Genetic Algorithms for Smooth Path Planning Sophia Zell University - PowerPoint PPT Presentation

MIN Faculty Department of Informatics Genetic Algorithms for Smooth Path Planning Sophia Zell University of Hamburg Faculty of Mathematics, Informatics and Natural Sciences Department of Informatics Technical Aspects of Multimodal Systems 19. November 2019 S. Zell – Genetic Algorithms for Smooth Path Planning 1 / 17

Outline Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and 1. Motivation 2. Path Planning Smoothness 3. B-Splines for Smoothing 4. Genetic Algorithms 5. Probabilistic Roadmaps vs. GAs for PP 6. GAs for Smooth PP 7. Conclusion and Outlook 8. References S. Zell – Genetic Algorithms for Smooth Path Planning 2 / 17

Motivation Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and Where am I now? Localization. Where do I want to go? Mapping. How do I get there? Motion/Path Planning S. Zell – Genetic Algorithms for Smooth Path Planning 3 / 17

Path Planning Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and Position and goal are known -> best way? Basic conditions: ◮ Avoid obstacles ◮ Reduce path length ◮ Additional features Major concern: ◮ Efficiency (Time and energy) ◮ Safety (Obstacle avoidance) ◮ Accuracy (Follow path) S. Zell – Genetic Algorithms for Smooth Path Planning 4 / 17

Path Planning (continued) Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and Various categories for PP: Based on environment: ◮ Static ◮ Dynamic Based on map knowledge: ◮ Global ◮ Local Based on completeness: ◮ Exact ◮ Heuristic S. Zell – Genetic Algorithms for Smooth Path Planning 6 / 17

Path Planning (continued) Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and PP problem components: ◮ Geometry of robot ◮ Environment ◮ Degrees of freedom (of robot motion) ◮ Start and goal configuration + simplify search Define a configuration space: ◮ Robot mapped as point ◮ Environment is a 2D plane S. Zell – Genetic Algorithms for Smooth Path Planning 7 / 17

Smoothness Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and Why? ◮ More natural ◮ Less problems with overshooting ◮ Energy and time efficient Definition: Trajectory is smooth if its first and second derivative are continuous. S. Zell – Genetic Algorithms for Smooth Path Planning 8 / 17

B-Splines for Smoothing Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and “Splines [...] are functions consisting of pieces of smooth functions glued together in a certain smooth way.” A. Kunoth, T. Lyche, G. Sangalli, S. Serra-Capizzano, T. Lyche, C. Manni, and H. Speleers, (2018). “Splines and PDEs: From approximation theory to numerical linear algebra.” Cham, Switzerland: Springer, p. 1 ◮ Piecewise polynomials ◮ Globally smooth ◮ More flexible than regular interpolation through piecewise definition ◮ Connection points are called knots ◮ Powerful (for computer-aided geometry) S. Zell – Genetic Algorithms for Smooth Path Planning 9 / 17

Genetic Algorithms Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and ◮ Population of solutions ◮ Chromosome ◮ Gene ◮ Initialization ◮ Parent Selection ◮ Recombination (Crossover) S. Zell – Genetic Algorithms for Smooth Path Planning 10 / 17

Genetic Algorithms (continued) Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and ◮ Mutation ◮ Fitness function ◮ Survivor selection ◮ Stopping criterion S. Zell – Genetic Algorithms for Smooth Path Planning 11 / 17

Probabilistic Roadmaps vs. GAs for PP Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and PRM GA Discretized or continuous Environment Free configuration space configuration space Generate random configurations Create chromosomes Build roadmap R from random grid cells Initialising way by interconnecting First gene is start configurations locally Last gene is goal Connect initial and goal configuration to R Search edges of R for Perform genetic algorithm Finding way continuous path from Evaluate fitness function initial to goal config. based on pathlength S. Zell – Genetic Algorithms for Smooth Path Planning 12 / 17

