Jekyll2021-12-09T19:50:14+00:00http://www.rkcosner.com/feed.xmlRyan CosnerRyan Cosner's Personal WebsiteRyan CosnerMeasure Zero2021-09-29T12:35:00+00:002021-09-29T12:35:00+00:00http://www.rkcosner.com/errata/Measure-Zero<p>Millenial Pop/Rock Bands</p>
<p><strong>Members</strong>: Robby Gray (Vocals, Keys), Ryan Cosner (Guitar), Berthy Fend (Guitar), Mason McGill (Bass), Drummer TBD.</p>
<p>Thanks to Nikhil for some great times! Good luck in the bay area! We’ll miss your drumming skills!</p>
<p>Current Covers:</p>
<ul>
<li>Cough Syrup - Young the Giant</li>
<li>1979 - Smashing Pumpkins</li>
<li>All These Things I’ve Done - the Killers</li>
<li>Reptilia - the Strokes</li>
<li>Karma Police - Radiohead</li>
<li>Take Me Out - Franz Ferdinand</li>
</ul>Ryan CosnerMillenial Pop/Rock BandsSouthland Tri2021-09-29T12:35:00+00:002021-09-29T12:35:00+00:00http://www.rkcosner.com/errata/Southland-Tri<p>Caltech-USC-UCLA collaboration to put on 3 virtual triathlons.</p>
<iframe src="https://drive.google.com/file/d/18m2vaOU1eNOcsRM0uhvsDSWGY7Se3pBW/preview" width="640" height="480" allow="autoplay"></iframe>
<iframe src="https://drive.google.com/file/d/15_PNN3xtC0o0wSSu9kL5T20buc8VOl_s/preview" width="640" height="480" allow="autoplay"></iframe>
<iframe src="https://drive.google.com/file/d/1TszGXsAAI51PsXNvNTLtTU3w9aqw6xMQ/preview" width="640" height="480" allow="autoplay"></iframe>
<iframe src="https://drive.google.com/file/d/1UeRE0cIjMeXqr3FPVlkS2m-uNOFlyPkO/preview" width="640" height="480" allow="autoplay"></iframe>Ryan CosnerCaltech-USC-UCLA collaboration to put on 3 virtual triathlons.Caltech Tri2021-09-29T12:35:00+00:002021-09-29T12:35:00+00:00http://www.rkcosner.com/errata/Caltech-Tri<p>Caltech Triathlon Team.</p>
<p><img src="/assets/images/maddies_clear.png" style="width:500px;" /></p>Ryan CosnerCaltech Triathlon Team.ICRA 2022: Self-Supervised Online Learning for Safety-Critical Control using Stereo Vision2021-09-14T12:35:00+00:002021-09-14T12:35:00+00:00http://www.rkcosner.com/research/OnlineStereo<p><strong>Ryan K. Cosner<sup>*</sup></strong>, Ivan D. Jimenez Rodriguez<sup>*</sup>, Tamas G. Molnar, Wyatt Ubellacker, Yisong Yue, Aaron D. Ames, Katherine L. Bouman.</p>
<hr />
<p><strong>Abstract</strong>: With the increasing prevalence of complex vision sensing methods for use in obstacle identification and state estimation, characterizing environment-dependent measurement errors has become a difficult and essential part of modern robotics.
This paper presents a self-supervised learning approach to safety-critical control. In particular, the uncertainty associated with stereo vision is estimated, and adapted online to new visual environments, wherein this estimate is leveraged in a safety-critical controller in a robust fashion.
