An integral predictive/nonlinear H∞ control structure for a quadrotor helicopter
TL;DR: An integral predictive and nonlinear robust control strategy to solve the path following problem for a quadrotor helicopter with parametric and structural uncertainties presented to corroborate the effectiveness and the robustness of the proposed strategy.
About: This article is published in Automatica.The article was published on 2010-01-01. It has received 643 citations till now. The article focuses on the topics: Model predictive control & Nonlinear control.
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16 May 2016
TL;DR: This work proposes to combine MPC with reinforcement learning in the framework of guided policy search, where MPC is used to generate data at training time, under full state observations provided by an instrumented training environment, and a deep neural network policy is trained, which can successfully control the robot without knowledge of the full state.
Abstract: Model predictive control (MPC) is an effective method for controlling robotic systems, particularly autonomous aerial vehicles such as quadcopters. However, application of MPC can be computationally demanding, and typically requires estimating the state of the system, which can be challenging in complex, unstructured environments. Reinforcement learning can in principle forego the need for explicit state estimation and acquire a policy that directly maps sensor readings to actions, but is difficult to apply to unstable systems that are liable to fail catastrophically during training before an effective policy has been found. We propose to combine MPC with reinforcement learning in the framework of guided policy search, where MPC is used to generate data at training time, under full state observations provided by an instrumented training environment. This data is used to train a deep neural network policy, which is allowed to access only the raw observations from the vehicle's onboard sensors. After training, the neural network policy can successfully control the robot without knowledge of the full state, and at a fraction of the computational cost of MPC. We evaluate our method by learning obstacle avoidance policies for a simulated quadrotor, using simulated onboard sensors and no explicit state estimation at test time.
425 citations
Additional excerpts
...quently used to control autonomous aerial vehicles such as quadrotors [38], [35], [34], [3], [2], [4], [29]....
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TL;DR: A method based on second order sliding mode control (2-SMC) is proposed to design controllers for a small quadrotor UAV by using Lyapunov theory, which guarantees that all system state trajectories reach and stay on the sliding surfaces.
Abstract: A method based on second order sliding mode control (2-SMC) is proposed to design controllers for a small quadrotor UAV. For the switching sliding manifold design, the selection of the coefficients of the switching sliding manifold is in general a sophisticated issue because the coefficients are nonlinear. In this work, in order to perform the position and attitude tracking control of the quadrotor perfectly, the dynamical model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. For the former, a sliding manifold is defined by combining the position and velocity tracking errors of one state variable, i.e., the sliding manifold has two coefficients. For the latter, a sliding manifold is constructed via a linear combination of position and velocity tracking errors of two state variables, i.e., the sliding manifold has four coefficients. In order to further obtain the nonlinear coefficients of the sliding manifold, Hurwitz stability analysis is used to the solving process. In addition, the flight controllers are derived by using Lyapunov theory, which guarantees that all system state trajectories reach and stay on the sliding surfaces. Extensive simulation results are given to illustrate the effectiveness of the proposed control method.
365 citations
TL;DR: In this paper, the control problem of an unmanned quadrotor in an indoor environment where there is lack of absolute localization data is addressed based on an attached Inertia Measurement Unit.
Abstract: This article addresses the control problem of an unmanned quadrotor in an indoor environment where there is lack of absolute localization data. Based on an attached Inertia Measurement Unit, a sona ...
328 citations
TL;DR: The proposed MPC algorithm with Hammerstein model in this paper can ensure that the UAV exactly tracking the target while maintaining stability, even with external disturbances.
323 citations
TL;DR: In this article, a Switching Model Predictive Attitude Controller for an Unmanned quadrotor Helicopter subject to atmospheric disturbances is presented, and the proposed control scheme is computed based on the predicted attitude.
308 citations
Cites background from "An integral predictive/nonlinear H∞..."
...…Sliding Mode control (Waslander et al. (2005)), c) Backstepping control (Bouabdallah and Siegwart (2007)), d) Integral predictive–nonlinear H∞ control (Raffo et al. (2010)), e) Constrained Finite Time Optimal Control Scheme (Alexis et al. (2010a,b)), and f) bounded control (Guerrero-Castellanos et…...
