Optimal, Robust Predictive Control of Nonlinear Systems under Probabilistic Uncertainty using Particles

Blackmore, Lars; Williams, Brian

doi:10.1109/acc.2007.4282699

Cited by 25 publications

(17 citation statements)

References 13 publications

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“…A piecewise linear cost function and a static environment are assumed. This work was extended in [12] to nonlinear systems, using linearization and then applying the same particle method. Again, due to the use of open-loop predictions, the uncertainty of the evolved states grows, and a formalism is needed to incorporate the anticipated future measurements in the planning process.…”

Section: Literature Reviewmentioning

confidence: 99%

“…jointly Gaussian distributed state variables and convert the chance constraints into constraints on the means of the states (e.g., [10,59]), and (ii) evaluate the constraints by Monte Carlo simulation (the state distribution is sampled and the number of samples that violate the deterministic constraint are counted, from which the probability of constraint violation can be approximated (e.g., [8,12]…”

Section: Chance Constraintsmentioning

confidence: 99%

“…As with the OLC approximation to the DP ISI problem, measurements beyond the current stage are ignored in the Open-Loop Receding Horizon Control (OLRHC) approach [9,10,12,36,48,57,59,58,61]. Since it is assumed that no future measurements will be available, the future belief states …”

Section: Open-loop Receding Horizon Controlmentioning

confidence: 99%

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Robotic motion planning in dynamic, cluttered, uncertain environments

Toit

Burdick

2010

2010 IEEE International Conference on Robotics and Automation

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This thesis is concerned with robot motion planning in dynamic, cluttered, and uncertain environments. Successful and efficient robot operation in such environments requires reasoning about the future system evolution and the uncertainty associated with obstacles and moving agents in the environment. Current motion planning strategies ignore future information and are limited by the resulting growth of uncertainty as the system is evolved. This thesis presents an approach that accounts for future information gathering (and the quality of that information) in the planning process.The Partially Closed-Loop Receding Horizon Control approach, introduced in this thesis, is based on Dynamic Programming with imperfect state information. Probabilistic collision constraints, due to the need for obstacle avoidance between the robot and obstacles with uncertain locations and geometries, are developed and imposed. By accounting for the anticipated future information, the uncertainty associated with the system evolution is managed, allowing for greater numbers of moving agents and more complex agent behaviors to be handled. Simulation results demonstrate the benefit of the proposed approach over existing approaches in static and dynamic environments. Complex agent behaviors, including multimodal and interactive agent-robot models, are considered. vi

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Section: Literature Reviewmentioning

confidence: 99%

Section: Chance Constraintsmentioning

confidence: 99%

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Robotic motion planning in dynamic, cluttered, uncertain environments

Toit

Burdick

2010

2010 IEEE International Conference on Robotics and Automation

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“…Similar approach was utilized in [Oldewurtel et al, 2008] for affine input policies. We also mentions related works employing randomized algorithms as in [Batina, 2004, Blackmore and Williams, 2007, Maciejowski et al, 2005. Results on obtaining lower bounds on the value functions of the stochastic optimization problem have been recently reported in [Wang and Boyd, 2009], and a novel stochastic MPC scheme based on the scenario approach has appeared in [Bernardini and Bemporad, 2009].…”

Section: Introductionmentioning

confidence: 99%

Stochastic MPC with Imperfect State Information and Bounded Controls

Hokayem¹,

Cinquemani

Chatterjee³

et al. 2010

UKACC International Conference on CONTROL 2010

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This paper addresses the problem of output feedback Model Predictive Control for stochastic linear systems, with hard and soft constraints on the control inputs as well as soft constraints on the state. We use the so-called purified outputs along with a suitable nonlinear control policy and show that the resulting optimization program is convex. We also show how the proposed method can be applied in a receding horizon fashion. Contrary to the state feedback case, the receding horizon implementation in the output feedback case requires the update of several optimization parameters and the recursive computation of the conditional probability densities of the state given the previous measurements. Algorithms for performing these tasks are developed.

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“…[2], [3], and [4]. Therefore, all disturbances affecting the system are described by random variables characterized by the underlying probability density functions.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Model Predictive Control considering stochastic and systematic uncertainties with sets of densities

Hekler

Lyons

Noack

et al. 2010

2010 IEEE International Conference on Control Applications

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Abstract-In Model Predictive Control, the quality of control is highly dependent upon the model of the system under control. Therefore, a precise deterministic model is desirable. However, in real-world applications, modeling accuracy is typically limited and systems are generally affected by disturbances. Hence, it is important to systematically consider these uncertainties and to model them correctly. In this paper, we present a novel Nonlinear Model Predictive Control method for systems affected by two different types of perturbations that are modeled as being either stochastic or unknown but bounded quantities. We derive a formal generalization of the Nonlinear Model Predictive Control principle for considering both types of uncertainties simultaneously, which is achieved by using sets of probability densities. In doing so, a more robust and reliable control is obtained. The capabilities and benefits of our approach are demonstrated in real-world experiments with miniature walking robots.

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Optimal, Robust Predictive Control of Nonlinear Systems under Probabilistic Uncertainty using Particles

Cited by 25 publications

References 13 publications

Robotic motion planning in dynamic, cluttered, uncertain environments

Robotic motion planning in dynamic, cluttered, uncertain environments

Stochastic MPC with Imperfect State Information and Bounded Controls

Nonlinear Model Predictive Control considering stochastic and systematic uncertainties with sets of densities

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