Legged locomotion : Balance, control and tools - from equation to action

Abstract: This thesis is about control and balance stability of leggedlocomotion. It also presents a combination of tools that makesit easier to design controllers for large and complicated robotsystems. The thesis is divided into four parts.The first part studies and analyzes how walking machines arecontrolled, examining the literature of over twenty machinesbriefly, and six machines in detail. The goal is to understandhow the controllers work on a level below task and pathplanning, but above actuator control. Analysis and comparisonis done in terms of: i) generation of trunk motion; ii)maintaining balance; iii) generation of leg sequence andsupport patterns; and iv) reflexes.The next part describes WARP1, a four-legged walking robotplatform that has been builtwith the long term goal of walkingin rough terrain. First its modular structure (mechanics,electronics and control) is described, followed by someexperiments demonstrating basic performance. Finally themathematical modeling of the robot’s rigid body model isdescribed. This model is derived symbolically and is general,i.e. not restricted to WARP1. It is easily modified in case ofa different number of legs or joints.During the work with WARP1, tools for model derivation,control design and control implementation have been combined,interfaced and augmented in order to better support design andanalysis. These tools and methods are described in the thirdpart. The tools used to be difficult to combine, especially fora large and complicated system with many signals and parameterssuch as WARP1. Now, models derived symbolically in one tool areeasy to use in another tool for control design, simulation andfinally implementation, as well as for visualization andevaluation—thus going from equation to action.In the last part we go back to“equation”wherethese tools aid the study of balance stability when complianceis considered. It is shown that a legged robot in a“statically balanced”stance may actually beunstable. Furthermore, a criterion is derived that shows when aradially symmetric“statically balanced”stance on acompliant surface is stable. Similar analyses are performed fortwo controllers of legged robots, where it is the controllerthat cause the compliance.Keywordslegged locomotion, control, balance, leggedmachines, legged robots, walking robots, walking machines,compliance, platform stability, symbolic modeling