To this end, we propose an algorithm that exploits the structure of stereo-vision to learn an uncertainty estimate without the need for ground-truth data. We then robustify existing Control Barrier Function-based controllers to provide safety in the presence of this uncertainty estimate. We demonstrate the efficacy of our method on a quadrupedal robot in a variety of environments. When not using our method safety is violated. With offline training alone we observe the robot is safe, but overly-conservative. With our online method the quadruped remains safe and conservatism is reduced.</p>
<iframe src="https://player.vimeo.com/video/605281037?h=28fb476545" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen=""></iframe>Ryan CosnerRyan K. Cosner*, Ivan D. Jimenez Rodriguez*, Tamas G. Molnar, Wyatt Ubellacker, Yisong Yue, Aaron D. Ames, Katherine L. Bouman. Abstract: With the increasing prevalence of complex vision sensing methods for use in obstacle identification and state estimation, characterizing environment-dependent measurement errors has become a difficult and essential part of modern robotics. This paper presents a self-supervised learning approach to safety-critical control. In particular, the uncertainty associated with stereo vision is estimated, and adapted online to new visual environments, wherein this estimate is leveraged in a safety-critical controller in a robust fashion. To this end, we propose an algorithm that exploits the structure of stereo-vision to learn an uncertainty estimate without the need for ground-truth data. We then robustify existing Control Barrier Function-based controllers to provide safety in the presence of this uncertainty estimate. We demonstrate the efficacy of our method on a quadrupedal robot in a variety of environments. When not using our method safety is violated. With offline training alone we observe the robot is safe, but overly-conservative. With our online method the quadruped remains safe and conservatism is reduced.ICRA 2022: Enforcing Motion Primitive Transitions via Flow-Control Barrier Functions2021-09-13T12:35:00+00:002021-09-13T12:35:00+00:00http://www.rkcosner.com/research/FlowCBF<p>Wyatt Ubellacker, <strong>Ryan K. Cosner</strong>, Tamas G. Molnar, Andrew W. Singletary, Aaron D. Ames.</p>
<hr />
<p><strong>Abstract</strong>: Transitions between individual dynamic primitive behaviors, termed “motion primitives,” play an essential role in realizing complex dynamic behaviors on robotic systems.
This paper considers the flow, φ<sub>t</sub>(x), under the action of a “primitive” control law as a means for determining which motion primitives can be transitioned between.
To this end, it is taken into account that state uncertainty and modelling error present on
real-world systems can result in unsafe deviations from the desired behavior. To
combat unsafe behavior, a natural method is to enforce safety through the use of
a <em>control barrier function</em> (CBF) to render a safe set forward invariant. This paper
applies this concept to the flow of the system, and introduces a <em>flow-control barrier function</em>, (φ-CBF), as a minimally invasive filter to augment a
nominal control law and provide input-to-state safety to a set over some
finite time T. This method enforces desired transition behavior even in
presence of uncertainties. The efficacy of the flow-control barrier function approach is
experimentally demonstrated on a quadrupedal robot wherein case-study transitions are considered on a variety of terrains.</p>
<p>This is work performed in collaboration with Sarah Dean and Ben Recht (UC Berkeley) and Andrew Taylor and Aaron Ames (Caltech). It was originally published at the 2020 Conference on Robotic Learning. The extended publication can be found <a href="https://arxiv.org/pdf/2010.16001.pdf">here</a>.</p>