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References
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Book•
01 Jan 1986
TL;DR: This chapter discusses Jacobians: Velocities and Static Forces, Robot Programming Languages and Systems, and Manipulator Dynamics, which focuses on the role of Jacobians in the control of Manipulators.
Abstract: 1. Introduction. 2. Spatial Descriptions and Transformations. 3. Manipulator Kinematics. 4. Inverse Manipulator Kinematics. 5. Jacobians: Velocities and Static Forces. 6. Manipulator Dynamics. 7. Trajectory Generation. 8. Manipulator Mechanism Design. 9. Linear Control of Manipulators. 10. Nonlinear Control of Manipulators. 11. Force Control of Manipulators. 12. Robot Programming Languages and Systems. 13. Off-Line Programming Systems.
5,992 citations
Book•
26 Jan 2012
TL;DR: In this article, the authors present a model predictive controller for a water heating system, which is based on the T Polynomial Process (TOP) model of the MPC.
Abstract: 1 Introduction to Model Predictive Control.- 1.1 MPC Strategy.- 1.2 Historical Perspective.- 1.3 Industrial Technology.- 1.4 Outline of the Chapters.- 2 Model Predictive Controllers.- 2.1 MPC Elements.- 2.1.1 Prediction Model.- 2.1.2 Objective Function.- 2.1.3 Obtaining the Control Law.- 2.2 Review of Some MPC Algorithms.- 2.3 State Space Formulation.- 3 Commercial Model Predictive Control Schemes.- 3.1 Dynamic Matrix Control.- 3.1.1 Prediction.- 3.1.2 Measurable Disturbances.- 3.1.3 Control Algorithm.- 3.2 Model Algorithmic Control.- 3.2.1 Process Model and Prediction.- 3.2.2 Control Law.- 3.3 Predictive Functional Control.- 3.3.1 Formulation.- 3.4 Case Study: A Water Heater.- 3.5 Exercises.- 4 Generalized Predictive Control.- 4.1 Introduction.- 4.2 Formulation of Generalized Predictive Control.- 4.3 The Coloured Noise Case.- 4.4 An Example.- 4.5 Closed-Loop Relationships.- 4.6 The Role of the T Polynomial.- 4.6.1 Selection of the T Polynomial.- 4.6.2 Relationships with Other Formulations.- 4.7 The P Polynomial.- 4.8 Consideration of Measurable Disturbances.- 4.9 Use of a Different Predictor in GPC.- 4.9.1 Equivalent Structure.- 4.9.2 A Comparative Example.- 4.10 Constrained Receding Horizon Predictive Control.- 4.10.1 Computation of the Control Law.- 4.10.2 Properties.- 4.11 Stable GPC.- 4.11.1 Formulation of the Control Law.- 4.12 Exercises.- 5 Simple Implementation of GPC for Industrial Processes.- 5.1 Plant Model.- 5.1.1 Plant Identification: The Reaction Curve Method.- 5.2 The Dead Time Multiple of the Sampling Time Case.- 5.2.1 Discrete Plant Model.- 5.2.2 Problem Formulation.- 5.2.3 Computation of the Controller Parameters.- 5.2.4 Role of the Control-weighting Factor.- 5.2.5 Implementation Algorithm.- 5.2.6 An Implementation Example.- 5.3 The Dead Time Nonmultiple of the Sampling Time Case.- 5.3.1 Discrete Model of the Plant.- 5.3.2 Controller Parameters.- 5.3.3 Example.- 5.4 Integrating Processes.- 5.4.1 Derivation of the Control Law.- 5.4.2 Controller Parameters.- 5.4.3 Example.- 5.5 Consideration of Ramp Setpoints.- 5.5.1 Example.- 5.6 Comparison with Standard GPC.- 5.7 Stability Robustness Analysis.- 5.7.1 Structured Uncertainties.- 5.7.2 Unstructured Uncertainties.- 5.7.3 General Comments.- 5.8 Composition Control in an Evaporator.- 5.8.1 Description of the Process.- 5.8.2 Obtaining the Linear Model.- 5.8.3 Controller Design.- 5.8.4 Results.- 5.9 Exercises.- 6 Multivariable Model Predictive Control.- 6.1 Derivation of Multivariable GPC.- 6.1.1 White Noise Case.- 6.1.2 Coloured Noise Case.