A Generalized Stiffness Matrix Method for Force Distribution of Robotic Systems with Indeterminancy

Foot forces in walking machines and finger forces in multi-fingered grippers are usually indeterminate due to the multi-closed-chain geometry of the systems. While many methods were proposed to solve the force distribution of such systems, a method called stiffness matrix method [2] was developed based on the concept that the force must satisfy the equations of material deformations. However, only leg compliances were considered in the stiffness matrix method. In this paper, the stiffness matrix method is generalized to include all the major system compliances, i.e., those of legs (fingers), actuators and terrain (object to be grasped). Based on the developed generalized stiffness matrix method, an example of foot force analysis of a quadruped is presented to demonstrate the effects of different system compliances on the foot forces.

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A stiffness matrix method for foot force distribution of walking vehicles

IEEE Transactions on Systems Man and Cybernetics ◽

10.1109/21.179850 ◽

1992 ◽

Vol 22 (5) ◽

pp. 1131-1138 ◽

Cited By ~ 2

Author(s):

X. Gao ◽

S.-M. Song

Keyword(s):

Stiffness Matrix ◽

Matrix Method ◽

Force Distribution ◽

Foot Force

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Stiffness matrix method for foot force distribution of walking vehicles

Proceedings., IEEE International Conference on Robotics and Automation ◽

10.1109/robot.1990.126213 ◽

2002 ◽

Cited By ~ 6

Author(s):

X.C. Gao ◽

S.M. Song

Keyword(s):

Stiffness Matrix ◽

Matrix Method ◽

Force Distribution ◽

Foot Force

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Body Vibrations of a Legged Walking Machine

22nd Biennial Mechanisms Conference: Flexible Mechanisms, Dynamics, and Analysis ◽

10.1115/detc1992-0428 ◽

1992 ◽

Author(s):

Xiaochun Gao ◽

Shin-Min Song

Keyword(s):

The Body ◽

Robotic Systems ◽

Force Distribution ◽

Walking Machine ◽

Foot Force ◽

Robot Hands ◽

Machine Systems ◽

External Loads ◽

Wheeled Vehicles ◽

Quadrupedal Walking

Abstract Unlike in wheeled vehicles, compliance in walking machine systems changes due to the variation of leg geometry, as its body proceeds. This variation in compliance will cause vibration, even if external loads remain constant. A theory is thus developed to predict the body vibrations of a walking machine during walking. On the other hand, dynamic foot forces under body vibrations can be computed by application of the existing numerical methods. As an example, the body vibrations of a quadrupedal walking chair under different walking conditions are simulated in terms of the developed theory. The results show that the influence of body vibrations on the foot force distribution is essential and, in some cases, the walking chair may lose its stability due to its body vibrations, even though it is identified to be stable in a quasi-static analysis. The developed theory can also be extended to other similar multi-limbed robotic systems, such as multi-fingered robot hands.

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Body Vibration of a Legged Walking Machine

Journal of Mechanical Design ◽

10.1115/1.2919279 ◽

1993 ◽

Vol 115 (4) ◽

pp. 856-862

Author(s):

Xiaochun Gao ◽

Shin-Min Song

Keyword(s):

The Body ◽

Robotic Systems ◽

Force Distribution ◽

Walking Machine ◽

Foot Force ◽

Robot Hands ◽

Machine Systems ◽

External Loads ◽

Wheeled Vehicles ◽

Quadrupedal Walking

Unlike wheeled vehicles, compliance in walking machine systems changes due to the variation of leg geometry, as its body proceeds. This variation in compliance will cause vibration, even if external loads remain constant. A theory is thus developed to predict the body vibrations of a walking machine during walking. On the other hand, dynamic foot forces under body vibrations can be computed by application of the existing numerical methods. As an example, the body vibrations of a quadrupedal walking chair under different walking conditions are simulated in terms of the developed theory. The results show that the influence of body vibrations on the foot force distribution is essential and, in some cases, the walking chair may lose its stability due to its body vibrations, even though it is identified to be stable in a quasistatic analysis. The developed theory can also be extended to other similar multilimbed robotic systems, such as multifingered robot hands.

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Lateral Stable Workspace of Hexapod Walking Machines With Constant Orientation Platform

Volume 4: 18th Design for Manufacturing and the Life Cycle Conference; 2013 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications ◽

10.1115/detc2013-12463 ◽

2013 ◽

Cited By ~ 2

Author(s):

Long Qu ◽

Mahdi Agheli ◽

Stephen S. Nestinger

Keyword(s):

Mobile Robot ◽

Dynamic Control ◽

Force Distribution ◽

Hexapod Robot ◽

Stability Criteria ◽

Geometrical Characteristics ◽

Walking Machines ◽

Foot Force ◽

The Stability

Due to the importance of the workspace and stability in mobile robot dynamic control, a variety of workspace and stability criteria exist in the field of multi-legged and wheeled robotics. This paper presents a methodology for determining the stable workspace, the subspace of the workspace for which the system is considered stable. The presented derivation utilizes the normal foot force distribution of the system to determine stability and integrates the stability into the lateral workspace of a mobile machining hexapod robot. The analytical inequalities governing the boundary of the stable workspace are derived. A discussion on the effects of physical and geometrical characteristics of the hexapod robot on the stable workspace methodology is given. The stable workspace methodology is validated through a simulation and an application to mobile machining is presented.

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