Model predictive control of non-holonomic systems: Beyond differential-drive vehicles

Rosenfelder, Mario; Ebel, Henrik; Krauspenhaar, Jasmin; Eberhard, Peter

doi:10.1016/j.automatica.2023.110972

Cited by 8 publications

(20 citation statements)

References 15 publications

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“…In general, Assumption 8 does not hold and there may not exist any finite horizon N ensuring asymptotic stability when using a quadratic stage cost ℓ (Müller and Worthmann, 2017). Systematic choices of ℓ can be derived using homogeneity (Coron et al, 2020) and non-holonomic vehicles are explored by Worthmann et al (2015); Rosenfelder et al (2023).…”

Section: Cost Controllabilitymentioning

confidence: 99%

“…However, derivation of a sufficiently long horizon N also becomes more challenging and in general a long prediction horizon N may be needed due to the absence of terminal ingredients. Such MPC formulations without terminal ingredients are also particularly popular in robotics experiments with dynamic operation, cf., e.g., Liniger et al (2015); Faulwasser et al (2016);Rosenfelder et al (2023); Romero et al (2022); Rickenbach et al (2023). This important factor is often neglected in discussions regarding benefits and drawbacks of terminal ingredients in MPC, cf.…”

Section: On Terminal Ingredients In Mpcmentioning

confidence: 99%

See 1 more Smart Citation

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

123

133

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In this paper, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set-membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared to robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean-squared point estimate in the objective function the framework ensures finite-gain L2 stability w.r.t. additive disturbances.As a first contribution we derive suitable monotonicity and non-increasing properties on general parameter estimation algorithms and tube/set based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this paper, we provide similar conditions for a tube based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared to state of the art approaches.

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Section: Cost Controllabilitymentioning

confidence: 99%

Section: On Terminal Ingredients In Mpcmentioning

confidence: 99%

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

123

133

View full text Add to dashboard Cite

show abstract

“…As the robot should rotate independently from its translational velocity , the input used to compute (1) is rotated by an angle of about the vertical axis after each cycle unless a new input is received. Without this counter-rotation, the robot would drive arcs, similar to a differential-drive [6] or car-like mobile robot, which would not fully utilize the robot’s omnidirectional capabilities [7]. The custom control software runs on an onboard BeagleBone Blue Linux-based computer with integrated motor drivers.…”

Section: The Omnidirectional Mobile Robotmentioning

confidence: 99%

“…Note that, when a differential-drive or car-like mobile robot is used instead of an omnidirectional mobile robot, some modifications to the cost function (24a) might be necessary to retain some theoretical properties, see [6] for details.…”

Section: Trajectory Tracking Of Periodic Referencesmentioning

confidence: 99%

Exploration-exploitation-based trajectory tracking of mobile robots using Gaussian processes and model predictive control

2023

Self Cite

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Mobile robots are a key component for the automation of many tasks that either require high precision or are deemed too hazardous for human personnel. One of the typical duties for mobile robots in the industrial sector is to perform trajectory tracking, which involves pursuing a specific path through both space and time. In this paper, an iterative learning-based procedure for highly accurate tracking is proposed. This contribution shows how data-based techniques, namely Gaussian process regression, can be used to tailor a motion model to a specific reoccurring reference. The procedure is capable of explorative behavior meaning that the robot automatically explores states around the prescribed trajectory, enriching the data set for learning and increasing the robustness and practical training accuracy. The trade-off between highly accurate tracking and exploration is done automatically by an optimization-based reference generator using a suitable cost function minimizing the posterior variance of the underlying Gaussian process model. While this study focuses on omnidirectional mobile robots, the scheme can be applied to a wide range of mobile robots. The effectiveness of this approach is validated in meaningful real-world experiments on a custom-built omnidirectional mobile robot where it is shown that explorative behavior can outperform purely exploitative approaches.

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“…In the literature [3], a special quartic-quadratic cost function was proven to work specifically for the differential-drive vehicle. More generally, in our recent work [4], a condition is set forward on when quadratic costs do not work for the class of driftless underactuated controllable systems. Moreover, therein, a design procedure applicable to controllable driftless non-holonomic systems is proposed that yields predictive controllers for which there exist finite prediction horizons so that the closed loop is provably asymptotically stable.…”

Section: Introductionmentioning

confidence: 99%

A note on the predictive control of non‐holonomic systems and underactuated vehicles in the presence of drift

Ebel,

Rosenfelder,

Eberhard

2023

Proc Appl Math and Mech

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Motion planning and control of non‐holonomic systems is challenging. Only very recently, it has become clear how model predictive controllers for such systems can be generally furnished in the driftless case, where the key is to design a cost function conforming to the geometry arising from the non‐holonomic constraints. However, in some applications, one cannot neglect drift since the time needed to accelerate is non‐negligible, for example, when operating vehicles with high inertia or at high velocities. Therefore, this contribution extends our previous work on the class of driftless non‐holonomic systems to systems with simple kinds of actuator dynamics that allow to represent the boundedness of acceleration in the model. Moreover, we show in a prototypical example of a simple boat‐like vehicle model that a similar procedure can also work for systems that are not non‐holonomic but still under‐actuated. While the contribution is rather technical in nature, to the knowledge of the authors, it is the first time that MPC controllers with theoretical guarantees are proposed for these kinds of models. Moreover, we expect that the resulting controllers are directly of practical value since even the simpler driftless models are employed successfully in various approaches to motion planning.

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Model predictive control of non-holonomic systems: Beyond differential-drive vehicles

Cited by 8 publications

References 15 publications

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Exploration-exploitation-based trajectory tracking of mobile robots using Gaussian processes and model predictive control

A note on the predictive control of non‐holonomic systems and underactuated vehicles in the presence of drift

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