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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
Intelligen...
Mobile Robot Navigation
• Global Navigation – from knowledge of goal point
• Local Navigation – from knowledge of near by ...
Static Path Planning
• Probabilistic Roadmap (PRM) - Two phase navigation:
• Learning phase
• Query phase
• Visibility Gra...
Dynamic Path Planning
• Bug Algorithms
• Artificial Potential Field (APF) Algorithm
• Harmonic Potential Field (HPF) Algor...
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 R...
Field of view
• The sector region within the range of robot’s sensors to get
information of environment.
• Two quantitativ...
Nonholonomic Constraints
• If the vector space of the possible motion directions of a mechanical
system is restricted
• An...
Nonholonomic Constraints and Field of View
of Robot
Nonholonomic Constraint
Field of View
Bug Algorithms
• Common sense approach of moving directly to goal.
• Contour the obstacle when found, until moving straigh...
Possible paths with Bug Algorithm
Artificial Potential Field (APF)
• Presently very popular
• Obstacles represent “repulsive potential”
• Goal represent “at...
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 c...
Virtual Force Field method (VFF)
• 2D Cartesian histogram grid for obstacle representation.
• Each cell has certainty valu...
VFF contd…
Virtual Field Histogram (VFH)
• Uses a 2D Cartesian histogram grid like in VFF.
• Reduces it to a one dimensional polar hi...
VFH Confidence value and 1D polar histogram
Follow the Gap Method (FGM)
• Point Robot Approach
• Obstacle representation
• Construction a gap array among obstacles.
•...
Problem Definition
• The Algorithm
• Should find a purely reactive heading to achieve goal co-ordinates
• Should avoiding ...
Point Robot Approach
Xrob = Abscissa of robot point
Yrob = Ordinate of robot point
Rrob = Robot circle’s radius
Xobsn = Ab...
Distance to Obstacle
Distance of nth obstacle from robot
d = ((Xobsn – Xrob)2 + (Yobsn – Yrob)2)1/2
Using Pythogoras theor...
Obstacle Representation
• Two parameter representation
• Φ obs_l_1 – Border left angle of obstacle 1
• Φ obs_r_1 -- Border...
Gap Border Evaluation
If, 𝑑𝑛ℎ𝑜𝑙 < 𝑑𝑓𝑜𝑣 => 𝛷𝑙𝑖𝑚 = 𝛷𝑛ℎ𝑜𝑙
Else if, 𝑑𝑛ℎ𝑜𝑙 ≥ 𝑑𝑓𝑜𝑣 => 𝛷𝑙𝑖𝑚 = 𝛷𝑓𝑜𝑣
In order to understand which b...
Gap boarder parameters
• 1. Φlim: Gap border angle
• 2. Φnhol: Border angle coming from nonholonomic constraint
• 3. Φfov:...
Gap border parameters
.
Construction of gap array
Robot
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_...
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.
• ...
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...
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 stuc...
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 ...
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 ...
Advantages of FGM
• Single tuning parameter (α) in weightage to gap center angle
(α/dmin)
• No local minima problem like e...
Limitation of FGM
Remedy
• Unable to come out of dead-end-scenario
• Hybridizing FGM with local planner techniques like vi...
Conclusion
• Dynamic path planning literature and algorithms were explained.
• Follow the Gap Method(FGM) was explained in...
Thank You!
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Dynamic Path Planning

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Dynamic Path Planning

  1. 1. Dynamic Path Planning FOLLOW THE GAP METHOD [FGM] FOR MOBILE ROBOTS Presented by: Vikrant Kumar M. Tech. MED CIM 133569
  2. 2. 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
  3. 3. 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:
  4. 4. 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
  5. 5. 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
  6. 6. Some terms of concern • Point Robot Approach • Field of view of Robot • Non-holonomic constraints
  7. 7. 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.
  8. 8. 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.
  9. 9. 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.
  10. 10. Nonholonomic Constraints and Field of View of Robot Nonholonomic Constraint Field of View
  11. 11. 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
  12. 12. Possible paths with Bug Algorithm
  13. 13. 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
  14. 14. APF contd..
  15. 15. APF contd.. • Main drawback – • Robot gets trapped in local minima. • The Method Ignores nonholonomic constraints
  16. 16. 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.
  17. 17. 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
  18. 18. VFF contd…
  19. 19. 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
  20. 20. VFH Confidence value and 1D polar histogram
  21. 21. 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.
  22. 22. 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
  23. 23. Point Robot Approach Xrob = 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
  24. 24. Distance to Obstacle Distance 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
  25. 25. 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 Φobs_l_1 Φobs_r_1 Φobs_l_2 Φobs_r_2 Obst. 1 Obst. 2
  26. 26. Gap Border Evaluation If, 𝑑𝑛ℎ𝑜𝑙 < 𝑑𝑓𝑜𝑣 => 𝛷𝑙𝑖𝑚 = 𝛷𝑛ℎ𝑜𝑙 Else if, 𝑑𝑛ℎ𝑜𝑙 ≥ 𝑑𝑓𝑜𝑣 => 𝛷𝑙𝑖𝑚 = 𝛷𝑓𝑜𝑣 In order to understand which boundary is active for a boundary obstacle, decision rule are illustrated as follows:
  27. 27. 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
  28. 28. Gap border parameters .
  29. 29. Construction of gap array Robot Goal Gap 4 Gap 2 Gap 3 Field of View Gap 1 Gap 5  N + 1 gaps for N obstacles
  30. 30. 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.
  31. 31. Gap array and Maximum Gap
  32. 32. Gap Center angle Calculation
  33. 33. Gap center angle • The gap center angle (φgap_c ) is found in terms of the measurable d1, d2, φ1, φ2 parameters
  34. 34. 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.
  35. 35. Final Heading Angle
  36. 36. 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
  37. 37. Relation of final angle with α
  38. 38. Comparison - FGM with APF on local minima
  39. 39. 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.
  40. 40. Comparison of Safety and Travel length
  41. 41. 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
  42. 42. 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.
  43. 43. 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.
  44. 44. 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.
  45. 45. 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.
  46. 46. Thank You!

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