A
Comparative Study of Stability Margins for Walking Machines
Abstract
Several
static and dynamic stability criteria have been defined in the course of
walking robot history. Nevertheless, different applications may require
different stability criteria and, up to day, there is no qualitative
classification of such stability measurements. Using the wrong stability
criterion to control a robot gait may prevent the task from succeeding. Furthermore,
if the optimum criterion is found, the robot gait can also be optimised. In
this work, the stability criteria that have
been applied to walking robots with at least four legs are examined in terms of
their stability margins in different static and dynamic situations. As a
result, a qualitative classification of stability criteria for walking machines
is proposed so that the proper criterion can be chosen for every desired
application.
Research on walking-robot stability began
in 1968, when McGhee and Frank first defined the static stability of an ideal
walking robot [McGhee68]. Following
their definition, an ideal robot is statically stable if the horizontal
projection of its center of gravity lies inside the support pattern. The ideal
robot is supposed to have massless legs, and system dynamics are assumed to be
absent.
The idea of static stability was inspired by insects, whose massless legs must support their body during walking and at the same time provide propulsion. For this reason, their sequence of steps must ensure their static stability. The first generation of walking machines emulated this mechanism of locomotion [Kumar89]. These robots were huge mechanisms featuring heavy limbs too difficult to control (see Figure 1) [Song89]. The adoption of statically stable gaits could simplify their control. However, during the motion of the heavy limbs and body some inertial effects and other dynamic components (friction, elasticity, etc.) were found to arise, restricting the robot's movements to low, constant velocities. Thus, the adoption of static stability limited these robots' speed of motion.
|
Figure 1: The Adaptive Suspensión Vehicle
(The Ohio State University, 1989) |
In the last two decades the walking-robots community has displayed increasing interest in the field of biped robots. Research on dynamic stability has focused on this particular design [Arimoto84, Fujimoto98, Furusho90, Hirai98, Loffler00, Raibert86]. Although some dynamically stable quadrupeds exist, they are very mechanically simplified machines having only a few degrees of freedom, which adopt the stability criteria designed for bipeds, extended to a couple of legs (see Figure 2) [Buehler98, Raibertetal86, Wong93]. The motion of these quadrupeds is limited to even terrain, because the stability criterion used (Zero Moment Point) is only valid for that kind of surface [Goswami99, Kimura90, Yoneda96].
|
Figure 2: Quadruped (The MIT Leg Lab, 1985) |
Little effort has been made to cope with
the dynamic effects that limit statically stable machines' performance [Gonzalez98,
Kang97, Lin93, Papadopoulos96,
Yoneda97]. However, one of the main goals of research on legged locomotion is the application of walking robots in
industrial processes and services, and such robots are not meant to trot or
gallop but to walk.
The few
dynamic stability criteria defined for quadrupedal walking seem to give
different forms and names to a single idea: the sign of the moment around the
edges of the support polygon caused by dynamic effects acting on the vehicle's
center of mass. The suitability of each criterion for each particular
application
(i.e.
manipulation forces and moment present,
uneven terrain, etc.) is not
clear at all. Nevertheless, the use of a stability criterion not suitable for
the current application may prevent the task from succeeding. Therefore, a
qualitative classification of the existing static and dynamic stability
criteria for robots of four or more legs is absolutely required.
Furthermore,
if the optimum criterion were found for each application, robot speed could be
increased. Moreover, if some velocity-optimization technique were used for the leg's transfer phase [Bobrow85,
Garcia01], overall machine performance could be optimized.
In this work, the existing stability criteria
have been briefly reviewed. Then, a comparative study of their stability
margins has been carried out through simulation using the model of the SILO4 quadruped
robot as testbed in different static and dynamic situations. The simulation has
been programmed in Java, using the Yobotics!
Simulation Construction Set software (see Figure 3). A comparative study on
stability margins according to their suitability for measuring stability for a number
of representative situations has been performed. Also, the final qualitative
classification of the stability criteria has been proposed.
|
Figure 3: Simulation of the SILO4 robot. |
