Measurement of robustness of the control of a kneeless biped robot via Integral Sliding Mode Control

When dealing with walking or hopping biped robots, one of the main objectives is to stand for stable periodic trajectories during regular displacements. From a state space point of view, such objective may correspond to achieve stable limit cycles (e.g. [1] [2] [3]). In such case, the major problem is to look for these potential limit cycles (i.e to prove their existence), and, if existing, to stabilize the involved periodic or quasi-periodic trajectories (within a chosen state subspace of the biped state space). A brief survey of existing works points out that several approaches has been investigated to solve a such problem. For instance, bipedal walking might be largely understood as a passive mechanical process, as shown for part by McGeer [5], Mochon and MacMahon respectively [4]. Indeed, McGeer [5] demonstrated by both computer simulations and experimental applications, that some legged systems can walk on a range of shallow slopes with no actuation and no control (energy lost in friction and impact is recovered from gravity). Since then, many researchers have considered this passivity based approach (e.g. Goswami et al. [6], Coleman, Garcia et al. [7] Mark.W.Spong[8], F.Asano[9] et al. M.Haruna [10], and reference therein). However, to our knowledge, none have found a method to define initial conditions under which passive dynamic walking in a downhill slope is generated for an under actuated biped robot with torso. This motivates the main part of the present work which considers the walking motion of a straight legged biped robot on level ground, imitating the passive walking on a given slope. The paper will be organized as follows: First we will present the modelling of the biped robot under consideration (that is a kneeless robot with torso). Then, we will focus on the study of the passive dynamic walking of this robot, on inclined slopes (e.g. [11]). Moreover, we will show that under a simple PD control applied to the lonely actuated link (link between the torso and the stance leg), trajectories of the biped robot can converge towards stable limit cycles. In this context, we will present some results based on Poincaré map method and trajectory sensitivity analysis to efficiently characterize the stability of the almost-passive limit cycles. However, as such limit cycles may not exist for all ground configurations, a complementary control schemes is required. Thus, we will present some theoretical and simulation results based on the use of a recent control method (referred to as Controlled Limit Cycle [1][2][3]), which considers the system energy for both controller design and system stabilization. The last contribution deals with the use of a new control called “Integral Sliding Mode Control” which consists of a test of robustness. The concept of “Integral Sliding Mode Control” ensures the robustness of system trajectory with respect to some bounded perturbations. This approach permit to test the robustness of the so called “CLC” control. Finally, some potential extensions for future works will be discussed. References: [1] N.K.M’Sirdi, N.Manamani and D.Elghanami, “Control approach for legged robots with fast gaits: Controlled Limit Cycles”, Journal of intelligent and robotic systems, Vol. 27, n°4, pp 321-324, 2000 [2] N.K.M’Sirdi, N.Manamani and N.NadjarGauthier “Methodology based on CLC for control of fast legged robots, Intl. Conference on intelligent robots and systems, proceedings of IEEE/RSJ, October 1998. [3] N.K.M’Sirdi, D.Elghanami, T.Boukhobza and N.khraief “Gait stabilization for legged robots using energetic regulation”, accepted for IEEE/ICAR’2001. [4] Mochon, S. and McMahon, Ballistic walking : an improved model, Mathematical Biosciences, 1980, 52 : 241-260. [5] T.McGeer, “Passive Dynamic Walking”, the international journal of robotics reseach, 9(2), 62-82, April 1990 [6] Goswami, A., Tuillot, B., and Espiau, B., “Compass like bipedal robot part I : Stability and bifurcation of passive gaits” INRIA Research report, N°2996, 1996. 1 As the others links are free of actuation [7] Mariano, Anindya, C., Ruina, A., and Coleman, M. “The simplest walking model : Stability, complexity and scaling, 1998 [8] Mark.W.Spong, “Passivity based control of the compass gait biped” In: IFAC, world congress, 1999 [9] Asano, F., Yamakita, M, and Furuta, K., “Virtual passive dynamic walking and energy based control laws” Proc on int conf on intelligent robots and systems, vol 2 pp 11491154, 2000 [10] Haruna, M., Ogino, M, Hosoda, K. and Minour, A., “Yet another humanoid walking Passive dynamic walking with torso under a simple control-“ Int, Conf on intelligent robots and system, 2001 [11] Nahla.khraief, N.K.M’Sirdi, M.W.Spong “Nearly passive dynamic walking of a biped robot”, International conference Signals, Systems, Decision & Information Technology, Mars 2003.