Probabilistic Roadmaps vs. GAs for PP (continued) Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and PRM GA Always reach (near) global optimum Don’t get stuck in local optima Probabilistic complete Explore while preserving best Pros Easy to implement Simultaneous search Computationally cheap For continuous or discrete config. space Good performance in complex environment Versatile Computationally expensive Cons Tuning necessary S. Zell – Genetic Algorithms for Smooth Path Planning 13 / 17

GAs for Smooth PP Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and Instead of smoothing a path afterwards (e.g. with B-Splines), we generate a smooth path. Regular GA Bézier GA Generate way points Bézier control points Path connected way points Bézier curve Fitness function length of way length of Bézier curve collide when point or collide when Bézier curve Obstacles part of path between intersects two points intersects S. Zell – Genetic Algorithms for Smooth Path Planning 14 / 17

GAs for Smooth PP (continued) Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and Regular GA: Vol. 38, pp. 1564–1572 GA with Bézier: Source: M. Elhoseny, A. Shehab and X. Yuan (2017) Source: A. Tuncer and M. Yildirim (2012) “Dynamic “Optimizing robot path in dynamic environments using path planning of mobile robots with improved genetic Genetic Algorithm and Bezier Curve”, in Journal of algorithm” in Computers and Electrical Engineering, Intelligent and Fuzzy Systems, Vol. 33, pp. 2305–2316 ◮ Increases computation S. Zell – Genetic Algorithms for Smooth Path Planning 15 / 17

Conclusion and Outlook Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and Conclusion: ◮ PRMs are simple and sufficient ◮ Together with B-splines it can produce smooth paths ◮ GAs are powerful tools for finding (near) optimal path in a complex environment ◮ Incorpoarted with Bézier curve promising for smooth path generation Outlook: ◮ Investigate possible problems of GAs for Smooth PP ◮ Is the extra effort worth it? S. Zell – Genetic Algorithms for Smooth Path Planning 16 / 17

References Motivation Path Planning B-Splines for Smoothing Genetic Algorithms Probabilistic Roadmaps vs. GAs for PP GAs for Smooth PP Conclusion and A. E. Eiben and J. E. Smith, (2015) “Introduction to Evolutionary Computing”, in Plastics, 2nd ed., G. Rozenberg, Ed. Berlin: Springer, pp. 99–100. M. Elhoseny, A. Shehab and X. Yuan (2017) “Optimizing robot path in dynamic environments using Genetic Algorithm and Bezier Curve”, in Journal of Intelligent and Fuzzy Systems, Vol. 33, pp. 2305–2316 H. Eren, C.C. Fung and J. Evans (1999) “Implementation of the spline method for mobile robot path con- trol”, in Proceedings of the 1999 16th IEEE Instrumentation and Measurement Technology Conference, pp. 739–744. L. Kavraki, M. Kolountzakis and J. Latombe (1998) “Analysis of probabilistic roadmaps for path planning”, in IEEE Transactions on Robotics and Automation, 14(1), pp.166–171. A. Kunoth, T. Lyche, G. Sangalli, S. Serra-Capizzano, T. Lyche, C. Manni, and H. Speleers, (2018). “Splines and PDEs: From approximation theory to numerical linear algebra.” Cham, Switzerland: Springer, pp. 1–13 B. Song, Z. Wang and L. Sheng (2016) “A new genetic al- gorithm approach to smooth path planning for mobile robots” in Assembly Automation, Vol. 36 Issue 2, pp. 138–145 A. Tuncer and M. Yildirim (2012) “Dynamic path planning of mobile robots with improved genetic algorithm” in Computers and Electrical Engineering, Vol. 38, pp. 1564–1572 J. Zhang and L. Einig (2018) “Introduction to Robotics, Lecture 6” J. Zhang and L. Einig (2018) “Introduction to Robotics, Lecture 7” S. Zell – Genetic Algorithms for Smooth Path Planning 17 / 17