<p>Below is a simplified version of the paper meant for a general audience. (This one’s for you mom!)</p>
<h1 id="introduction">Introduction</h1>
<p>Safety is really important, but most of our methods of assuring safety really on highly accurate system measurements. We explored the problem of ensuring safety despite the measurement errors. We apply our solution to a simulated segway system with a camera-in-the-loop sensor.</p>
<h1 id="background">Background</h1>
<p>When designing a system we often require that the final design is “safe”. But what exactly does it mean to be safe? For our purposes we define a safe set as a region of space where our system is considered safe. Like an autonomous vehicle is safe if it’s one the road and unsafe if it’s not on the road. More precisely, we say that a system is safe if that safe set is <em>invariant</em>.</p>
<blockquote>
<p><strong>Safety (Invariance)</strong>: A system is safe if starting in the safe set implies that it will stay in the safe set.</p>
</blockquote>
<p>To ensure this type of safety we consider the dynamics of the system:</p>
<center>
$$\dot{\mathbf{x}} = \mathbf{f}(\mathbf{x}) + \mathbf{g}(\mathbf{x})\mathbf{u}$$
</center>
<p>and a safe set defined as a 0-superlevel set of a continuously differentiable safety function \(h\) (aka places where \(h(\mathbf{x})>0\)).</p>
<p>This function \(h\) is a <strong>Control Barrier Function</strong> if there exists inputs such that:</p>
<center>
$$\dot{h}( \mathbf{x}, \mathbf{u}) \geq - \alpha(h(\mathbf{x})).$$
</center>
<p>When this inequality is ensured, the system is guaranteed to be safe (Thrm 1).</p>
<h1 id="new-theory-measurement-robust-control-barrier-functions">New Theory: Measurement-Robust Control Barrier Functions</h1>
<p>Often when working with real systems we can’t measure things exactly, but Control Barrier Functions incorporate the current value of \(\mathbf{x}\). In this work we found a way of extending existing CBF theory to ensure that the system remains safe even despite thesse measurement errors.</p>
<p>The CBF \(h\) is <strong>Measurement Robust</strong> if there exists a controller that satisfies the constraint:</p>
<center>
$$\dot{h}(\hat{\mathbf{x}},\mathbf{u}) - \epsilon (\mathfrak{L}_{L_fh} + \mathfrak{L}_{\alpha \circ h} + \mathfrak{L}_{L_gh} ||\mathbf{u}||_2) \geq - \alpha ( h (\hat{\mathbf{x}}))$$
</center>
<p>The difference between this Meausrement Robust CBF condition and the standard CBF condition is the addition of the term:</p>
<center>
$$-\epsilon (\mathfrak{L}_{L_fh} + \mathfrak{L}_{\alpha \circ h} + \mathfrak{L}_{L_gh} ||\mathbf{u}||_2) $$
</center>
<p>Here \(\epsilon\) is represents how bad our measurement is and the \(\mathfrak{L}\) terms represent how “smooth” our dynamics are. Intuitively, if the dynamics are really “smooth” then small measurement errors will have little effect, but if the dynamics aren’t smooth and change really quickly then small measurement errors can result in large mispredictions of the system’s behavior.</p>
<h1 id="learning-for-measurement-model-uncertainty-reduction">Learning for Measurement Model Uncertainty Reduction</h1>
<p>Because the input, \(\mathbf{u}\), appears in this smoothed term, it is possible that no inputs exist that ensure safety. In particular, our formulation implies that if the following condition does not hold, then it is impossible to render the system safe:</p>
<center>
$$\epsilon \leq \textrm{max}\left\{ \frac{||L_gh(\hat{\mathbf{x})}||_2}{\mathfrak{L}_{L_gh}}, \frac{L_fh(\hat{\mathbf{x}}) + \alpha(h(\hat{mathbf{x}}))}{\mathfrak{L_fh} + \mathfrak{L}_{\alpha\circ h}} \right\}$$.
