Dynamic Modeling of the Dissipative Contact and Friction Forces of a Passive Biped-Walking Robot (original) (raw)
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Applied Mathematical Modelling, 2013
The 'heel to toe' rolling contact has a great influence on the dynamics of biped robots. Here this contact is modelled using the roll-over shape defined in the local coordinate system aligned with the stance leg. The roll-over shape is characterised by six constants: forefoot, midfoot and hindfoot gains and length values. A piecewise parabolic polynomial constructed from these six values is able to match the realistic roll-over shape with continuous slope and variable curvature. The effect of these constants and the roll-over shape arc length has been studied on various gait descriptors such as average velocity, step period, inter-leg angle (and hence step length), mechanical energy. The bifurcation diagrams have been plotted for point feet and different gain values. The insight gained by studying the bifurcation diagrams for different gain and length values is not only useful in understanding the stability of the biped walking process but also in the design of prosthetic feet. The discovery of 'critical values' for the length and mass ratios for the inter-leg angle d (and hence step length) bifurcation diagrams, or a 'critical value' for forefoot gain in the step period bifurcation diagram, is of particular interest as it would mean a constant step length or step period for a range of acceptable values of forefoot and hindfoot gains. The dependence of the horizontal roll-over shape length and hindfoot/forefoot gains on the actual stance leg angular velocity _ h s and angular displacement (h s) values along with the corresponding existence of critical values has also been demonstrated.
Simulation of an autonomous biped walking robot including environmental force interaction
IEEE Robotics & Automation Magazine, 1998
This autonomous biped walking control system is based on the reactive force interaction at the foothold. The precise 3D (three dimensional) dynamic simulation presented includes: 1) a posture controller which accommodate the physical constraints of the reactive force/torque on the foot by quadratic programming. 2) a real-time COM (center of mass) tracking controller for foot placement, with a discrete inverted pendulum model. 3) a 3D dynamic simulation scheme with precise contact with the environment. The proposed approach realizes the robust biped locomotion because the environmental interaction is directly controlled. The proposed method is applied to the 20 axes simulation model, and the stable biped locomotion with velocity of 0.25 m/sec and stepping time of 0.5 sec/step is realized.
Semi-Passive Dynamic Walking Approach for Bipedal Humanoid Robot Based on Dynamic Simulation
Biped Robots, 2011
The research on the principles of legged locomotion is an interdisciplinary endeavor. Such principles are coming together from research in biomechanics, neuroscience, control theory, mechanical design, and artificial intelligence. Such research can help us understand human and animal locomotion in implementing useful legged vehicles. There are three main reasons for exploring the legged locomotion. The first reason is to develop vehicles that can move on uneven and rough terrain. Vehicles with wheels can only move on prepared surfaces such as roads and rails; however, most surfaces are not paved. The second reason is to understand human and animal locomotion mechanics. The study of the mechanisms and principles of control found in nature can help us develop better legged vehicles. The third reason which motivated the study of legged locomotion is the need to build artificial legs for amputees. Although some effective artificial legs have been built to date, more indepth research is required to fully understand the mechanisms and movements necessary to substitute the actual limbs. The research in this paper concerns a group of legged robots known as bipedal walking robots. Research on this subject has a long history; however, it is only in the last two decades that successful experimental prototypes have been developed. The vast majority of humanoid and bipedal robots control the joint angle profiles to carry out the locomotion. Active walking robots (robots with actuators) can do the above task with reasonable speed and position accuracy at the cost of high control efforts, low efficiencies, and most of the time unnatural gaits. WABIAN-2R is among the most successful bipedal walking humanoid robots. In spite of the extensive research on humanoid robots, the actions of walking, running, jumping and manipulation are still difficult for robots. Passive-dynamic walking robots have been developed by researchers to mimic human walking. The main goal of building passive-dynamic walking robots is to study the role of natural dynamics in bipedal walking. Passive-dynamic walkers use gravitational energy to walk down a ramp without any actuators. They are energy efficient but have weak stability in the gait. In addition, the major cause of the energy loss in the current passive-dynamic www.intechopen.com
Dynamics and energetics of a class of bipedal walking systems
Mechanism and Machine Theory, 2009
The mechanical analysis of bipedal walking is a fundamental subject of research in biomechanics. Such analysis is useful to better understand the principles underlying human locomotion, as well as to improve the design and control of bipedal robotic prototypes. Modelling the dynamics of walking involves the analysis of its two phases of motion: (1) the single support phase, which represents finite motion; and (2) the impulsive motion of the impact that occurs at the end of each step (heel strike). The latter is an important event since it is the main cause of energy loss during motion and, in turn, it makes the topology of the system change. In this paper, we present a unified method to analyze the dynamics of both phases of walking. Emphasis is given to the heel strike event, for which we introduce a novel method that gives a complete decomposition of the dynamic equations and the kinetic energy of the system at topology change. As an application example, the presented approach is applied to a compass-gait biped with point feet. Based on this, the work includes a thorough analysis and discussions about the effect of the biped configuration and its inertial parameters on the dynamics and energetics of heel strike.
