From linear to nonlinear MPC: bridging the gap via the real-time iteration

Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization iterations are distributed over time by maintaining a running solution estimate for the optimal control problem and updating it at each sampling instant. The resulting controller can be viewed as a dynamic compensator which is placed in closedloop with the plant. This paper presents a general systems theoretic analysis framework for time distributed optimization. The coupled plant-optimizer system is analyzed using input-to-state stability concepts and sufficient conditions for stability and constraint satisfaction are derived. When applied to time distributed sequential quadratic programming, the framework significantly extends the existing theoretical analysis for the real-time iteration scheme. Numerical simulations are presented that demonstrate the effectiveness of the scheme.

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“…Next, assuming (20) holds for k − 1 and recalling that a( ) < 1, we can apply (29) at iteration k to show that…”

Section: Liss Of Time-distributed Optimizationmentioning

confidence: 99%

Time-distributed optimization for real-time model predictive control: Stability, robustness, and constraint satisfaction

2020

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“…Here, we only give a brief summary of the methodology. For any further details we refer the reader to [17], [18]. Following the SQP approach we linearize the system model with a previous guess (x g k ,ū g k ) and use any numerical discretization scheme to obtain the sensitivities…”

Section: Problem Statementmentioning

confidence: 99%

“…At every sampling instant, Problem (3) is solved, and only the first control input u 0 is applied to the system. However, the solutionsx andū are used to update the guesses (x g k ,ū g k ) = (x k+1 ,ū k+1 ), where k spans the prediction horizon, following the shifting approach in [17], [18].…”

Section: Problem Statementmentioning

confidence: 99%

Real-Time Constrained Trajectory Planning and Vehicle Control for Proactive Autonomous Driving With Road Users

Batkovic

Zanon

Ali

et al. 2019

2019 18th European Control Conference (ECC)

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For motion planning and control of autonomous vehicles to be proactive and safe, pedestrians' and other road users' motions must be considered. In this paper, we present a vehicle motion planning and control framework, based on Model Predictive Control, accounting for moving obstacles. Measured pedestrian states are fed into a prediction layer which translates each pedestrians' predicted motion into constraints for the MPC problem.Simulations and experimental validation were performed with simulated crossing pedestrians to show the performance of the framework. Experimental results show that the controller is stable even under significant input delays, while still maintaining very low computational times. In addition, real pedestrian data was used to further validate the developed framework in simulations.

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“…To address these problems, we propose the Sampling Augmented Adaptive RTI (SAA-RTI) algorithm, which decomposes the method of solving (2) into two distinct steps: feasible trajectory planning and trajectory optimization. The approach augments the existing RTI-SQP [16] strategy with state space sampling [10]. The horizon and sampling time for both trajectory planning and optimization steps are chosen as N and T s respectively, as in (2).…”

Section: Problem Formulationmentioning

confidence: 99%

“…However, solving (2) locally around the feasible but suboptimal trajectoryX ⋆ t can be done efficiently using a convex Quadratic Program (QP) approximation. We obtain the QP approximation of (2) through the linear time varying model predictive control paradigm [16]. At any given time t, the model and constraints in (2) are linearized aroundX ⋆ t .…”

Section: B Trajectory Optimizationmentioning

confidence: 99%

Adaptive Trajectory Planning and optimization at Limits of Handling

Svensson

Bujarbaruah

Kapania

et al. 2019

2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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In this paper, we tackle the problem of trajectory planning and control of a vehicle under locally varying traction limitations, in the presence of suddenly appearing obstacles. We employ concepts from adaptive model predictive control for run-time adaptation of tire force constraints that are imposed by local traction conditions. To solve the resulting optimization problem for real-time control synthesis with such time varying constraints, we propose a novel numerical scheme based on Real Time Iteration Sequential Quadratic Programming (RTI-SQP), which we call Sampling Augmented Adaptive RTI (SAA-RTI). Sampling augmentation of conventional RTI-SQP provides additional feasible candidate trajectories for warmstarting the optimization procedure. Thus, the proposed SAA-RTI algorithm enables real time constraint adaptation and reduces sensitivity to local minima. Through extensive numerical simulations we demonstrate that our method increases the vehicle's capacity to avoid accidents in scenarios with unanticipated obstacles and locally varying traction, compared to equivalent non-adaptive control schemes and traditional planning and tracking approaches.

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From linear to nonlinear MPC: bridging the gap via the real-time iteration

Cited by 234 publications

References 39 publications

Time-distributed optimization for real-time model predictive control: Stability, robustness, and constraint satisfaction

Time-distributed optimization for real-time model predictive control: Stability, robustness, and constraint satisfaction

Real-Time Constrained Trajectory Planning and Vehicle Control for Proactive Autonomous Driving With Road Users

Adaptive Trajectory Planning and optimization at Limits of Handling

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