Walking trajectory planning on stairs using virtual slope for biped robots

Tomoya Sato, Sho Sakaino, Eijiro Ohashi, Kouhei Ohnishi

Research output: Contribution to journalArticlepeer-review

81 Citations (Scopus)


In this paper, a virtual slope method for walking trajectory planning on stairs for biped robots is proposed. In conventional methods for walking on stairs, there are two problems about the zero-moment point (ZMP). One is a ZMP equation problem, and the other is a ZMP definition problem in a double-support phase. First, a ZMP equation on stairs is different from that on flat ground. Therefore, the same trajectory generation as flat ground cannot be implemented. This problem is defined as a ZMP equation problem. Second, the ZMP cannot be defined in the double-support phase on stairs because contact points of the feet do not constitute a plane. The ZMP can be defined only on the plane. This problem is defined as a ZMP definition problem. These two problems are solved concurrently by the virtual slope method. It is the method that regards the stairs as a virtual slope. In walking trajectory planning on a slope of the constant gradient, the two problems about the ZMP do not exist. Additionally, a trajectory planning procedure based on the virtual slope method is explained. The validity of the proposed method is confirmed by some simulations and experiments.

Original languageEnglish
Article number5475250
Pages (from-to)1385-1396
Number of pages12
JournalIEEE Transactions on Industrial Electronics
Issue number4
Publication statusPublished - 2011 Apr
Externally publishedYes


  • Biped robot
  • stairs
  • trajectory planning
  • walking
  • zero-moment point (ZMP)

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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