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Book ChapterDOI

Recursive Dynamics for Fixed-Base Robotic Systems

TL;DR: The improvement in the computational efficiency in the presence of multiple-DOF joints are addressed in this chapter and dynamic analyses, namely, the inverse and forward dynamics, of several systems are performed.
Abstract: In this chapter, dynamic analyses of fixed-base robotic systems are presented using the dynamic modeling presented in Chap. 5. For this, recursive inverse and forward dynamics algorithms are developed. The algorithms take care of the multiple-DOF joints in an efficient manner, as explained in Sect. 4.2.1; in contrast to treating them as a combination of several 1-DOF joints by taking into account the total number of links equal to number of 1-DOF joints or joint variables. In the presence of many multiple-DOF joints in a robotic system the latter approach is relatively inefficient due to the burden of unnecessary computations with zeros. The improvement in the computational efficiency in the presence of multiple-DOF joints are addressed in this chapter. Dynamic analyses, namely, the inverse and forward dynamics, of several systems are performed in this chapter.
References
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Journal ArticleDOI
TL;DR: In this article, a family of embedded Runge-Kutta formulae RK5 (4) are derived from these and a small principal truncation term in the fifth order and extended regions of absolute stability.

3,106 citations

Book
31 Jul 1987
TL;DR: This work extends the Dynamics Algorithms to include contact, impact, and Kinematic Loops, and aims to improve accuracy and efficiency in the management of contact and impact.
Abstract: Spatial Kinematics.- Spatial Dynamics.- Inverse Dynamics - The Recursive Newton-Euler Method.- Forward Dynamics - The Composite-Rigid-Body Method.- Forward Dynamics - The Articulated-Body Method.- Extending the Dynamics Algorithms.- Coordinate Systems and Efficiency.- Contact, Impact, and Kinematic Loops.- Accuracy and Efficiency.- Contact and Impact.

791 citations

Journal ArticleDOI
TL;DR: In this article, a new method for calculating the acceleration of a robot in response to given actuator forces is described, which is applicable to open-loop kinematic chains containing revolute and prismatic joints.
Abstract: This paper describes a new method for calculating the acceleration of a robot in response to given actuator forces. The method is applicable to open-loop kinematic chains containing revolute and prismatic joints. The algorithm is based on recursive formulas involving quantities called articulated-body inertias, which represent the inertia properties of collections of rigid bodies connected together by joints allowing constrained relative motion between the bodies. A new, matrix-based notation is introduced to represent articulated-body inertias and other spatial quantities. This notation is used to develop the algorithm, and results in a compact representation of the equations. The new algorithm has a computational requirement that varies linearly with the number of joints, and its efficiency is compared with other published algorithms.

590 citations

Proceedings ArticleDOI
09 Apr 1991
TL;DR: Under the control method in the linear inverted pendulum mode, walking on a particular rugged ground is shown to be equivalent to Walking on a level ground, and it is shown that the additional use of the ankle torque makes the proposed control scheme robust and applicable to a real biped robot with mass legs.
Abstract: A novel control method for biped locomotion on rugged terrain is introduced, assuming an ideal robot model which has massless legs. By applying constraint control to the robot body so that it moves on a particular straight line and rotates at a constant angular velocity, the dynamics of the center of mass of the body becomes completely linear. Such motion of the ideal model is called the linear inverted pendulum mode, and it is used to develop the control scheme of the biped walking on rugged terrain. Under the control method in the linear inverted pendulum mode, walking on a particular rugged ground is shown to be equivalent to walking on a level ground. It is also shown that the additional use of the ankle torque makes the proposed control scheme robust and applicable to a real biped robot with mass legs. Simulation results are presented. >

415 citations