- 6.1.3 Measurable Disturbances.- 6.2 Obtaining a Matrix Fraction Description.- 6.2.1 Transfer Matrix Representation.- 6.2.2 Parametric Identification.- 6.3 State Space Formulation.- 6.3.1 Matrix Fraction and State Space Equivalences.- 6.4 Case Study: Flight Control.- 6.5 Convolution Models Formulation.- 6.6 Case Study: Chemical Reactor.- 6.6.1 Plant Description.- 6.6.2 Obtaining the Plant Model.- 6.6.3 Control Law.- 6.6.4 Simulation Results.- 6.7 Dead Time Problems.- 6.8 Case Study: Distillation Column.- 6.9 Multivariable MPC and Transmission Zeros.- 6.9.1 Simulation Example.- 6.9.2 Tuning MPC for Processes with OUD Zeros.- 6.10 Exercises.- 7 Constrained Model Predictive Control.- 7.1 Constraints and MPC.- 7.1.1 Constraint General Form.- 7.1.2 Illustrative Examples.- 7.2 Constraints and Optimization.- 7.3 Revision of Main Quadratic Programming Algorithms.- 7.3.1 The Active Set Methods.- 7.3.2 Feasible Direction Methods.- 7.3.3 Initial Feasible Point.- 7.3.4 Pivoting Methods.- 7.4 Constraints Handling.- 7.4.1 Slew Rate Constraints.- 7.4.2 Amplitude Constraints.- 7.4.3 Output Constraints.- 7.4.4 Constraint Reduction.- 7.5 1-norm.- 7.6 Case Study: A Compressor.- 7.7 Constraint Management.- 7.7.1 Feasibility.- 7.7.2 Techniques for Improving Feasibility.- 7.8 Constrained MPC and Stability.- 7.9 Multiobjective MPC.- 7.9.1 Priorization of Objectives.- 7.10 Exercises.- 8 Robust Model Predictive Control.- 8.1 Process Models and Uncertainties.- 8.1.1 Truncated Impulse Response Uncertainties.- 8.1.2 Matrix Fraction Description Uncertainties.- 8.1.3 Global Uncertainties.- 8.2 Objective Functions.- 8.2.1 Quadratic Cost Function.- 8.2.2 ?-? norm.- 8.2.3 1-norm.- 8.3 Robustness by Imposing Constraints.- 8.4 Constraint Handling.- 8.5 Illustrative Examples.- 8.5.1 Bounds on the Output.- 8.5.2 Uncertainties in the Gain.- 8.6 Robust MPC and Linear Matrix Inequalities.- 8.7 Closed-Loop Predictions.- 8.7.1 An Illustrative Example.- 8.7.2 Increasing the Number of Decision Variables.- 8.7.3 Dynamic Programming Approach.- 8.7.4 Linear Feedback.- 8.7.5 An Illustrative Example.- 8.8 Exercises.- 9 Nonlinear Model Predictive Control.- 9.1 Nonlinear MPC Versus Linear MPC.- 9.2 Nonlinear Models.- 9.2.1 Empirical Models.- 9.2.2 Fundamental Models.- 9.2.3 Grey-box Models.- 9.2.4 Modelling Example.- 9.3 Solution of the NMPC Problem.- 9.3.1 Problem Formulation.- 9.3.2 Solution.- 9.4 Techniques for Nonlinear Predictive Control.- 9.4.1 Extended Linear MPC.- 9.4.2 Local Models.- 9.4.3 Suboptimal NPMC.- 9.4.4 Use of Short Horizons.- 9.4.5 Decomposition of the Control Sequence.- 9.4.6 Feedback Linearization.- 9.4.7 MPC Based on Volterra Models.- 9.4.8 Neural Networks.- 9.4.9 Commercial Products.- 9.5 Stability and Nonlinear MPC.- 9.6 Case Study: pH Neutralization Process.- 9.6.1 Process Model.- 9.6.2 Results.- 9.7 Exercises.- 10 Model Predictive Control and Hybrid Systems.- 10.1 Hybrid System Modelling.- 10.2 Example: A Jacket Cooled Batch Reactor.- 10.2.1 Mixed Logical Dynamical Systems.- 10.2.2 Example.- 10.3 Model Predictive Control of MLD Systems.- 10.3.1 Branch and Bound Mixed Integer Programming.- 10.3.2 An Illustrative Example.- 10.4 Piecewise Affine Systems.- 10.4.1 Example: Tankwith Different Area Sections.- 10.4.2 Reach Set, Controllable Set, and STG Algorithm.- 10.5 Exercises.- 11 Fast Methods for Implementing Model Predictive Control.- 11.1 Piecewise Affinity of MPC.- 11.2 MPC and Multiparametric Programming.- 11.3 Piecewise Implementation of MPC.- 11.3.1 Illustrative Example: The Double Integrator.