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Bloch, A.M., Leok, M., Marsden J.E. and Zenkov, D.V. (2005) Controlled Lagrangians and Stabilization of the Discrete Cart-Pendulum System. Proceedings of the 44th IEEE Conference CDC-ECC, Seville, 12-15 December 2005, 6579-6584. http://dx.doi.org/10.1109/cdc.2005.1583218

has been cited by the following article:

• TITLE: Circular Obstacle Avoidance Control of the Compass-Type Biped Robot Based on a Blending Method of Discrete Mechanics and Nonlinear Optimization

  AUTHORS: Tatsuya Kai

  KEYWORDS: Discrete Mechanics, Compass-Type Biped Robot, Obstacle Avoidance Control, Nonlinear Optimization, Zero-Order Hold Input

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.4 No.3, August 7, 2015

  ABSTRACT: This paper considers an obstacle avoidance control problem for the compass-type biped robot, especially circular obstacles are dealt with. First, a sufficient condition such that the swing leg does not collide the circular obstacle is derived. Next, an optimal control problem for the discrete compass-type robot is formulated and a solving method of the problem by the sequential quadratic programming is presented in order to calculate a discrete control input. Then, a transformation method that converts a discrete control input into a continuous zero-order hold input via discrete Lagrange-d’ Alembert principle is explained. From the results of numerical simulations, it turns out that obstacle avoidance control for the continuous compass-type robot can be achieved by the proposed method.