Direct Dynamic Problem Research Articles

Multibody Simulation Model of Human Walking

A three-dimensional simulational model of a human walking is presented. The biped is anthropomorphic, i.e., its inertial and kinematical properties are similar to human ones. The biped consists of eight rigid bodies. Each leg consists of three parts: thigh, shank, and foot. The trunk is modeled as two rigid bodies connected by a revolute joint. The inertia properties of head and arms are included in trunk properties. Each leg has 7 degrees of freedom. The whole modelled biped has 21 degrees of freedom. The impact and friction effects are considered in the ground reaction force modeling. The ground is represented by a flat, rigid surface. The normal to the ground component of reaction force depends on penetration of the foot into the ground and on the velocity of this penetration. The tangential reaction is represented in terms of a pseudo-Coulomb friction model (in this model of friction there is no stiction phase, i.e., the bodies are moving relative to each other at a negligibly small velocity). The direction of friction force depends on the relative movement velocity; the magnitude depends on the friction coefficient, the normal force magnitude, and also (nonlinearly) on the relative velocity. The direct dynamic problem is solved. Human gait patterns, derived from measurements of human walking, are used to calculate the necessary driving torques. A simple closed-loop control algorithm for stabilizing the motion is applied. The control system of the biped is not engaged in the planning of the trajectory; this task is realized following the gait pattern. The main task of the control system is to modify slightly and instantaneously the prescribed gait to prevent the biped from losing stability. To account for the elasticity of human tissues, so-called wobbling masses are introduced to the model. Both rigid body and wobbling mass models are validated by comparing obtained results of simulations with measurements of human walking. Advantages and disadvantages of the direct dynamics approach to human walking analysis are discussed.

Parametric uncertainty on manipulators dynamics

Abstract This paper presents an efficient dynamic formulation for modeling and control of realistic six degrees-of-freedom robot manipulators. The basic dynamic formulation is based upon Kane’s approach. The zero-reference-position method is used to represent the robot and to formulate its governing kinematic equations. Both the inverse dynamics and the direct dynamic problems are discussed. The dynamic system model is controlled by utilizing a sophisticated feedback control scheme. The dynamic behavior of a robot with realistic complexity is examined with a view to investigate the effect of the system model errors on the precision of trajectory execution for the case when a good knowledge of the robot physical parameters may not be available.

Dynamic Analysis Tool for Legged Robots

The paper introduces a systematic approach for dealing with legged robot mechanism analysis. First, we briefly summarize basic mathematical tools for studying the dynamics of these multi-loop and parallel mechanisms using a unified spatial formulation which is useful for computer algorithms. The dynamic behavior analysis is based on two stages. The first one deals with establishing the equations of motion of the whole mechanism including legs tip impact effects and allowing us to solve the direct and inverse dynamic problems. The second concerns the feet–ground interaction aspect which is one of the major problem in the context of dynamic simulation for walking devices. We focus on the phenomenon of contact by introducing a general model for dynamic simulation of contacts between a walking robot and ground. This model considers a force distribution and uses an analytical form for each force depending only on the known state of the robot system. Finally, some simulation results of biped robot are given. The simulation includes all phenomena that may occur during the locomotion cycle: impact, transition from impact to contact, contact during support with static friction, transition from static to sliding friction and sliding friction.

Efficient computation of manipulator inertia matrices and the direct dynamics problem

A modeling scheme that uses the concepts of generalized and augmented links is proposed for computing joint-space inertia matrices of open-chain rigid body systems. Expressions for evaluating these matrices are derived, utilizing orthogonal Cartesian tensors and the Newton-Euler equations of motion. The resulting recursive algorithm is applicable to all rigid-link manipulators having open-chain kinematic structures with revolute and/or prismatic joints. An efficient implementation of the algorithm shows that the joint-space inertia-matrix of a six degree-of-freedom manipulator with revolute joints can be computed in approximately 420 multiplications and 339 additions. For manipulators with 0 degrees to 90 degrees twist angles, the number of computations is reduced to 271 multiplications and 250 additions. >

A recursive free-body approach to computer simulation of human postural dynamics.

A recursive, free-body approach to the estimation of joint torques associated with observed motion in linkage mechanisms has recently been shown to be computationally more efficient than any other known approach to this problem. This paper applies this method to the analysis of human postural dynamics and shows how it can also be used to compute accelerations for specified joint torques. The latter calculation, referred to here as the direct dynamics problem, has until now involved symbolic complexity to such an extent as to generally limit computer simulation studies of postural control to very simple models. The model presented in this paper is both straightforward and general, and removes this obstacle to the investigation of possible neural control mechanisms by means of computer simulation. A computationally oriented linearization procedure for the direct dynamics problem is also included in the paper. Finally, example simulation results and corresponding measured body motions for human subjects are presented to validate the method.

A Recursive Free-Body Approach to Computer Simulation of Human Postural Dynamics

Abstract A recursive, free-body approach to the estimation of joint torques associated with observed motion in linkage mechanisms has recently been shown to be computationally more efficient than any other known approach to this problem. This paper applies this method to the analysis of human postural dynamics and shows how it can also be used to compute accelerations for specified joint torques. The latter calculation, referred to here as the direct dynamics problem, has until now involved symbolic complexity to such an extent as to generally limit computer simulation studies of postural control to very simple models. The model presented in this paper is both straightforward and general, and removes this obstacle to the investigation of possible neural control mechanisms by means of computer simulation. A computationally oriented linearization procedure for the direct dynamics problem is also included in the paper. Finally, example simulation results and corresponding measured body motions for human subjects are presented to validate the method.

Computer-Oriented Algorithm for Modeling Active Spatial Mechanisms for Robotics Applications

Based on a comparison of the computational complexity of different spatial mechanisms dynamics formulations it is shown that the most appropriate one is the Newton-Euler formulation using recurrence relations for velocities, accelerations, and generalized forces. This is based on numerical efficiency and intermediate results. A general algorithm which solves both the direct and inverse problem of dynamics for an open-chained spatial mechanism of an arbitrary mechanical configuration is developed and realized. It is pointed out that for control algorithms which assume knowledge of system dynamics in real time, it is necessary to compute the inertial matrix and the term taking into account the rest of the dynamical effects separately. The "accelerated" computational algorithm for real-time implementation with this property has been developed and realized. Up to now reported real-time computational schemes do not have this feature directly implementable. Depending on the control law, manipulator configuration, type of functional tasks, and given ranges of operational speed it can appear that it is sufficient to compute only the dominant dynamical influences and not the complete dynamics. The criterion for the optimal choice of the level of the approximation of the dynamical model is formulated based on nominal regimes for specific functional tasks. For this purpose the algorithm for generation of the mathematical model of variable complexity is developed and realized. The procedure is implemented on two typical manipulator mechanical configurations of six degrees of freedom (d.o.f.) and a comparison of exact and various approximate models is performed.