Cooperative Distributed Model Predictive Formation Control of Non-Holonomic Robotic Agents

Rosenfelder, Mario; Ebel, Henrik; Eberhard, Peter

doi:10.1109/mrs50823.2021.9620683

Cited by 11 publications

(17 citation statements)

References 35 publications

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“…Since it holds that w j < 3, it immediately follows from ( 8) that the privileged coordinates read z = y. Illustratively, these coordinates describe the unicycle's position in a rotated frame of reference having its x-axis pointing along the desired orientation d 3 . Note that the resulting privileged coordinates ( 14) match the derivation from the mechanical point of view presented in [18,19]. Finally, the homogeneous nilpotent approximation can be obtained by expanding the control vector fields for the system described in the privileged coordinates, i.e.,…”

Section: Differentially Driven Mobile Robot (Unicycle)mentioning

confidence: 76%

“…Therein, proof and derivation are very technical, without much system theoretic or mechanical interpretation given, leaving little hope to directly generalize the approach to more intricate non-holonomic vehicles. However, in [18], we notice that the setup of the cost function proposed in [26,25] and our generalization to arbitrary, nonzero setpoints suggest a mechanical interpretation based on Lie brackets and directions of non-holonomic constraints.…”

Section: Introductionmentioning

confidence: 83%

“…This intuitive human behavior when parking in parallel does not correspond to a cost-minimal behavior in the Euclidean sense; after all, that one would correspond to a motion made impossible by the non-holonomic constraint. Extensive numerical convergence studies in our previous work show that this interpretation enables us to come up with what seems like an asymptotically stabilizing non-quadratic cost function also for a system more complicated than the differentially driven robot, namely the kinematic car [18]. However, our previous work presents mostly conjectures and empirical evidence and, thus, leaves many open questions regarding the formalization of the relationship between mechanical interpretation and control theory.…”

Section: Introductionmentioning

confidence: 92%

“…It is now evident for which special cases the authors' original suggestion [18] of a direct mechanical interpretation of the cost function, namely that the tailored cost follows from dot products of the state x and the vector fields spanning the Lie algebra evaluated at the setpoint, applies. In case that there is an adapted frame which is an orthogonal basis of T d R nx , it holds that A −T = A in the first transformation step (7) of Bellaïche's algorithm.…”

Section: Tailored Mpc Based On Homogeneous Approximationmentioning

confidence: 99%

“…The key observation made in [18] based on [26,25] is that different exponents are employed for the cost terms, so that, close to the setpoint, the cost function penalizes errors more in those directions that are harder to control, i.e., directions not covered directly by the input vector fields but only by vectors obtained from their Lie brackets. Intuitively, close to the setpoint, this allows the MPC controller to perform more extensive motions into easily controllable directions to compensate smaller deviations in directions that are not directly actuated.…”

Section: Introductionmentioning

confidence: 99%

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Model Predictive Control of Non-Holonomic Vehicles: Beyond Differential-Drive

Rosenfelder¹,

Ebel²,

Krauspenhaar³

et al. 2022

Preprint

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Non-holonomic vehicles are of immense practical value and increasingly subject to automation. However, controlling them accurately, e.g., when parking, is known to be challenging for automatic control methods, including model predictive control (MPC). Combining results from MPC theory and sub-Riemannian geometry in the form of homogeneous nilpotent system approximations, this paper proposes a comprehensive, ready-to-apply design procedure for MPC controllers to steer controllable, driftless nonholonomic vehicles into given setpoints. It can be ascertained that the resulting controllers nominally asymptotically stabilize the setpoint for a large-enough prediction horizon. The design procedure is exemplarily applied to four vehicles, including the kinematic car and a differentially driven mobile robot with up to two trailers. The controllers use a non-quadratic cost function tailored to the non-holonomic kinematics. Novelly, for the considered example vehicles, it is proven that a quadratic cost employed in an otherwise similar controller is insufficient to reliably asymptotically stabilize the closed loop. Since quadratic costs are the conventional choice in control, this highlights the relevance of the findings. To the knowledge of the authors, it is the first time that MPC controllers of the proposed structure are applied to non-holonomic vehicles beyond very simple ones, in particular (partly) on hardware.

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Section: Differentially Driven Mobile Robot (Unicycle)mentioning

confidence: 76%

Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 92%

Section: Tailored Mpc Based On Homogeneous Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Model Predictive Control of Non-Holonomic Vehicles: Beyond Differential-Drive

Rosenfelder¹,

Ebel²,

Krauspenhaar³

et al. 2022

Preprint

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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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