- 11.3.2 Nonconstant References and Measurable Disturbances.- 11.3.3 Example.- 11.3.4 The 1-norm and ?-norm Cases.- 11.4 Fast Implementation of MPC forUncertain Systems.- 11.4.1 Example.- 11.4.2 The Closed-Loop Min-max MPC.- 11.5 Approximated Implementation for MPC.- 11.6 Fast Implementation of MPC and Dead Time Considerations.- 11.7 Exercises.- 12 Applications.- 12.1 Solar Power Plant.- 12.1.1 Selftuning GPC Control Strategy.- 12.1.2 Gain Scheduling Generalized Predictive Control.- 12.2 Pilot Plant.- 12.2.1 Plant Description.- 12.2.2 Plant Control.- 12.2.3 Flow Control.- 12.2.4 Temperature Control at the Exchanger Output.- 12.2.5 Temperature Control in the Tank.- 12.2.6 Level Control.- 12.2.7 Remarks.- 12.3 Model Predictive Control in a Sugar Refinery.- 12.4 Olive Oil Mill.- 12.4.1 Plant Description.- 12.4.2 Process Modelling and Validation.- 12.4.3 Controller Synthesis.- 12.4.4 Experimental Results.- 12.5 Mobile Robot.- 12.5.1 Problem Definition.- 12.5.2 Prediction Model.- 12.5.3 Parametrization of the Desired Path.- 12.5.4 Potential Function for Considering Fixed Obstacles.- 12.5.5 The Neural Network Approach.- 12.5.6 Training Phase.- 12.5.7 Results.- A Revision of the Simplex Method.- A.1 Equality Constraints.- A.2 Finding an Initial Solution.- A.3 Inequality Constraints.- B Dynamic Programming and Linear Quadratic Optimal Control.- B.1 LinearQuadratic Problem.- B.2 InfiniteHorizon.- References.
3,913 citations
Book•
16 Aug 1996TL;DR: In this article, a small gain and passivity of input-output maps are discussed. But the authors focus on the Hamiltonian system as passive systems and do not consider the Hamilton-Jacobi Inequalities.
Abstract: 1 Input-Output Stability.- 2 Small-gain and Passivity of Input-Output Maps.- 3 Dissipative Systems Theory.- 4 Hamiltonian Systems as Passive Systems.- 5 Passivity by Feedback.- 6 Factorizations of Nonlinear Systems.- 7 Nonlinear H? Control.- 8 Hamilton-Jacobi Inequalities.
1,909 citations
TL;DR: In this article, the results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field.
Abstract: Previously obtained results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. On the basis of these results a nonlinear analog is obtained of the simplest part of a state-space approach to linear H/sub infinity / control, namely the state feedback H/sub infinity / optimal control problem. Furthermore, the relation with H/sub infinity / control of the linearized system is dealt with. >
1,481 citations
28 Sep 2004
TL;DR: The results of two model-based control techniques applied to an autonomous four-rotor micro helicopter called quadrotor are presented, a classical approach (PID) assumed a simplified dynamics and a modern technique based on a more complete model.
Abstract: The development of miniature flying robots has become a reachable dream, thanks to the new sensing and actuating technologies. Micro VTOL systems represent a useful class of flying robots because of their strong abilities for small-area monitoring and building exploration. In this paper, we present the results of two model-based control techniques applied to an autonomous four-rotor micro helicopter called quadrotor. A classical approach (PID) assumed a simplified dynamics and a modern technique (LQ) based on a more complete model. Various simulations were performed and several tests on the bench validate the control laws. Finally, we present the results of the first test in flight with the helicopter released. These developments are part of the OS4 project in our lab.
1,264 citations