Self-contained Measurement of Dynamic Legged Locomotion:
Design for Robot and Field Environments

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Currently there is no robotic solution that surpasses the grace, capabilities, and speed of mammalian legged locomotion. Consider, for example, the precision of a mountain goat negotiating craggy hillsides, or the agility of a cheetah adeptly chasing down its quarry on the veldt. This pedestrian mechanism remains one of engineering's most intractable problems. Namely, how to efficiently navigate over rough terrain?

The solution to this question is critical in mobile robot design. As robots become more sophisticated and move out of the laboratory, they will need to be able to reliably traverse difficult and rugged environments. Recent strides in biology, biomechanics, and robotics have shed new light on the governing principles underlying the nature of some of these animal motions. The dynamics, it appears, are central to modeling and driving the legged motion. Based on this concept, dynamic legged locomotion may be defined as that subset for which the momentum is central to the stability and distances covered. In quadrupeds, for example, this is principally manifest in the galloping gait.

Consideration of these principles has lead to the research and design of the Kinetically Ordered Locomotion Tetrapod (KOLT) galloping robot. This robot is fully actuated and features a powerful transmission mechanism capable of thrusting it into a gallop. Ironically, control and operation of KOLT is complicated by its very dynamics. For instance, in laboratory testing, the KOLT experiences impact forces that are nearly double those seen in galloping mammals. Such severe dynamics, in turn, unduly stress on-board controls and navigation systems. In addition, obstacles and irregularities of the terrain impose chaotic disturbances that further complicate the sensing problem.

This research explores one aspect of this fascinating design challenge: the experimental qualification of dynamic quadrupeds, such as KOLT, in a self-contained manner. In particular, it considers the estimation of motion and ground reaction forces in terrain without external aids (just as in nature). The classic approach for estimating these forces is through the use of force sensors between the foot and the ground; most often in the form of an embedded force-plate. While this approach has been successful in laboratory environments, it is too restrictive for field operations. A result from mechanics is quite insightful for this problem. If the location of the body is known, the reaction forces may be solved by using knowledge of the mass (or rather the inertia), the kinematics, and the dynamics.

The challenge, however, is in estimating the dynamics and kinetics simultaneously because they are intricately coupled, especially when considering the compliance that defines natural locomotion. The analysis is further complicated as there is no single compact (self-contained) sensing modality that provides location and attitude with high-bandwidth and long-term stability. This is treated by using multiple measurement modalities and taking advantage of the hybrid-dynamical structure of dynamic legged locomotion.

This research leverages theory in sensor design, noise modeling, visual processing, and kinematics to develop a method that provides online estimation of the driving locomotive force vector. Experiments on KOLT and field testing have shown improved motion estimation by combining kinetic state models with inertial measurements and measurement aids (such as: visual or range data). The major contributions of this research program are three-fold:

The matter of how a robot (or animal) reacts over terrain is deceptively simple, i.e., it thrusts and the rest is governed by Newton's laws of motion. Understanding and modeling this in detail, however, still remains a significant challenge. By providing a robust estimate of the motion, the methods presented in this thesis move one step closer towards the great promise of fielded dynamic legged locomotion.



KOLT at night



author = {Surya P. N. Singh},
title = {{Self-contained Measurement of Dynamic Legged Locomotion: Design for Robot and Field Environments}},
school = {Stanford University},
year = {2006},
url = {}
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SpnS - Jan/24/2007