Inverse Optimal Control for Multiphase Cost Functions

Wanxin Jin, Dana Kulić, Jonathan Feng Shun Lin, Shaoshuai Mou, Sandra Hirche

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


In this paper, we consider a dynamical system whose trajectory is a result of minimizing a multiphase cost function. The multiphase cost function is assumed to be a weighted sum of specified features (or basis functions) with phase-dependent weights that switch at some unknown phase transition points. A new inverse optimal control approach for recovering the cost weights of each phase and estimating the phase transition points is proposed. The key idea is to use a length-adapted window moving along the observed trajectory, where the window length is determined by finding the minimal observation length that suffices for a successful cost weight recovery. The effectiveness of the proposed method is first evaluated on a simulated robot arm, and then, demonstrated on a dataset of human participants performing a series of squatting tasks. The results demonstrate that the proposed method reliably retrieves the cost function of each phase and segments each phase of motion from the trajectory with a segmentation accuracy above 90%.

Original languageEnglish
Article number8778698
Pages (from-to)1387-1398
Number of pages12
JournalIEEE Transactions on Robotics
Issue number6
StatePublished - Dec 2019


  • Human motion segmentation
  • inverse optimal control (IOC)
  • multiphase cost functions
  • recovery matrix


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