{"product_id":"hybrid-control-and-motion-planning-of-dynamical-legged-locomotion-9781118317075","title":"Hybrid Control and Motion Planning of Dynamical","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book addresses the need in the field for a comprehensive review of motion planning algorithms and hybrid control methodologies for complex legged robots.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix  \u003cp\u003e\u003cb\u003e1. Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Objectives of Legged Locomotion and Challenges in Controlling Dynamic Walking and Running 1\u003c\/p\u003e \u003cp\u003e1.2 Literature Overview 4\u003c\/p\u003e \u003cp\u003e1.2.1 Tracking of Time Trajectories 4\u003c\/p\u003e \u003cp\u003e1.2.2 Poincar´e Return Map and Hybrid Zero Dynamics 5\u003c\/p\u003e \u003cp\u003e1.3 The Objective of the Book 7\u003c\/p\u003e \u003cp\u003e1.3.1 Hybrid Zero Dynamics in Walking with Double Support Phase 7\u003c\/p\u003e \u003cp\u003e1.3.2 Hybrid Zero Dynamics in Running with an Online Motion Planning Algorithm 8\u003c\/p\u003e \u003cp\u003e1.3.3 Online Motion Planning Algorithms for Flight Phases of Running 9\u003c\/p\u003e \u003cp\u003e1.3.4 Hybrid Zero Dynamics in 3D Running 10\u003c\/p\u003e \u003cp\u003e1.3.5 Hybrid Zero Dynamics in Walking with Passive Knees 11\u003c\/p\u003e \u003cp\u003e1.3.6 Hybrid Zero Dynamics with Continuous-Time Update Laws 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Preliminaries in Hybrid Systems 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Basic Definitions 13\u003c\/p\u003e \u003cp\u003e2.2 Poincar´e Return Map for Hybrid Systems 16\u003c\/p\u003e \u003cp\u003e2.3 Low-Dimensional Stability Analysis 23\u003c\/p\u003e \u003cp\u003e2.4 Stabilization Problem 28\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Asymptotic Stabilization of Periodic Orbits forWalking with Double Support Phase 35\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 35\u003c\/p\u003e \u003cp\u003e3.2 Mechanical Model of a Biped Walker 37\u003c\/p\u003e \u003cp\u003e3.2.1 The Biped Robot 37\u003c\/p\u003e \u003cp\u003e3.2.2 Dynamics of the Flight Phase 37\u003c\/p\u003e \u003cp\u003e3.2.3 Dynamics of the Single Support Phase 39\u003c\/p\u003e \u003cp\u003e3.2.4 Dynamics of the Double Support Phase 40\u003c\/p\u003e \u003cp\u003e3.2.5 Impact Model 43\u003c\/p\u003e \u003cp\u003e3.2.6 Transition from the Double Support Phase to the Single Support Phase 45\u003c\/p\u003e \u003cp\u003e3.2.7 Hybrid Model of Walking 45\u003c\/p\u003e \u003cp\u003e3.3 Control Laws for the Single and Double Support Phases 46\u003c\/p\u003e \u003cp\u003e3.3.1 Single Support Phase Control Law 46\u003c\/p\u003e \u003cp\u003e3.3.2 Double Support Phase Control Law 49\u003c\/p\u003e \u003cp\u003e3.4 Hybrid Zero Dynamics (HZD) 54\u003c\/p\u003e \u003cp\u003e3.4.1 Analysis of HZD in the Single Support Phase 55\u003c\/p\u003e \u003cp\u003e3.4.2 Analysis of HZD in the Double Support Phase 57\u003c\/p\u003e \u003cp\u003e3.4.3 Restricted Poincar´e Return Map 58\u003c\/p\u003e \u003cp\u003e3.5 Design of an HZD Containing a Prespecified Periodic Solution 60\u003c\/p\u003e \u003cp\u003e3.5.1 Design of the Output Functions 