03 Oct

Motion Planning 3: Trajectory Optimization

Yuki-shirai Motion Planning

Optimization-based motion planning approaches, such asNonlinear Programming (NLP) and Mixed-Integer Programming (MIP), solve optimization problems, and find solutions using gradient descent while satisfying constraints. For instance, CHOMP optimizes a cost functional using covariant gradient descent while TrajOpt solves a sequential convex optimization and performs convex collision checking. You can use trajectory optimization for various tasks including navigation, grasping, manipulation, collision-avoidance, running, cooking, and flying under various conditions. You can read reference papers to know more details, or send me an email and chat with me!

The drawback of trajectory optimization algorithms is that they can get stuck in poor local optima easily.

N. Ratliff, M. Zucker, J. A. Bagnell, and S. Srinivasa, “CHOMP: Gradient optimization techniques for efficient motion planning,” 2009 IEEE International Conference on Robotics and Automation, pp. 489–494, May 2009, doi: 10.1109/robot.2009.5152817. 
 @inproceedings{Ratliff_2009, title={CHOMP: Gradient optimization techniques for efficient motion planning}, url={http://dx.doi.org/10.1109/robot.2009.5152817}, DOI={10.1109/robot.2009.5152817}, booktitle={2009 IEEE International Conference on Robotics and Automation}, publisher={IEEE}, author={Ratliff, Nathan and Zucker, Matt and Bagnell, J. Andrew and Srinivasa, Siddhartha}, year={2009}, month=may, pages={489–494} }
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J. Schulman, J. Ho, A. Lee, I. Awwal, H. Bradlow, and P. Abbeel, “Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization,” Robotics: Science and Systems IX, Jun. 2013, doi: 10.15607/rss.2013.ix.031. 
 @inproceedings{Schulman_2013, series={RSS2013}, title={Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization}, url={http://dx.doi.org/10.15607/RSS.2013.IX.031}, DOI={10.15607/rss.2013.ix.031}, booktitle={Robotics: Science and Systems IX}, publisher={Robotics: Science and Systems Foundation}, author={Schulman, John and Ho, Jonathan and Lee, Alex and Awwal, Ibrahim and Bradlow, Henry and Abbeel, Pieter}, year={2013}, month=jun, collection={RSS2013} }
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S. Dai, S. Schaffert, A. Jasour, A. Hofmann, and B. Williams, “Chance Constrained Motion Planning for High-Dimensional Robots,” 2019 International Conference on Robotics and Automation (ICRA), pp. 8805–8811, May 2019, doi: 10.1109/icra.2019.8793660. 
 @inproceedings{Dai_2019, title={Chance Constrained Motion Planning for High-Dimensional Robots}, url={http://dx.doi.org/10.1109/ICRA.2019.8793660}, DOI={10.1109/icra.2019.8793660}, booktitle={2019 International Conference on Robotics and Automation (ICRA)}, publisher={IEEE}, author={Dai, Siyu and Schaffert, Shawn and Jasour, Ashkan and Hofmann, Andreas and Williams, Brian}, year={2019}, month=may, pages={8805–8811} }
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J. Carius, R. Ranftl, V. Koltun, and M. Hutter, “Trajectory Optimization With Implicit Hard Contacts,” IEEE Robotics and Automation Letters, vol. 3, no. 4, pp. 3316–3323, Oct. 2018, doi: 10.1109/lra.2018.2852785. 
 @article{Carius_2018, title={Trajectory Optimization With Implicit Hard Contacts}, volume={3}, ISSN={2377-3774}, url={http://dx.doi.org/10.1109/LRA.2018.2852785}, DOI={10.1109/lra.2018.2852785}, number={4}, journal={IEEE Robotics and Automation Letters}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Carius, Jan and Ranftl, Rene and Koltun, Vladlen and Hutter, Marco}, year={2018}, month=oct, pages={3316–3323} }