</center>
<p>In the context of machine learning, this inequality suggests the use of a sampling scheme that will ensure that the measurement error never reaches an unsafe level.</p>
<h1 id="simulation-results">Simulation Results</h1>
<p>Due to Covid19 restrictions, the experiments for this work were performed exclusively in simulation. They were performed using on a simulated Segway. The system was considered safe as long as it remained upright within a certain angle window.</p>
<center>
<img src="/assets/images/segway_sim.png" alt="segway_sim" style="width:300px;height:360px;" />
</center>
<p>Two types of errors were considered: the worst case error synthetically added to the measurement and the error found when measuring the system using a learned model which estimated the position based on camera data.</p>
<p>In both cases the standard CBF controller failed to ensure safety and the MRCBF controller succeeded.</p>Ryan CosnerWyatt Ubellacker, Ryan K. Cosner, Tamas G. Molnar, Andrew W. Singletary, Aaron D. Ames. Abstract: Transitions between individual dynamic primitive behaviors, termed “motion primitives,” play an essential role in realizing complex dynamic behaviors on robotic systems. This paper considers the flow, φt(x), under the action of a “primitive” control law as a means for determining which motion primitives can be transitioned between. To this end, it is taken into account that state uncertainty and modelling error present on real-world systems can result in unsafe deviations from the desired behavior. To combat unsafe behavior, a natural method is to enforce safety through the use of a control barrier function (CBF) to render a safe set forward invariant. This paper applies this concept to the flow of the system, and introduces a flow-control barrier function, (φ-CBF), as a minimally invasive filter to augment a nominal control law and provide input-to-state safety to a set over some finite time T. This method enforces desired transition behavior even in presence of uncertainties. The efficacy of the flow-control barrier function approach is experimentally demonstrated on a quadrupedal robot wherein case-study transitions are considered on a variety of terrains.LCSS 2022: A Constructive Method for Designing Safe Multirate Controllers for Differentially-Flat Systems2021-09-12T12:35:00+00:002021-09-12T12:35:00+00:00http://www.rkcosner.com/research/Unicycle<p>Devansh R. Agrawal<sup>*</sup>, Hardik Parwana, <strong>Ryan K. Cosner<sup>*</sup></strong>, Ugo Rosolia, Aaron D. Ames, Dmitra Panagou.</p>
<hr />
<p><strong>Abstract</strong>: We present a multi-rate control architecture that leverages fundamental properties of differential flatness to synthesize controllers for safety-critical nonlinear dynamical systems subject to input constraints. We propose a two-layer architecture, where the high-level generates reference trajectories using a linear Model Predictive Controller, and the low-level tracks this reference using a feedback controller. The novelty lies in how we couple these layers, to achieve formal guarantees on recursive feasibility of the MPC problem, and safety of the nonlinear system. Furthermore, using differential-flatness, we provide a constructive means to synthesize the multi-rate controller, thereby removing the need to search for suitable Lyapunov or barrier functions, or to approximately linearize/discretize nonlinear dynamics. We show the synthesized controller is a convex optimization problem, making it amenable to real-time implementations. The method is demonstrated experimentally on a ground rover and a quadruped robotic system.</p>
<p>This is work performed in collaboration with Sarah Dean and Ben Recht (UC Berkeley) and Andrew Taylor and Aaron Ames (Caltech). It was originally published at the 2020 Conference on Robotic Learning. The extended publication can be found <a href="https://arxiv.org/pdf/2010.16001.pdf">here</a>.</p>
<p>Below is a simplified version of the paper meant for a general audience. (This one’s for you mom!)</p>
<h1 id="introduction">Introduction</h1>
<p>Safety is really important, but most of our methods of assuring safety really on highly accurate system measurements. We explored the problem of ensuring safety despite the measurement errors. We apply our solution to a simulated segway system with a camera-in-the-loop sensor.</p>
<h1 id="background">Background</h1>
<p>When designing a system we often require that the final design is “safe”. But what exactly does it mean to be safe? For our purposes we define a safe set as a region of space where our system is considered safe. Like an autonomous vehicle is safe if it’s one the road and unsafe if it’s not on the road. More precisely, we say that a system is safe if that safe set is <em>invariant</em>.</p>
<blockquote>
<p><strong>Safety (Invariance)</strong>: A system is safe if starting in the safe set implies that it will stay in the safe set.</p>
</blockquote>
<p>To ensure this type of safety we consider the dynamics of the system:</p>
<center>