60\u003c\/p\u003e \u003cp\u003e3.5.2 Design of u1d and u2d 62\u003c\/p\u003e \u003cp\u003e3.6 Stabilization of the Periodic Orbit 67\u003c\/p\u003e \u003cp\u003e3.7 Motion Planning Algorithm 71\u003c\/p\u003e \u003cp\u003e3.7.1 Motion Planning Algorithm for the Single Support Phase 72\u003c\/p\u003e \u003cp\u003e3.7.2 Motion Planning Algorithm for the Double Support Phase 73\u003c\/p\u003e \u003cp\u003e3.7.3 Constructing a Period-One Orbit for the Open-Loop Hybrid Model of Walking 76\u003c\/p\u003e \u003cp\u003e3.8 Numerical Example for the Motion Planning Algorithm 77\u003c\/p\u003e \u003cp\u003e3.9 Simulation Results of the Closed-Loop Hybrid System 82\u003c\/p\u003e \u003cp\u003e3.9.1 Effect of Double Support Phase on Angular Momentum Transfer and Stabilization 82\u003c\/p\u003e \u003cp\u003e3.9.2 Effect of Event-Based Update Laws on Momentum Transfer and Stabilization 92\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Asymptotic Stabilization of Periodic Orbits for Planar Monopedal Running 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 95\u003c\/p\u003e \u003cp\u003e4.2 Mechanical Model of a Monopedal Runner 97\u003c\/p\u003e \u003cp\u003e4.2.1 The Monopedal Runner 97\u003c\/p\u003e \u003cp\u003e4.2.2 Dynamics of the Flight Phase 97\u003c\/p\u003e \u003cp\u003e4.2.3 Dynamics of the Stance Phase 98\u003c\/p\u003e \u003cp\u003e4.2.4 Open-Loop Hybrid Model of Running 99\u003c\/p\u003e \u003cp\u003e4.3 Reconfiguration Algorithm for the Flight Phase 99\u003c\/p\u003e \u003cp\u003e4.3.1 Determination of the Reachable Set 103\u003c\/p\u003e \u003cp\u003e4.4 Control Laws for Stance and Flight Phases 120\u003c\/p\u003e \u003cp\u003e4.4.1 Stance Phase Control Law 121\u003c\/p\u003e \u003cp\u003e4.4.2 Flight Phase Control Law 122\u003c\/p\u003e \u003cp\u003e4.4.3 Event-Based Update Law 124\u003c\/p\u003e \u003cp\u003e4.5 Hybrid Zero Dynamics and Stabilization 125\u003c\/p\u003e \u003cp\u003e4.6 Numerical Results 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Online Generation of Joint Motions During Flight Phases of Planar Running 137\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 137\u003c\/p\u003e \u003cp\u003e5.2 Mechanical Model of a Planar Open Kinematic Chain 138\u003c\/p\u003e \u003cp\u003e5.3 Motion Planning Algorithm to Generate Continuous Joint Motions 140\u003c\/p\u003e \u003cp\u003e5.3.1 Determining the Reachable Set from the Origin 143\u003c\/p\u003e \u003cp\u003e5.3.2 Motion Planning Algorithm 150\u003c\/p\u003e \u003cp\u003e5.4 Motion Planning Algorithm to Generate Continuously Differentiable Joint Motions 152\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Stabilization of Periodic Orbits for 3D Monopedal Running 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 159\u003c\/p\u003e \u003cp\u003e6.2 Open-Loop Hybrid Model of a 3D Running 160\u003c\/p\u003e \u003cp\u003e6.2.1 Dynamics of the Flight Phase 162\u003c\/p\u003e \u003cp\u003e6.2.2 Dynamics of the Stance Phase 163\u003c\/p\u003e \u003cp\u003e6.2.3 Transition Maps 164\u003c\/p\u003e \u003cp\u003e6.2.4 Hybrid Model 166\u003c\/p\u003e \u003cp\u003e6.3 Design of a Period-One Solution for the Open-Loop Model of Running 167\u003c\/p\u003e \u003cp\u003e6.4 Numerical Example 172\u003c\/p\u003e \u003cp\u003e6.5 Within-Stride Controllers 175\u003c\/p\u003e \u003cp\u003e6.5.1 Stance Phase Control Law 175\u003c\/p\u003e \u003cp\u003e6.5.2 Flight Phase Control Law 178\u003c\/p\u003e \u003cp\u003e6.6 Event-Based Update Laws for Hybrid Invariance 181\u003c\/p\u003e \u003cp\u003e6.6.1 Takeoff Update Laws 184\u003c\/p\u003e \u003cp\u003e6.6.2 Impact Update Laws 185\u003c\/p\u003e \u003cp\u003e6.7 Stabilization Problem 186\u003c\/p\u003e \u003cp\u003e6.8 Simulation Results 189\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Stabilization of Periodic Orbits for Walking with Passive Knees 193\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 193\u003c\/p\u003e \u003cp\u003e7.2 Open-Loop Model of Walking 194\u003c\/p\u003e \u003cp\u003e7.2.1 Mechanical Model of the Planar Bipedal Robot 194\u003c\/p\u003e \u003cp\u003e7.2.2 Dynamics of the Single Support Phase 195\u003c\/p\u003e \u003cp\u003e7.2.3 Impact Map 195\u003c\/p\u003e \u003cp\u003e7.2.4 Open-Loop Impulsive Model of Walking 196\u003c\/p\u003e \u003cp\u003e7.3 Motion Planning Algorithm 197\u003c\/p\u003e \u003cp\u003e7.4 Numerical Example 200\u003c\/p\u003e \u003cp\u003e7.5 Continuous-Times Controllers 202\u003c\/p\u003e \u003cp\u003e7.6 Event-Based Controllers 209\u003c\/p\u003e \u003cp\u003e7.6.1 Hybrid Invariance 209\u003c\/p\u003e \u003cp\u003e7.6.2 Continuity of the Continuous-Time Controllers During the Within-Stride Transitions 212\u003c\/p\u003e \u003cp\u003e7.7 Stabilization Problem 213\u003c\/p\u003e \u003cp\u003e7.8 Simulation of the Closed-Loop Hybrid System 217\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Continuous-Time Update Laws During Continuous Phases of Locomotion 221\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 221\u003c\/p\u003e \u003cp\u003e8.2 Invariance of the Exponential Stability Behavior for a Class of Impulsive Systems 222\u003c\/p\u003e \u003cp\u003e8.3 Outline of the Proof of Theorem 8.1 224\u003c\/p\u003e \u003cp\u003e8.4 Application to Legged Locomotion 227\u003c\/p\u003e \u003cp\u003eA. Proofs Associated with Chapter 3 229\u003c\/p\u003e \u003cp\u003eA.1 Proof of Lemma 3.3 229\u003c\/p\u003e \u003cp\u003eA.2 Proof of Lemma 3.4 230\u003c\/p\u003e \u003cp\u003eA.3 Proof of Lemma 3.7 230\u003c\/p\u003e \u003cp\u003eB. Proofs Associated with Chapter 4 233\u003c\/p\u003e \u003cp\u003eB.1 Proof of Lemma 4.2 233\u003c\/p\u003e \u003cp\u003eB.2 Proof of Theorem 4.2 234\u003c\/p\u003e \u003cp\u003eC. Proofs Associated with Chapter 6 237\u003c\/p\u003e \u003cp\u003eC.1 Proof of Lemma 6.1 237\u003c\/p\u003e \u003cp\u003eC.2 Proof of Lemma 6.2 238\u003c\/p\u003e \u003cp\u003eC.3 Invertibility of the Stance Phase Decoupling Matrix on the Periodic Orbit 240\u003c\/p\u003e \u003cp\u003eBibliography 241\u003c\/p\u003e \u003cp\u003eIndex 249\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406850859351,"sku":"9781118317075","price":91.15,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118317075.jpg?v=1730497337","url":"https:\/\/bookcurl.com\/products\/hybrid-control-and-motion-planning-of-dynamical-legged-locomotion-9781118317075","provider":"Book Curl","version":"1.0","type":"link"}