Disturbance rejection control for bipedal robot walkers

Description

This dissertation contributes to the theoretical and experimental foundation of disturbance rejection control in dynamic bipedal robots. Disturbances produced by model uncertainties and external disturbances are studied as lumped signals that can be rejected through feedback control techniques. The disturbance rejection problem is addressed with the design of trajectory tracking controllers working complementary with an adaptive reference trajectory generator. Two trajectory tracking control strategies were developed: (i) a novel model-based active disturbance rejection control and (ii) a robust multivariable generalized proportional integral control. The methodology adopted allows the design of trajectory generators with the ability to produce periodic stable gait patterns and reject disturbances through the use of an adaptive reference trajectory generator. A discrete control action resets the gait trajectory references after the impact produced by the robot's support-leg exchange in order to maintain a zero tracking error in the controlled joints. In addition, an extended hybrid zero dynamics is introduced to examine the periodic stability of the system with the use of a lower-dimensional representation of the full hybrid dynamics with uncertainties. A physical bipedal robot testbed, named as Saurian, was fabricated for validation purposes. Numerical simulation and physical experiments show the robustness of the proposed control strategies against external disturbances and model uncertainties that could affect both the swing motion phase and the support-leg exchange. Table of contents List of figures List of tables Abbreviations Nomenclature 1 Introduction 1.1 State of the art in control of bipedal robots 1.2 Highlights 1.3 Outline 2 Model of a Dynamic Bipedal Robot 2.1 Single support phase model 2.2 Discrete dynamic model 2.3 Hybrid dynamic model 3 Disturbance Rejection Control for Trajectory Tracking 3.1 Robust multivariable generalized proportional integral (GPI) controller 3.1.1 Model decomposition 3.1.2 Partial feedback linearization 3.1.3 Integral reconstructors 3.2 Hybrid zero dynamics with uncertainties (HZDU) 3.2.1 Derivation of HZDU 3.2.2 Orbital Gait Stability Analysis for HZDU 3.3 Model-based active disturbance rejection control (ADRC) 3.3.1 Local coordinate transformation 3.3.2 Nonlinear extended state observer (NESO) 3.3.3 Feedback control law 3.4 Extended hybrid zero dynamics (EHZD) 3.4.1 Derivation of EHZD 3.4.2 Asymptotic periodic orbits in EHZD 4 Disturbance Rejection in Trajectory Generation 4.1 Virtual holonomic constraints definition 4.1.1 Behavioral constraints 4.1.2 Nonlinear equality constraints 4.1.3 Nonlinear inequality constraints 4.2 Surface of virtual holonomic constraints 4.3 Reset control law for support-leg exchange 4.3.1 Optimal reset transition for support-leg exchange 4.3.2 Smooth transition from the passive to target dynamics 5 Numerical Simulations 5.1 Parameters definition 5.1.1 Robot parameters 5.1.2 Robust multivariable GPI controller tuning 5.1.3 Model-based ADRC tuning 5.1.4 Trajectory generation parameters 5.2 Simulation under nominal conditions 5.3 Simulation over uneven terrain 5.4 Simulation with external disturbances 5.5 Simulation with parameter uncertainties 6 Design of the Testbed (Saurian) and Physical Experiments 6.1 Mechanism design 6.2 Sensors, actuators, and control hardware 6.3 Walking experiments 6.4 Discussion of experiments 7 Concluding Remarks 7.1 Summary 7.1.1 Robust multivariable GPI controller for hybrid dynamical systems 7.1.2 Asymptotic periodic orbits in HZDU 7.1.3 Model-based ADRC for hybrid dynamical systems 7.1.4 Asymptotic periodic orbits in EHZD 7.1.5 Disturbance rejection in trajectory generation 7.1.6 Reset control law to reject disturbances at the support-leg exchange 7.1.7 Numerical simulations 7.1.8 Experiments 7.2 Perspectives for future studies References Appendix A Lagrange Formulation