$$\dot{\mathbf{x}} = \mathbf{f}(\mathbf{x}) + \mathbf{g}(\mathbf{x})\mathbf{u}$$
</center>
<p>and a safe set defined as a 0-superlevel set of a continuously differentiable safety function \(h\) (aka places where \(h(\mathbf{x})>0\)).</p>
<p>This function \(h\) is a <strong>Control Barrier Function</strong> if there exists inputs such that:</p>
<center>
$$\dot{h}( \mathbf{x}, \mathbf{u}) \geq - \alpha(h(\mathbf{x})).$$
</center>
<p>When this inequality is ensured, the system is guaranteed to be safe (Thrm 1).</p>
<h1 id="new-theory-measurement-robust-control-barrier-functions">New Theory: Measurement-Robust Control Barrier Functions</h1>
<p>Often when working with real systems we can’t measure things exactly, but Control Barrier Functions incorporate the current value of \(\mathbf{x}\). In this work we found a way of extending existing CBF theory to ensure that the system remains safe even despite thesse measurement errors.</p>
<p>The CBF \(h\) is <strong>Measurement Robust</strong> if there exists a controller that satisfies the constraint:</p>
<center>
$$\dot{h}(\hat{\mathbf{x}},\mathbf{u}) - \epsilon (\mathfrak{L}_{L_fh} + \mathfrak{L}_{\alpha \circ h} + \mathfrak{L}_{L_gh} ||\mathbf{u}||_2) \geq - \alpha ( h (\hat{\mathbf{x}}))$$
</center>
<p>The difference between this Meausrement Robust CBF condition and the standard CBF condition is the addition of the term:</p>
<center>
$$-\epsilon (\mathfrak{L}_{L_fh} + \mathfrak{L}_{\alpha \circ h} + \mathfrak{L}_{L_gh} ||\mathbf{u}||_2) $$
</center>
<p>Here \(\epsilon\) is represents how bad our measurement is and the \(\mathfrak{L}\) terms represent how “smooth” our dynamics are. Intuitively, if the dynamics are really “smooth” then small measurement errors will have little effect, but if the dynamics aren’t smooth and change really quickly then small measurement errors can result in large mispredictions of the system’s behavior.</p>
<h1 id="learning-for-measurement-model-uncertainty-reduction">Learning for Measurement Model Uncertainty Reduction</h1>
<p>Because the input, \(\mathbf{u}\), appears in this smoothed term, it is possible that no inputs exist that ensure safety. In particular, our formulation implies that if the following condition does not hold, then it is impossible to render the system safe:</p>
<center>
$$\epsilon \leq \textrm{max}\left\{ \frac{||L_gh(\hat{\mathbf{x})}||_2}{\mathfrak{L}_{L_gh}}, \frac{L_fh(\hat{\mathbf{x}}) + \alpha(h(\hat{mathbf{x}}))}{\mathfrak{L_fh} + \mathfrak{L}_{\alpha\circ h}} \right\}$$.
</center>
<p>In the context of machine learning, this inequality suggests the use of a sampling scheme that will ensure that the measurement error never reaches an unsafe level.</p>
<h1 id="simulation-results">Simulation Results</h1>
<p>Due to Covid19 restrictions, the experiments for this work were performed exclusively in simulation. They were performed using on a simulated Segway. The system was considered safe as long as it remained upright within a certain angle window.</p>
<center>
<img src="/assets/images/segway_sim.png" alt="segway_sim" style="width:300px;height:360px;" />
</center>
<p>Two types of errors were considered: the worst case error synthetically added to the measurement and the error found when measuring the system using a learned model which estimated the position based on camera data.</p>
<p>In both cases the standard CBF controller failed to ensure safety and the MRCBF controller succeeded.</p>Ryan CosnerDevansh R. Agrawal*, Hardik Parwana, Ryan K. Cosner*, Ugo Rosolia, Aaron D. Ames, Dmitra Panagou. Abstract: We present a multi-rate control architecture that leverages fundamental properties of differential flatness to synthesize controllers for safety-critical nonlinear dynamical systems subject to input constraints. We propose a two-layer architecture, where the high-level generates reference trajectories using a linear Model Predictive Controller, and the low-level tracks this reference using a feedback controller. The novelty lies in how we couple these layers, to achieve formal guarantees on recursive feasibility of the MPC problem, and safety of the nonlinear system. Furthermore, using differential-flatness, we provide a constructive means to synthesize the multi-rate controller, thereby removing the need to search for suitable Lyapunov or barrier functions, or to approximately linearize/discretize nonlinear dynamics. We show the synthesized controller is a convex optimization problem, making it amenable to real-time implementations. The method is demonstrated experimentally on a ground rover and a quadruped robotic system.RAL 2022: Model-Free Safety-Critical Control for Robotic Systems2021-09-09T12:35:00+00:002021-09-09T12:35:00+00:00http://www.rkcosner.com/research/ReducedOrder<p>Tamas G. Molnar, <strong>Ryan K. Cosner</strong>, Andrew W. Singletary, Wyatt Ubellacker, Aaron D. Ames. <a href="https://arxiv.org/pdf/2109.09047.pdf">[pdf]</a></p>
<hr />
<p><strong>Abstract</strong>: This paper presents a framework for the safety-critical control of robotic systems, when safety is defined on safe regions in the configuration space.
