Improving Relaxation-Based Constrained Path Planning via Quadratic Programming

  • Franco Fusco
  • Olivier KermorgantEmail author
  • Philippe Martinet
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 867)


Many robotics tasks involve a set of constraints that limit the valid configurations the system can assume. Some of these constraints, such as loop-closure or orientation constraints to name some, can be described by a set of implicit functions which cause the valid Configuration Space of the robot to collapse to a lower-dimensional manifold. Sampling-based planners, which have been extensively studied in the last two decades, need some adaptations to work in this context.

A proposed approach, known as relaxation, introduces constraint violation tolerances, thus approximating the manifold with a non-zero measure set. The problem can then be solved using classical approaches from the randomized planning literature. The relaxation needs however to be sufficiently high to allow planners to work in a reasonable amount of time, and violations are counterbalanced by controllers during actual motion. We present in this paper a new component for relaxation-based path planning under differentiable constraints. It exploits Quadratic Optimization to simultaneously move towards new samples and keep close to the constraint manifold. By properly guiding the exploration, both running time and constraint violation are substantially reduced.


  1. 1.
    Berenson, D., Srinivasa, S.S., Ferguson, D., Kuffner, J.J.: Manipulation planning on constraint manifolds. In: IEEE International Conference on Robotics and Automation. IEEE (2009)Google Scholar
  2. 2.
    Bonilla, M., Farnioli, E., Pallottino, L., Bicchi, A.: Sample-based motion planning for soft robot manipulators under task constraints. In: IEEE International Conference on Robotics and Automation (2015)Google Scholar
  3. 3.
    Bonilla, M., Pallottino, L., Bicchi, A.: Noninteracting constrained motion planning and control for robot manipulators. In: IEEE International Conference on Robotics and Automation. IEEE (2017)Google Scholar
  4. 4.
    Cortes, J., Simeon, T.: Sampling-based motion planning under kinematic loop-closure constraints. In: Algorithmic Foundations of Robotics VI. Springer, Heidelberg (2004)Google Scholar
  5. 5.
    Jaillet, L., Porta, J.M.: Path planning under kinematic constraints by rapidly exploring manifolds. IEEE Trans. Robot. (2013)Google Scholar
  6. 6.
    Karaman, S., Frazzoli, E.: Sampling-based algorithms for optimal motion planning. Int. J. Robot. Res. (2011)Google Scholar
  7. 7.
    Kavraki, L.E., Svestka, P., Latombe, J.-C., Overmars, M.H.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. Robot. Autom. (1996)Google Scholar
  8. 8.
    Kim, B., Um, T.T., Suh, C., Park, F.C.: Tangent bundle RRT: a randomized algorithm for constrained motion planning. Robotica (2016)Google Scholar
  9. 9.
    Kuffner, J.J., LaValle, S.M.: RRT-connect: an efficient approach to single-query path planning. In: IEEE International Conference on Robotics and Automation. IEEE (2000)Google Scholar
  10. 10.
    LaValle, S.M.: Rapidly-exploring random trees: A new tool for path planning. Technical report, Department of Computer Science, Iowa State University (1998)Google Scholar
  11. 11.
    LaValle, S.M., Kuffner Jr., J.J.: Rapidly-exploring random trees. Progress and Prospects (2000)Google Scholar
  12. 12.
    Quigley, M., Conley, K., Gerkey, B., Faust, J., Foote, T., Leibs, J., Wheeler, R., Ng, A.Y.: ROS: an open-source robot operating system. In: ICRA Workshop on Open Source Software (2009)Google Scholar
  13. 13.
    Stilman, M.: Task constrained motion planning in robot joint space. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE (2007)Google Scholar
  14. 14.
    Sucan, I.A., Chitta, S.: Moveit! Accessed 30 Jun 2017
  15. 15.
    Sucan, I.A., Moll, M., Kavraki, L.E.: The Open Motion Planning Library. IEEE Robotics and Automation Magazine (2012). Accessed 30 Jun 2017
  16. 16.
    Voss, C., Moll, M., Kavraki, L.E.: Atlas+ x: Sampling-based planners on constraint manifolds. Technical report. Rice University (2017)Google Scholar
  17. 17.
    Yakey, J.H., LaValle, S.M., Kavraki, L.E.: Randomized path planning for linkages with closed kinematic chains. IEEE Trans. Robot. Autom. (2001)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Franco Fusco
    • 1
  • Olivier Kermorgant
    • 1
  • Philippe Martinet
    • 1
    • 2
  1. 1.Centrale NantesLaboratoire des Sciences du Numérique de Nantes LS2NNantesFrance
  2. 2.Inria Sophia AntipolisValbonneFrance

Personalised recommendations