A Method for Reducing the Complexity of Model Predictive Control in Robotics Applications

Muehlebach, Michael; D’Andrea, Raffaello

doi:10.1109/lra.2019.2907411

Cited by 8 publications

(3 citation statements)

References 28 publications

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“…Recently, parameterization methods have begun to gain attention a way to reduce the complexity of MPC. In [30] both inputs and states are parameterized, taking advantage of known properties. In [31] orthogonal basis polynomials are explored as a form of parameterization for MPC, while in [32] B splines are used to represent states and inputs in an MPC optimization.…”

Section: B Parallelized and Parameterized Mpcmentioning

confidence: 99%

Parameterized and GPU-Parallelized Real-Time Model Predictive Control for High Degree of Freedom Robots

Hyatt,

Williams,

Killpack

2020

Preprint

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This work presents and evaluates a novel input parameterization method which improves the tractability of model predictive control (MPC) for high degree of freedom (DoF) robots. Experimental results demonstrate that by parameterizing the input trajectory more than three quarters of the optimization variables used in traditional MPC can be eliminated with practically no effect on system performance. This parameterization also leads to trajectories which are more conservative, producing less overshoot in underdamped systems with modeling error. In this paper we present two MPC solution methods that make use of this parameterization. The first uses a convex solver, and the second makes use of parallel computing on a graphics processing unit (GPU). We show that both approaches drastically reduce solve times for large DoF, long horizon MPC problems allowing solutions at real-time rates. Through simulation and hardware experiments, we show that the parameterized convex solver MPC has faster solve times than traditional MPC for high DoF cases while still achieving similar performance. For the GPU-based MPC solution method, we use an evolutionary algorithm and that we call Evolutionary MPC (EMPC). EMPC is shown to have even faster solve times for high DoF systems. Solve times for EMPC are shown to decrease even further through the use of a more powerful GPU. This suggests that parallelized MPC methods will become even more advantageous with the improvement and prevalence of GPU technology.

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Section: B Parallelized and Parameterized Mpcmentioning

confidence: 99%

Parameterized and GPU-Parallelized Real-Time Model Predictive Control for High Degree of Freedom Robots

Hyatt,

Williams,

Killpack

2020

Preprint

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“…The use of Laguerre polynomials to parameterize the input sequence was investigated in [40], which also examines other choices of orthogonal functions. Laguerre polynomials were also used to parameterize both the input and state sequences [41], in a way that these are invariant to time shifts and hence amenable for warm-starting the new optimization problem with the shifted solution of the previous problem. Note that the use of basis functions as in ( 7) becomes necessary when the free optimization variables s have no system theoretical meaning, such as in case the QR method described in Section V-A is used to eliminate equality constraints, for which there is no direct and intuitive method like blocking moves to reduce the number of free variables, unless blockingmoves are introduced before removing equality constraints.…”

Section: B Reduction Of the Number Of Variablesmentioning

confidence: 99%

Reduction of the Number of Variables in Parametric Constrained Least-Squares Problems

Bemporad¹,

Cimini²

2020

Preprint

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For linearly constrained least-squares problems that depend on a vector of parameters, this paper proposes techniques for reducing the number of involved optimization variables. After first eliminating equality constraints in a numerically robust way by QR factorization, we propose a technique based on singular value decomposition (SVD) and unsupervised learning, that we call K-SVD, and neural classifiers to automatically partition the set of parameter vectors in K nonlinear regions in which the original problem is approximated by using a smaller set of variables. For the special case of parametric constrained least-squares problems that arise from model predictive control (MPC) formulations, we propose a novel and very efficient QR factorization method for equality constraint elimination. Together with SVD or K-SVD, the method provides a numerically robust alternative to standard condensing and move blocking, and to other complexity reduction methods for MPC based on basis functions. We show the good performance of the proposed techniques in numerical tests and in a linearized MPC problem of a nonlinear benchmark process.