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A. Wang, A. Jasour, and B. C. Williams, “Non-Gaussian Chance-Constrained Trajectory Planning for Autonomous Vehicles Under Agent Uncertainty,” IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 6041–6048, Oct. 2020, doi: 10.1109/lra.2020.3010755. 
 @article{Wang_2020, title={Non-Gaussian Chance-Constrained Trajectory Planning for Autonomous Vehicles Under Agent Uncertainty}, volume={5}, ISSN={2377-3774}, url={http://dx.doi.org/10.1109/LRA.2020.3010755}, DOI={10.1109/lra.2020.3010755}, number={4}, journal={IEEE Robotics and Automation Letters}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Wang, Allen and Jasour, Ashkan and Williams, Brian C.}, year={2020}, month=oct, pages={6041–6048} }
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J. Tordesillas, B. T. Lopez, and J. P. How, “FASTER: Fast and Safe Trajectory Planner for Flights in Unknown Environments,” 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1934–1940, Nov. 2019, doi: 10.1109/iros40897.2019.8968021. 
 @inproceedings{Tordesillas_2019, title={FASTER: Fast and Safe Trajectory Planner for Flights in Unknown Environments}, url={http://dx.doi.org/10.1109/IROS40897.2019.8968021}, DOI={10.1109/iros40897.2019.8968021}, booktitle={2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, publisher={IEEE}, author={Tordesillas, Jesus and Lopez, Brett T. and How, Jonathan P.}, year={2019}, month=nov, pages={1934–1940} }
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R. Bonalli, A. Cauligi, A. Bylard, and M. Pavone, “GuSTO: Guaranteed Sequential Trajectory optimization via Sequential Convex Programming,” 2019 International Conference on Robotics and Automation (ICRA), May 2019, doi: 10.1109/icra.2019.8794205. 
 @inproceedings{Bonalli_2019, title={GuSTO: Guaranteed Sequential Trajectory optimization via Sequential Convex Programming}, url={http://dx.doi.org/10.1109/ICRA.2019.8794205}, DOI={10.1109/icra.2019.8794205}, booktitle={2019 International Conference on Robotics and Automation (ICRA)}, publisher={IEEE}, author={Bonalli, Riccardo and Cauligi, Abhishek and Bylard, Andrew and Pavone, Marco}, year={2019}, month=may }
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R. Tedrake, I. R. Manchester, M. Tobenkin, and J. W. Roberts, “LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification,” The International Journal of Robotics Research, vol. 29, no. 8, pp. 1038–1052, Apr. 2010, doi: 10.1177/0278364910369189. 
 @article{Tedrake_2010, title={LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification}, volume={29}, ISSN={1741-3176}, url={http://dx.doi.org/10.1177/0278364910369189}, DOI={10.1177/0278364910369189}, number={8}, journal={The International Journal of Robotics Research}, publisher={SAGE Publications}, author={Tedrake, Russ and Manchester, Ian R. and Tobenkin, Mark and Roberts, John W.}, year={2010}, month=apr, pages={1038–1052} }
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Y. Shirai, X. Lin, Y. Tanaka, A. Mehta, and D. Hong, “Risk-Aware Motion Planning for a Limbed Robot with Stochastic Gripping Forces Using Nonlinear Programming,” IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 4994–5001, Oct. 2020, doi: 10.1109/lra.2020.3001503. 
 @article{Shirai_2020, title={Risk-Aware Motion Planning for a Limbed Robot with Stochastic Gripping Forces Using Nonlinear Programming}, volume={5}, ISSN={2377-3774}, url={http://dx.doi.org/10.1109/lra.2020.3001503}, DOI={10.1109/lra.2020.3001503}, number={4}, journal={IEEE Robotics and Automation Letters}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Shirai, Yuki and Lin, Xuan and Tanaka, Yusuke and Mehta, Ankur and Hong, Dennis}, year={2020}, month=oct, pages={4994–5001} }
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