Feasibilty Analysis of Walking of Passive Dynamic Biped Robot
Journal of Advances in Mathematics, 2015
Passive dynamic walking is an essential development for the biped robots. So the focus of our work is a systematic analysis of the passive walk of a planar biped robot on an inclined slope. The dynamics of passive biped robot is only caused of gravity. The biped robot with two point masses at kneeless legs and a third point mass at the hip-joint is kinematically equivalent to a double pendulum. In this paper, we represent a general method for developing the equations of motion and impact equations for the study of multi-body systems, as in bipedal models. The solution of this system depends on the initial conditions. But it is difficult to find the proper initial conditions for which the system has solutions, in other words, the initial conditions for which the robot can walk. In this paper, we describe the cell mapping method which able to compute the feasible initial conditions for which the biped robot can move forward on the inclined ramp. The results of this method described th...
Rigid vs compliant contact: an experimental study on biped walking
Multibody System Dynamics, 2018
Contact modeling plays a central role in motion planning, simulation and control of legged robots, as legged locomotion is realized through contact. The two prevailing approaches to model the contact consider rigid and compliant premise at interaction ports. Contrary to the dynamics model of legged systems with rigid contact (without impact) which is straightforward to develop, there is no consensus among researchers to employ a standard compliant contact model. Our main goal in this paper is to study the dynamics model structure of bipedal walking systems with rigid contact and a novel compliant contact model, and to present experimental validation of both models. For the model with rigid contact, after developing the model of the articulated bodies in flight phase without any contact with environment, we apply the holonomic constraints at contact points and develop a constrained dynamics model of the robot in both single and double support phases. For the model with compliant contact, we propose a novel nonlinear contact model and simulate motion of the robot using this model. In
European Journal of Computational Mechanics
Traditional biped walkers based on passive dynamic walking usually have flat or circular feet. This foot contact may be modelled with an effective rocker-represented as a roll-over shape-to describe the function of the knee-ankle-foot complex in human ambulation. Mahmoodi et al. has represented this roll-over shape as a polygon with a discretized set of collisions. In this paper point foot, collisional and smooth rolling contact models are compared. An approach based on the Lagrangian mechanics are used to formulate the equations for the swing phase that conserves mechanical energy. Qualitative insight can be gained by studying the bifurcation diagrams of gait descriptors such as average velocity, step period, mechanical energy and inter-leg angle for different gain and length values for the feet, as well as different mass and length ratios. The results from the three approaches are compared and discussed. In the case of a rolling disk, the collisional contact model gives a negligible energy loss; incorporated into the double inverted pendulum system, however, reveals much greater errors. This research is not only useful for understanding the stability of bipedal walking, but also for the design of rehabilitative devices such as prosthetic feet and orthoses.
FEASIBILTY ANALYSIS OF WALKING OF PASSIVE DYNAMIC BIPED ROBOT Council for Innovative Research
Journal of Advances in Mathematics, 2015
Passive dynamic walking is an essential development for the biped robots. So the focus of our work is a systematic analysis of the passive walk of a planar biped robot on an inclined slope. The dynamics of passive biped robot is only caused of gravity. The biped robot with two point masses at kneeless legs and a third point mass at the hip-joint is kinematically equivalent to a double pendulum. In this paper, we represent a general method for developing the equations of motion and impact equations for the study of multi-body systems, as in bipedal models. The solution of this system depends on the initial conditions. But it is difficult to find the proper initial conditions for which the system has solutions, in other words, the initial conditions for which the robot can walk. In this paper, we describe the cell mapping method which able to compute the feasible initial conditions for which the biped robot can move forward on the inclined ramp. The results of this method described the region of feasible initial conditions is small and bounded. Moreover, the results of cell mapping method give the fixed of Poincare map which explains the symmetric gait cycle of the robot and describe the orientation of legs of robot.
Modeling and control of biped robot dynamics
Robotica, 1999
This paper addresses the problem of modeling biped dynamics and the use of such models for the control of walking, running and jumping robots. We describe two approaches to dynamic modeling: the basic Lagrange approach and the non-regular dynamic approach. The new non-regular dynamic approach takes into account discontinuities due to rigid contact between punctual feet and the ground without computing the exact impact time. The contact is close to the physical situation given by non-linear laws (impenetrability, non-smooth contact and real friction cone). Contact dynamics can be well managed with an accurate dynamic model that respects energy consistency during all the phases encountered during a step (0, 1 or 2 contacts). With this model, we can first study the equilibrum of a biped standing on one foot by a linearisation method. In the second stage, the unified modelized equation is used to establish a general control frame based on non-regular dynamical decoupling. A comparison i...