Control Theory and Technology

, Volume 17, Issue 1, pp 48–61 | Cite as

Axis-coupled trajectory generation for chains of integrators through smoothing splines

  • Shupeng LaiEmail author
  • Menglu Lan
  • Kehong Gong
  • Ben M. Chen


Integrator based model is used to describe a wide range of systems in robotics. In this paper, we present an axis-coupled trajectory generation algorithm for chains of integrators with an arbitrary order. Special notice has been given to problems with pre-existing nominal plans, which are common in robotic applications. It also handles various type of constraints that can be satisfied on an entire time interval, including non-convex ones which can be transformed into a series of convex constraints through time segmentation. The proposed approach results in a linearly constrained quadratic programming problem, which can be solved effectively with off-the-shelf solvers. A closed-form solution is achievable with only the boundary constraints considered. Finally, the proposed method is tested in real experiments using quadrotors which represent high-order integrator systems.


B-spline trajectory generation chains of integrators 


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Copyright information

© Editorial Board of Control Theory & Applications, South China University of Technology and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Shupeng Lai
    • 1
    Email author
  • Menglu Lan
    • 2
  • Kehong Gong
    • 1
  • Ben M. Chen
    • 1
    • 3
  1. 1.Department of Electrical and Computer EngineeringNational University of SingaporeSingaporeSingapore
  2. 2.Graduate School for Integrative Science & EngineeringNational University of SingaporeSingaporeSingapore
  3. 3.Department of Mechanical and Automation EngineeringThe Chinese University of Hong Kong, Shatin, N.T.Hong KongChina

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