To maintain safety, we synthesize a safe velocity based on control barrier function theory without relying on a – potentially complicated – high-fidelity dynamical model of the robot.
Then, we track the safe velocity with a tracking controller.
This culminates in <em>model-free safety critical control</em>.
We prove theoretical safety guarantees for the proposed method.
Finally, we demonstrate that this approach is application-agnostic.
We execute an obstacle avoidance task with a Segway in high-fidelity simulation, as well as with a Drone and a Quadruped in hardware experiments.</p>
<p>This is work performed in collaboration with Tamas Molnar, Andrew Singletary, Wyatt Ubellacker, and Aaron Ames. It was originally submitted to the IEEE RAL Journal. The extended publication can be found <a href="https://arxiv.org/pdf/2109.09047.pdf"><strong>here</strong></a> <a href="https://arxiv.org/pdf/2109.09047.pdf">(https://arxiv.org/pdf/2109.09047.pdf)</a>.</p>Ryan CosnerTamas G. Molnar, Ryan K. Cosner, Andrew W. Singletary, Wyatt Ubellacker, Aaron D. Ames. [pdf] Abstract: This paper presents a framework for the safety-critical control of robotic systems, when safety is defined on safe regions in the configuration space. To maintain safety, we synthesize a safe velocity based on control barrier function theory without relying on a – potentially complicated – high-fidelity dynamical model of the robot. Then, we track the safe velocity with a tracking controller. This culminates in model-free safety critical control. We prove theoretical safety guarantees for the proposed method. Finally, we demonstrate that this approach is application-agnostic. We execute an obstacle avoidance task with a Segway in high-fidelity simulation, as well as with a Drone and a Quadruped in hardware experiments.IROS 2021: Measurement-Robust Control Barrier Functions: Certainty in Safety with Uncertainty in State2021-03-30T12:35:00+00:002021-03-30T12:35:00+00:00http://www.rkcosner.com/research/Perception<p><strong>Ryan K. Cosner</strong>, Andrew W. Singletary, Andrew J Taylor, Tamas G. Molnar, Katherine L. Bouman, Aaron D. Ames. <a href="https://arxiv.org/pdf/2104.14030.pdf">[pdf]</a></p>
<hr />
<p><strong>Abstract</strong>: The increasing complexity of modern robotic systems and the environments they operate in necessitates the formal consideration of safety in the presence of imperfect measurements. In this paper we propose a rigorous framework for safety-critical control of systems with erroneous state estimates. We develop this framework by leveraging Control Barrier Functions (CBFs) and unifying the method of Backup Sets for synthesizing control invariant sets with robustness requirements—the end result is the synthesis of <em>Measurement-Robust Control Barrier Functions (MR-CBFs)</em>.
