Optimal multivehicle motion planning using bernstein approximants

Venanzio Cichella, Isaac Kaminer, Claire Walton, Naira Hovakimyan, Antonio M. Pascoal

Research output: Contribution to journalArticlepeer-review


This article presents a computational framework to efficiently generate feasible and safe trajectories for multiple autonomous vehicle operations. We formulate the optimal motion planning problem as a continuous-time optimal control problem, and approximate its solutions in a discretized setting using Bernstein polynomials. The latter possess convenient properties that allow to efficiently compute and enforce constraints along the vehicles' trajectories, such as maximum speed and angular rates, minimum distance between trajectories and between the vehicles and known obstacles, etc. Thus, the proposed method is particularly suitable for generating trajectories in real-time for safe operations in complex environments and multiple vehicle missions. We show, using a rigorous mathematical framework, that the solution to the discretized optimal motion planning problem converges to that of the continuous-time one. The advantages of the proposed method are investigated through numerical examples.

Original languageEnglish (US)
Article number9105082
Pages (from-to)1453-1467
Number of pages15
JournalIEEE Transactions on Automatic Control
Issue number4
StatePublished - Apr 2021


  • Bernstein polynomial
  • Bezier curve
  • Multiple vehicles
  • Optimal motion planning

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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