Finat, Javier 
  
ALGORITHMS FOR A STRUCTURAL MODEL OF BIPED LOCOMOTION IN THE 
CONFIGURATION SPACE 
Javier Finat 
Faculty of Sciences, University of Valladolid 
jfinat@nava.tel.uva.es 
Working Group MoBiVA Group, Neurotecno Institute 
KEY WORDS: Model-based processing, Navigation. 
ABSTRACT 
Mechanical models for locomotion are strongly hierarchised depending on the gait phase, tasks to be performed and 
constraints. There is an alternance between different constraints involving to different phases of any locomotion. This 
alternance suggests a hybrid approach for the algorithms design, with coarse-to-fine models for the automatic selection 
of rules relative to geometric motion planning, adaptive control and monitoring forces. One introduces doubly connected 
lists for the geometric data representation and updating of incidence elements between lines supporting actions with the 
corresponding pointers to points and planes. This geometric model supports the existence of spatio-temporal symmetries 
linked to spatial rigid transformations into the ambient space for representation and in the architecture for motion simula- 
tion, and to temporal alternant patterns for periodic motions. Both of them can be represented in terms of reflections which 
provide a modular approach to the design and implementation of algorithms. Velocity fields involving to mobile data pro- 
vide tools for spatial replication and periodicity phenomena and give modular, adaptable and reconfigurable patterns for 
the algorithms implementation. 
1 INTRODUCTION 
Locomotion tasks for biped or multilegged robots involve to the generation, transmission and coordination of movements 
for a regular gait. The design of algorithms for planning and execution of terrestrial locomotion requires to select objec- 
tives and to formulate simplifying assumptions for the models. The goal is to perform smooth periodic patterns including 
stance and swing phases separated by land-off and ground impact as phase transitions for each leg. 
To illustrate these general principles, the concatenation of all these phases is realised in terms of flexion/extensions oper- 
ations allowing shape changes in articulated mechanisms. So, we forget the dissipation effects and put emphasis on the 
alternance and periodic movements. So, along a regular walking whereas the left leg is falling in its extension phase under 
the effect of the gravity force (navigation phase), the right leg is contracting (in the flexion phase) along the stance phase 
(dynamic reflection). Regular phases correspond to stance and swing with an alternance between active and passive in- 
teraction with a wrenches exchange involving to the activation-inhibition of efforts generation and inertial effects holding 
onto the flexion and extension artificial modules (in correspondence with agonistic-antagonistic behavior in the biological 
case). Exchanges between kinematics and dynamics hold onto phase transitions (land-off and impact against the ground) 
which are assumed as instantaneous and modelled as singularities of the model. Along the regular phases, one applies 
superposition principles for kinematics and dynamics, by adopting a representation in terms of 3D lines. 
The diversity of phenomena appearing in a changing dynamics suggests a hybrid approach for the design and implemen- 
tation of algorithms. The hybrid character is relative to perception-action cycle; another said, it combines a propioceptive 
information based on geometric models for the behavior analysis and a mechanical model based on motion's equations. 
To the behavior analysis one can add a structural mechanical model to make easier the tracking, prediction and generation 
of motions, even in presence of partial occlusions. Furthermore the visual information it is convenient to have models for 
gait generation in legged mechanisms which provide a mechanical feedback for a more efficient control. 
It is important the reusability of routines in software libraries to allow an information transference between different 
perception-action modules in distributed systems. The hierarchies of this artificial model are symbolically represented in 
terms of like-tree graphs (including cycles for parallelizable questions), to make easier the maintainance of a queue of 
internal events associated to locomotion tasks. The information updating must be linked with the control system in an 
interactive way by some kind of velocity fields. Neural fields are given by potential fields which are active or passive, 
depending on the motion phase; they are in charge of generating velocities and forces acting onto rotational joints which 
  
238 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 
  
  
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