Reference Governors

Welcome: Victor

Anonymous — Tue, 16 Aug 2022 06:00:00 +0000

Welcome: Victor Anonymous (not verified) Tue, 08/16/2022 - 00:00

It is my pleasure to welcome Victor Freire Melgizo as the newest member of the ROCC lab.

Victor is joining us from the University of Wisconsin Madison, where he designed and implemented path planning algorithms and control barrier functions on UAVs as part of his master's thesis. Here in Boulder, Victor will be investigating possible ties and synergies between Control Barrier Functions and Reference Governors.

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Computation of Input-Saturated Output-Admissible Sets

Anonymous — Mon, 20 Jun 2022 19:39:47 +0000

Computation of Input-Saturated Output-Admissible Sets Anonymous (not verified) Mon, 06/20/2022 - 13:39

Yaashia Gautam , Marco M. Nicotra

Maximal Output Admissible Sets (MOAS) are the set of all initial states and references such that the output response is always constraint admissible. Introduced in [1], the MOAS holds a special place in constrained control theory and is often used in strategies such as Model Predictive Control and Reference Governors to guarantee constraint satisfaction.

As desirable as it is to find the Maximal Output Admissible Set, it is often very difficult to compute it in closed form. Depending on the system and the constraints, the MOAS may not even be convex, bounded, closed, etc. For discrete-time LTI systems subject to linear state and input constraints, [1] provides an algorithm for computing the MOAS. In our latest paper [2], we show that it is possible to compute a provably larger set by treating input saturations as a nonlinearity as opposed to a constraint.

This intuition gives rise to the Input-Saturated Output-Admissible Set (ISOAS), which is the MOAS for systems with a saturated control law.

INPUT-SATURATED OUTPUT-ADMISSIBLE SETS

The traditional MOAS for an LT-DTI system is computed by using a prestabilizing linear controller. Since the MOAS depends on the prestabilizing controller, it is possible to find a larger set (ISOAS) by using a saturated control law, rather than a linear one. The computation of ISOAS is done by leveraging the piecewise affine nature of the prestabilized system. We partition the state\reference space into three regions: Non-Saturated, Upper-Saturated, and Lower-Saturated.

The above animation shows the step-by-step computation of the ISOAS for a linear system with output constraints and input saturation. The specific system is described in [2, Section VI.C]. The Non-Saturated Region is shown in green, whereas the Upper and Lower-Saturated Regions are shown in yellow. The computation process of the ISOAS is as follows:

First, the constraints are propagated within each region, causing each polyhedron to evolve independently from the others;
Second, the constraints are shared between regions, thereby causing each reagion to be affected by the others.

This process is repeated until the final ISOAS is computed.

EROSION PREVENTION

One of the difficulties in the computation of ISOAS during the constraint sharing phase of the computation algorithm is that the constraints for one region might be harmful or redundant for the other one. To solve this issue, we introduced a erosion prevention step in our algorithm, whereby sharing constraints between regions is done only after eliminating any redundant constraints.

The above animations show the difference between the computation of the ISOAS with and without erosion prevention for the example detailed in [2, Section VI.A]. The first image has erosion prevention, while the second does not. As can be seen, the first set is both bigger and faster to compute than the second set.

EMPTY SET PREVENTION

Another complication that can arise in the saturated regions is that the constraint propagation may lead to an empty set if performed incorrectly. To solve this issue, we introduce the concept of empty set prevention, whereby we omit any constraint such that the 1-step violation requirement is fully redundant with respect to the 2-step violation requirements. Below is an example of computation of the ISOAS with and without empty set prevention algorithm for the system featured in [2, Section VI.B].

The first animation shows the computation with the empty set prevention algorithm, while the second does not have that feature. It can be observed that the saturated regions in the second animation eventually reduce to an empty set and the computation of the ISOAS can not continue further. However, the first computation shows the actual ISOAS, which is a polyhedron with non-empty saturated regions.

REFERENCES

[1] E. G. Gilbert and K. T. Tan, “Linear systems with state and control constraints: The theory and application of maximal output admissible sets,” IEEE Transactions on Automatic Control, vol. 36, no. 9, pp. 1008–1020, 1991.

[2] Y. Gautam and M. M. Nicotra, "Finite-Time Computation of Polyhedral Input-Saturated Output-Admissible Sets", IEEE Transactions on Automatic Control (under review)

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ERG for Safe Human Robot Interaction

Anonymous — Mon, 18 Jan 2021 07:00:00 +0000

ERG for Safe Human Robot Interaction Anonymous (not verified) Mon, 01/18/2021 - 00:00

K. Merckaert , B. Convens , C.-J. Wu , A. Roncone , M.M. Nicotra , B. Vanderborght

[video:https://www.youtube.com/watch?v=UzbhMzcKSbE&feature=youtu.be]

This video is represents a significant milestone in Kelly Merckaert's research on safe Human-Robot Interaction. The control laws used in these experiments were developed during Kelly's 6-month research internship at CU Boulder, although their implementation on a physical robot had to wait for her to return to the BruBotics research center in Brussels. The robot is able to operate safely thanks to the use of an Explicit Reference Governor, which guarantees constraint satisfaction while only having a computational footprint of ~1ms.

