Time-optimal control of rolling bodies

Giacomo Perantoni, David J.N. Limebeer

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The brachistochrone problem is usually solved in classical mechanics courses using the calculus of variations, although it is quintessentially an optimal control problem. In this paper, we address the classical brachistochrone problem and two vehicle-relevant generalisations from an optimal control perspective. We use optimal control arguments to derive closed-form solutions for both the optimal trajectory and the minimum achievable transit time for these generalisations. We then study optimal control problems involving a steerable disc rolling between prescribed points on the interior surface of a hemisphere. The effects of boundary and control constraints are examined. For three-dimensional problems of this type, which involve rolling bodies and nonholonomic constraints, numerical solutions are used.

Original languageEnglish
Pages (from-to)2006-2021
Number of pages16
JournalInternational Journal of Control
Issue number11
Publication statusPublished - 1 Nov 2013
Externally publishedYes


  • Brachistochrone
  • Hamiltonian
  • Mechanics
  • Optimal control
  • Rolling bodies

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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