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“…Besides, it is one speciality where Predictive Control has found growth in many aspects. Recent works are dedicated to the trajectory tracking and to reduce the complexity of the robotics applications [50], [51]. Meanwhile, in the field of civil engineering, many Predictive Control approaches has been suggested.…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

Design of a hysteresis predictive control strategy with engineering application cases

Ponce de León Puig

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This doctoral thesis exposes the development of a redesigned Predictive Control strategy that uses hysteresis to improve the performance of the controlled systems in different fields of application. The approach may use one of the three hysteresis models presented in this thesis. Moreover, the hysteresis may be used as a modulation stage or as a reference trajectory generator. The first step in the methodology of this research will be to validate the hysteresis dynamic model that will be used within the control scheme. Due to the three exposed hysteresis models have the same constitution , it is assumed that the test of one is enough to guarantee the validation of the other two hysteresis systems. This validation consists on implementing the hysteresis model in an experimental platform to confirm that the model is indeed feasible. Later, it will be seen that this application is within the scope of renewable energies. Once the hysteresis model is validated, the proposed strategy is developed. This is an Adaptive-Predictive control scheme with a modulation stage for the control signal. This stage employs hysteresis to improve the functioning of the adaptive phase and in general the entire closed-loop performance. lt will be shown how the use of this modulation scenario salves the parametric drift problem commonly present in some adaptive based controlled systems. Additionally, a fault detection system within the Adaptive-Predictive control scheme is also proposed and validated through a numerical simulation. Furthermore, it will be seen how the hysteresis also can be used as a model to generate the reference trajectory needed to accomplish the control objective. Finally, the proposed strategy is implemented in a varied set of control systems to validate it. These control systems are: a nonlinear Van der Poi oscillator, a nonlinear base-isolated system, a DC-DC buck converter, and a single-phase inverter. Esta tesis doctoral expone el desarrollo de una estrategia de Control Predictivo rediseñada que utiliza histéresis para mejorar el rendimiento de los sistemas controlados en diferentes campos de aplicación. Este esquema de control puede utilizar uno de los tres sistemas de histéresis presentados en esta tesis. Además, la histéresis se puede utilizar como etapa de modulación o como generador de trayectorias de referencia. El primer paso en la metodología de esta investigación será validar el modelo dinámico de histéresis que se utilizará dentro del esquema de control. Debido a que los tres modelos de histéresis expuestos tienen la misma constitución, se asume que la prueba de uno es suficiente para garantizar la validación de los otros dos modelos de histéresis. Esta validación consiste en implementar el modelo de histéresis en una plataforma experimental para confirmar que este es realmente factible. Posteriormente, se verá que esta aplicación está dentro del ámbito de las energias renovables. Una vez validado el modelo de histéresis, se desarrolla la estrategia propuesta. Es decir, un esquema de control Adaptativo-Predictivo con una etapa de modulación para la señal de control. Esta etapa emplea histéresis para mejorar el funcionamiento de la fase adaptativa y, en general, de todo el rendimiento del sistema en lazo cerrado. Se mostrará cómo el uso de este etapa de modulación resuelve el problema de la deriva paramétrica comúnmente presente en algunos sistemas basados en control adaptativo. Adicionalmente, también se propone y valida un sistema de detección de fallos dentro del esquema de control Adaptativo-Predictivo mediante una simulación numérica. Además, se verá cómo la histéresis también se puede utilitzar como modelo para generar la trayectoria de referencia necesaria para lograr el objetivo de control. Finalmente, la estrategia propuesta se implementa en un conjunto variado de sistemas de control para validarla. Estos sistemes de control son: un oscilador Van der Poi no lineal, un sistema no lineal de base aisladora, un convertidor Buck DC-DC y un inversor monofásico.

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A Method for Reducing the Complexity of Model Predictive Control in Robotics Applications

Cited by 8 publications

References 28 publications

Parameterized and GPU-Parallelized Real-Time Model Predictive Control for High Degree of Freedom Robots

Parameterized and GPU-Parallelized Real-Time Model Predictive Control for High Degree of Freedom Robots

Reduction of the Number of Variables in Parametric Constrained Least-Squares Problems

Design of a hysteresis predictive control strategy with engineering application cases

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