Hybrid Control and Motion Planning of Dynamical Legged Locomotion

Name: Hybrid Control and Motion Planning of Dynamical Legged Locomotion
Brand: Wiley-IEEE Press
Price: 98.99 EUR
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Nasser Sadati Guy A. Dumont Kaveh Akabri Hamed William A. Gruver(Autor*in)

Wiley-IEEE Press

Erschienen am 29. August 2012

272 Seiten

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Hybrid Control and Motion Planning of Dynamical Legged Locomotion
Contents
Preface
1. Introduction
1.1 Objectives of Legged Locomotion and Challenges in Controlling Dynamic Walking and Running
1.2 Literature Overview
1.2.1 Tracking of Time Trajectories
1.2.2 Poincar´e Return Map and Hybrid Zero Dynamics
1.3 The Objective of the Book
1.3.1 Hybrid Zero Dynamics in Walking with Double Support Phase
1.3.2 Hybrid Zero Dynamics in Running with an Online Motion Planning Algorithm
1.3.3 Online Motion Planning Algorithms for Flight Phases of Running
1.3.4 Hybrid Zero Dynamics in 3D Running
1.3.5 Hybrid Zero Dynamics in Walking with Passive Knees
1.3.6 Hybrid Zero Dynamics with Continuous-Time Update Laws
2. Preliminaries in Hybrid Systems
2.1 Basic Definitions
2.2 Poincaré Return Map for Hybrid Systems
2.3 Low-Dimensional Stability Analysis
2.4 Stabilization Problem
3. Asymptotic Stabilization of Periodic Orbits forWalking with Double Support Phase
3.1 Introduction
3.2 Mechanical Model of a Biped Walker
3.2.1 The Biped Robot
3.2.2 Dynamics of the Flight Phase
3.2.3 Dynamics of the Single Support Phase
3.2.4 Dynamics of the Double Support Phase
3.2.5 Impact Model
3.2.6 Transition from the Double Support Phase to the Single Support Phase
3.2.7 Hybrid Model of Walking
3.3 Control Laws for the Single and Double Support Phases
3.3.1 Single Support Phase Control Law
3.3.2 Double Support Phase Control Law
3.4 Hybrid Zero Dynamics (HZD)
3.4.1 Analysis of HZD in the Single Support Phase
3.4.2 Analysis of HZD in the Double Support Phase
3.4.3 Restricted Poincaré Return Map
3.5 Design of an HZD Containing a Prespecified Periodic Solution
3.5.1 Design of the Output Functions
3.5.2 Design of u1d and u2d
3.6 Stabilization of the Periodic Orbit
3.7 Motion Planning Algorithm
3.7.1 Motion Planning Algorithm for the Single Support Phase
3.7.2 Motion Planning Algorithm for the Double Support Phase
3.7.3 Constructing a Period-One Orbit for the Open-Loop Hybrid Model of Walking
3.7.3.1 Equality Constraints
3.7.3.2 Inequality Constraints
3.7.3.3 Cost Function
3.8 Numerical Example for the Motion Planning Algorithm
3.9 Simulation Results of the Closed-Loop Hybrid System
3.9.1 Effect of Double Support Phase on Angular Momentum Transfer and Stabilization
3.9.2 Effect of Event-Based Update Laws on Momentum Transfer and Stabilization
4. Asymptotic Stabilization of Periodic Orbits for Planar Monopedal Running
4.1 Introduction
4.2 Mechanical Model of a Monopedal Runner
4.2.1 The Monopedal Runner
4.2.2 Dynamics of the Flight Phase
4.2.3 Dynamics of the Stance Phase
4.2.4 Open-Loop Hybrid Model of Running
4.3 Reconfiguration Algorithm for the Flight Phase
4.3.1 Determination of the Reachable Set
4.4 Control Laws for Stance and Flight Phases
4.4.1 Stance Phase Control Law
4.4.2 Flight Phase Control Law
4.4.3 Event-Based Update Law
4.5 Hybrid Zero Dynamics and Stabilization
4.6 Numerical Results
5. Online Generation of Joint Motions During Flight Phases of Planar Running
5.1 Introduction
5.2 Mechanical Model of a Planar Open Kinematic Chain
5.3 Motion Planning Algorithm to Generate Continuous Joint Motions
5.3.1 Determining the Reachable Set from the Origin
5.3.2 Motion Planning Algorithm
5.4 Motion Planning Algorithm to Generate Continuously Differentiable Joint Motions
6. Stabilization of Periodic Orbits for 3D Monopedal Running
6.1 Introduction
6.2 Open-Loop Hybrid Model of a 3D Running
6.2.1 Dynamics of the Flight Phase
6.2.2 Dynamics of the Stance Phase
6.2.3 Transition Maps
6.2.4 Hybrid Model
6.3 Design of a Period-One Solution for the Open-Loop Model of Running
6.4 Numerical Example
6.5 Within-Stride Controllers
6.5.1 Stance Phase Control Law
6.5.2 Flight Phase Control Law
6.6 Event-Based Update Laws for Hybrid Invariance
6.6.1 Takeoff Update Laws
6.6.2 Impact Update Laws
6.7 Stabilization Problem
6.8 Simulation Results
7. Stabilization of Periodic Orbits for Walking with Passive Knees
7.1 Introduction
7.2 Open-Loop Model of Walking
7.2.1 Mechanical Model of the Planar Bipedal Robot
7.2.2 Dynamics of the Single Support Phase
7.2.3 Impact Map
7.2.4 Open-Loop Impulsive Model of Walking
7.3 Motion Planning Algorithm
7.4 Numerical Example
7.5 Continuous-Times Controllers
7.6 Event-Based Controllers
7.6.1 Hybrid Invariance
7.6.2 Continuity of the Continuous-Time Controllers During the Within-Stride Transitions
7.7 Stabilization Problem
7.8 Simulation of the Closed-Loop Hybrid System
8. Continuous-Time Update Laws During Continuous Phases of Locomotion
8.1 Introduction
8.2 Invariance of the Exponential Stability Behavior for a Class of Impulsive Systems
8.3 Outline of the Proof of Theorem 8.1
8.4 Application to Legged Locomotion
A. Proofs Associated with Chapter 3
A.1 Proof of Lemma 3.3
A.2 Proof of Lemma 3.4
A.3 Proof of Lemma 3.7
B. Proofs Associated with Chapter 4
B.1 Proof of Lemma 4.2
B.2 Proof of Theorem 4.2
C. Proofs Associated with Chapter 6
C.1 Proof of Lemma 6.1
C.2 Proof of Lemma 6.2
C.3 Invertibility of the Stance Phase Decoupling Matrix on the Periodic Orbit
Bibliography
Index
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