This experiment is a significant milestone for the development of computationally inexpensive strategies for the Constrained Control for Safe Human-Robot Interaction, and doubles up as a nontrivial validation of the Explicit Reference Governor framework in a highly non-convex setting.

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ERG for Robotic Manipulators

Anonymous — Mon, 02 Nov 2020 07:00:00 +0000

ERG for Robotic Manipulators Anonymous (not verified) Mon, 11/02/2020 - 00:00

K. Merckaert , B. Convens , I. El Makrini , G. Van der Perre , M.M. Nicotra , B. Vanderborght

[video:https://www.youtube.com/watch?v=VAYV9x25da4&feature=youtu.be]

This video, titled "The Explicit Reference Governor for Real-Time Safe Control of a Robotic Manipulator" was presented at the 2020 IROS Workshop: Bringing constraint-based robot programming to real-world applications. These experimental results showcase the interest in implementing an Explicit Reference Governor for real-time constratined control of robotic manipulators and is the first step towards Constrained Control for Safe Human-Robot Interaction.

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Distributed ERG for Crazyswarm Control

Anonymous — Fri, 28 Feb 2020 07:00:00 +0000

Distributed ERG for Crazyswarm Control Anonymous (not verified) Fri, 02/28/2020 - 00:00

B. Convens , K. Merckaert , B. Vanderborght , M.M. Nicotra

[video:https://www.youtube.com/watch?v=PsSrDJSchFM&feature=youtu.be]

This is the support video for the article "A Distributed Explicit Reference Governor for the Safe On-Board Control of a Nano-Quadrotor Swarm" submitted to IEEE Transactions on Robotics. The paper summarizes the work done by Bryan Convens during his six-month research stay at CU Boulder. These experiment represent a significant development in the formulation of on-board real-time strategies for the Formation Control of Multiple Unmanned Aerial Vehicles, and doubles up as an extension of the Explicit Reference Governor framework to distributed systems.

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Welcome: Terry

Anonymous — Tue, 20 Aug 2019 06:00:00 +0000

Welcome: Terry Anonymous (not verified) Tue, 08/20/2019 - 00:00

Terrence Skibik will be joining the ROCC lab to pursue his PhD in Systems and Control.

I met Terry at ACC '18 (and again at CDC '18), where he was presenting the results of his undergraduate research project. He made a lasting impression, so I was very happy when he opted to join our group to continue his graduate studies.

Here in CU he will be working on the development of a Real-Time Iteration Governor for Model Predictive Control, which is loosely connected with what he did in his undergraduate research.

I wish him the best of luck for this upcoming journey.

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Distributed ERG for Crazyswarm Control

Anonymous — Wed, 31 Jul 2019 06:00:00 +0000

Distributed ERG for Crazyswarm Control Anonymous (not verified) Wed, 07/31/2019 - 00:00

B. Convens , K. Merckaert , M.M. Nicotra , B. Vanderborght

[video:https://youtu.be/J9-RmQb_8v8]

The video is one of the final experiments performed by Bryan Convens at the end of his six-month stay at CU Boulder. During his research stay, Bryan developed a Distributed ERG add-on to the Crazyswarm framework. The addon enables crazyflies to perform real-time formation changes without requiring any form of off-line trajectory planning. The extremely limited computational footprint of the ERG ensures that the code can be implemented onboard each Crazyflie, thus enabling the swarm to reach the desired setpoint without violating constraints (e.g. actuator saturation, external obstacle avoidance, inter-agent collision avoidance).

The proposed method demonstrates the effectiveness of the ERG framework in scenarios where the controlled system has very limited computational capabilities.

This experiment is a significant milestone for the development of computationally inexpensive strategies for the Formation Control of Multiple Unmanned Aerial Vehicles, and doubles up as a nontrivial validation of the Explicit Reference Governor framework.

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ERG-Toolbox Released!

Anonymous — Thu, 06 Sep 2018 06:00:00 +0000

ERG-Toolbox Released! Anonymous (not verified) Thu, 09/06/2018 - 00:00

A. Cotorruelo Jiménez , E. Garone , D. Limón , M.M. Nicotra

It is my pleasure to announce the release of the Explicit Reference Governor Toolbox (ERGT), now available on GitHub.

At the present stage, this MATLAB toolbox can be used to systematically design an add-on unit for the constrained control of linear systems subject to the union and intersection of linear constraints. The development of the toolbox is being spearheaded by the Department of Control Engineering and System Analysis at the Université Libre de Bruxelles, where I did my PhD and with whom I continue to collaborate.

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