• Main drawback – • Robot gets trapped in local minima.• The Method Ignores nonholonomic constraints

APF contd..

APF contd..• Main drawback –

• Robot gets trapped in local minima.• The Method Ignores nonholonomic constraints

Harmonic Potential Field (HPF)• An HPF is generated using a Laplace boundary value problem (BVP).• HPF approach may be configured to operate in a model-based and/or

sensor-based mode• It can also be made to accommodate a variety of constraints.

• the robot must know the map of the whole environment .• contradicts reactiveness and local planning properties of obstacle

avoidance.

Virtual Force Field method (VFF)• 2D Cartesian histogram grid for obstacle representation.• Each cell has certainty value of confidence, that an obstacle is present there.• Then APF is applied.• Problems of APF method still exist in VFF

VFF contd…

Virtual Field Histogram (VFH)• Uses a 2D Cartesian histogram grid like in VFF.• Reduces it to a one dimensional polar histogram around the robot's

momentary location.• Selects lowest polar obstacle density sector • steers the robot in that direction• very much goal oriented since it always selects the sector which is in the same

direction as the goal.

• selected sector can be the wrong one in some cases.• does not consider nonholonomic constraints of robots

VFH Confidence value and 1D polar histogram

Follow the Gap Method (FGM)• Point Robot Approach• Obstacle representation• Construction a gap array among obstacles.• Determination of maximum gap, considering the Goal point location.• Calculation of angle to Center of Maximum gap• Robot proceeds to center of maximum gap.

Problem Definition• The Algorithm • Should find a purely reactive heading to achieve goal co-ordinates• Should avoiding obstacles with as large distance as possible• Should consider measurement and nonholonomic constraints• for obstacle avoidance must collaborate with global planner

• Goal point – obtained from the global planner• Obstacle co-ordinates - change with time

Point Robot ApproachXrob = Abscissa of robot point

Yrob = Ordinate of robot point

Rrob = Robot circle’s radius

Xobsn = Abscissa of nth obstacle

Yobsn = Ordinate of nth obstacle

Robsn = nth obstacle’s circle’s radius

Distance to ObstacleDistance of nth obstacle from robot

d = ((Xobsn – Xrob)2 + (Yobsn – Yrob)2)1/2

Using Pythogoras theorem

dn2 + (Robsn + Rrob)2 = d2

Or, dn = ((Xobsn – Xrob)2 + (Yobsn – Yrob)2 – (Robsn + Rrob)2)1/2

Obstacle Representation• Two parameter representation• Φ

obs_l_1 – Border left angle of obstacle 1• Φ

obs_r_1 -- Border right angle of obstacle 1• Φ

obs_l_1 – Border left angle of obstacle 2• Φ

obs_l_1 – Border right angle of obstacle 2

Φ obs_l_1

Φ obs_r_1

Φ obs_l_2

Φ obs_r_2

Obst. 1

Obst. 2

Gap Border Evaluation

If,

Else if,

In order to understand which boundary is active for a boundary obstacle, decision rule are illustrated as follows:

Gap boarder parameters• 1. Φlim: Gap border angle

• 2. Φnhol: Border angle coming from nonholonomic constraint

• 3. Φfov: Border angle coming from field of view

• 4. dnhol: Nearest distance between nonholonomic constraint arc and obstacle border

• 5. dfov: Nearest distance between field of view line and obstacle border

Gap border parameters.

Construction of gap array

Robot

3

41

2

Goal

Gap 4

Gap 2

Gap 3

Field of View

Gap 1

Gap 5

N + 1 gaps for N obstacles

Gap array and Maximum Gap

• Gap[N+1] = [(Φlim_l – Φobs1_l)(Φobs1_r – Φobs2_l)……(Φobs(n-1)_r –Φobs(n-1)_l)(Φobsn_r – Φlim_r)]

• Maximum gap is determined with a sorting algorithm in program.

Gap array and Maximum Gap

Gap Center angle Calculation

Gap center angle• The gap center angle (φgap_c ) is found in terms of the measurable d1,

d2, φ1, φ2 parameters

Calculation of final heading angle• Final angle is Combination of angle of center of maximum gap and

Goal point angle.• Determined by fusing weighted average function of gap center angle

and goal angle.• α is the weight to obstacle gap.• α acts as tuning parameter for FGM.• ß weight to goal point (assumed 1 for simplicity)• dmin is minimum distance to the approaching obstacle.

Final Heading Angle

Role of α value• Weightage to gap angle is α/dmin• α makes the path goal oriented or gap oriented.• For α= 0, φfinal is equal to φgoal • Increasing values of alpha brings φfinal closer to φgap_c and vice

versa

Relation of final angle with α

Comparison - FGM with APF on local minima

FGM and APF on local minima• FGM the robot can reach goal point while avoiding obstacles • In APF method, robot gets stuck because of the local minimum where

all vectors from the obstacles and goal point zero each other• FGM selects the first calculated gap value if there are equal maximum

gaps.• This provides FGM to move if at least one gap exists.

Comparison of Safety and Travel length

Comparison of Safety and Travel length• From table below, FGM is 23% safer than the FGM-basic and 40%

safer than the APF in terms of the norm of the defined metric while the total distance traveled values are almost the same

Dead end Scenario• A dead-end scenario of U-shaped obstacles is a problem for FGM as it

is for APF as both are more sort of local planners.• It needs upper level of intelligence.• Can be solved by approaches like Virtual Obstacle Method, Multiple

Goal Point method etc.

Advantages of FGM• Single tuning parameter (α) in weightage to gap center angle (α/dmin)• No local minima problem like earlier algorithms• Considers nonholonomic constraints for the robot.• Only feasible trajectories are generated, lesser ambiguity to decision,

lesser computation time.• Field of view of robot is taken into account.• Robot does not move in unmeasured directions.• Passage through maximum gap center – Safest path.

Limitation of FGM

Remedy

• Unable to come out of dead-end-scenario

• Hybridizing FGM with local planner techniques like virtual obstacles, virtual goal point method etc.

Conclusion• Dynamic path planning literature and algorithms were explained.• Follow the Gap Method(FGM) was explained in detail.• Major Contribution from FGM:

• Single tuning parameter • No local minima problem• Consideration to field of view and nonholonomic constraints.• Consideration to safety in trajectory planning.

Thank You!