Controlling a dynamic system with open and closed loops: Application to ladder climbing

Janzen Lo, Dimitris Metaxas, Norman I. Badler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


We develop a method for animating systems with open and closed loops and in particular ladder climbing for virtual world applications. Ladder climbing requires the modeling of dynamic open and closed-loop chains. We model the stance phase and the associated closed-loop dynamics, through the use of the Lagrange multiplier method which results in a system of differential algebraic equations (DAE). We use the Lagrange method for the dynamic formulation of the swing phase. The input to the algorithm is a given forward velocity, step length, step frequency and a chosen gait. The algorithm then determines the initial and final positions for each phase of ladder climbing. We use the Newton-Ralphson method to find the vector of joint torques that drives the dynamic system from the initial position to the final position. We use the Baumgarte stabilization method to achieve stability of the numerical integration. We present a series of real-time animations involving ladder climbing.

Original languageEnglish (US)
Title of host publication16th Biennial Conference on Mechanical Vibration and Noise
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791880401
StatePublished - 1997
Externally publishedYes
EventASME 1997 Design Engineering Technical Conferences, DETC 1997 - Sacramento, United States
Duration: Sep 14 1997Sep 17 1997

Publication series

NameProceedings of the ASME Design Engineering Technical Conference


ConferenceASME 1997 Design Engineering Technical Conferences, DETC 1997
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation


  • Animations.
  • Baumgarte stabilization
  • Control
  • Dynamic simulation
  • Ladder climbing
  • Lagrange multipliers
  • Lagrangian dynamics
  • Open and closed-loop dynamics
  • Virtual environments


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