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- 1. Dynamic Path Planning FOLLOW THE GAP METHOD [FGM] FOR MOBILE ROBOTS Presented by: Vikrant Kumar M. Tech. MED CIM 133569
- 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. 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. 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. 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. Some terms of concern • Point Robot Approach • Field of view of Robot • Non-holonomic constraints
- 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. 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. 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. Nonholonomic Constraints and Field of View of Robot Nonholonomic Constraint Field of View
- 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. Possible paths with Bug Algorithm
- 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. APF contd..
- 15. APF contd.. • Main drawback – • Robot gets trapped in local minima. • The Method Ignores nonholonomic constraints
- 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. 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. VFF contd…
- 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. VFH Confidence value and 1D polar histogram
- 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. 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. 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. 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. 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. 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. 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. Gap border parameters .
- 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. 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. Gap array and Maximum Gap
- 32. Gap Center angle Calculation
- 33. Gap center angle • The gap center angle (φgap_c ) is found in terms of the measurable d1, d2, φ1, φ2 parameters
- 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. Final Heading Angle
- 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. Relation of final angle with α
- 38. Comparison - FGM with APF on local minima
- 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. Comparison of Safety and Travel length
- 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. 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. 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. 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. 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. Thank You!

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