This provides theoretical guarantees on safe behavior in the presence of imperfect measurements and improved robustness over standard CBF approaches. We demonstrate the efficacy of this framework both in simulation and experimentally on a Segway platform using an onboard stereo-vision camera for state estimation.</p>
<p>This is work performed in collaboration with Andrew Singletary, Andrew Taylor, Tamas Molnar, Katie Bouman, and Aaron Ames (Caltech). It was originally published at the 2021 IEEE IROS Conference. The extended publication can be found <a href="https://arxiv.org/pdf/2104.14030.pdf"><strong>here</strong></a> <a href="https://arxiv.org/pdf/2104.14030.pdf">(https://arxiv.org/pdf/2104.14030.pdf)</a>.</p>
<iframe src="https://player.vimeo.com/video/618342367?h=dc28eec41b&badge=0&autopause=0&player_id=0&app_id=58479" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen="" title="MRCBF_IROS_VIDEO"></iframe>
<iframe src="https://player.vimeo.com/video/520247516?h=9994cd748c&badge=0&autopause=0&player_id=0&app_id=58479" width="2562" height="1440" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen="" title="Measurement-Robust Control Barrier Functions: Certainty in Safety with Uncertainty in State"></iframe>Ryan CosnerRyan K. Cosner, Andrew W. Singletary, Andrew J Taylor, Tamas G. Molnar, Katherine L. Bouman, Aaron D. Ames. [pdf] Abstract: The increasing complexity of modern robotic systems and the environments they operate in necessitates the formal consideration of safety in the presence of imperfect measurements. In this paper we propose a rigorous framework for safety-critical control of systems with erroneous state estimates. We develop this framework by leveraging Control Barrier Functions (CBFs) and unifying the method of Backup Sets for synthesizing control invariant sets with robustness requirements—the end result is the synthesis of Measurement-Robust Control Barrier Functions (MR-CBFs). This provides theoretical guarantees on safe behavior in the presence of imperfect measurements and improved robustness over standard CBF approaches. We demonstrate the efficacy of this framework both in simulation and experimentally on a Segway platform using an onboard stereo-vision camera for state estimation.LCSS 2021: Multi-rate control design under input constraints via fixed-time barrier functions2021-03-29T12:35:00+00:002021-03-29T12:35:00+00:00http://www.rkcosner.com/research/MultirateControl<p>Kunal Garg, <strong>Ryan K. Cosner</strong>, Ugo Rosolia, Aaron D. Ames, Dmitra Panagou. <a href="https://arxiv.org/pdf/2103.03695.pdf">[pdf]</a></p>
<hr />
<p><strong>Abstract</strong>: In this paper, we introduce the notion of periodic safety, which requires that the system trajectories periodically visit a subset of a forward-invariant safe set, and utilize it in a multi-rate framework where a high-level planner generates a reference trajectory that is tracked by a low-level controller under input constraints. We introduce the notion of fixed-time barrier functions which is leveraged by the proposed low-level controller in a quadratic programming framework. Then, we design a model predictive control policy for high-level planning with a bound on the rate of change for the reference trajectory to guarantee that periodic safety is achieved. We demonstrate the effectiveness of the proposed strategy on a simulation example, where the proposed fixed-time stabilizing low-level controller shows successful satisfaction of control objectives, whereas an exponentially stabilizing low-level controller fails.</p>
<p>This is work performed in collaboration with Kunal Garg and Dmitra Panagou (UC Berkeley) and Ugo Rosolia and Aaron Ames (Caltech). It was originally published in the 2021 IEEE LCSS Journal. The full publication can be found <a href="https://arxiv.org/pdf/2103.03695.pdf"><strong>here</strong></a> <a href="https://arxiv.org/pdf/2103.03695.pdf">(https://arxiv.org/pdf/2103.03695.pdf)</a>.</p>Ryan CosnerKunal Garg, Ryan K. Cosner, Ugo Rosolia, Aaron D. Ames, Dmitra Panagou. [pdf] Abstract: In this paper, we introduce the notion of periodic safety, which requires that the system trajectories periodically visit a subset of a forward-invariant safe set, and utilize it in a multi-rate framework where a high-level planner generates a reference trajectory that is tracked by a low-level controller under input constraints. We introduce the notion of fixed-time barrier functions which is leveraged by the proposed low-level controller in a quadratic programming framework. Then, we design a model predictive control policy for high-level planning with a bound on the rate of change for the reference trajectory to guarantee that periodic safety is achieved. We demonstrate the effectiveness of the proposed strategy on a simulation example, where the proposed fixed-time stabilizing low-level controller shows successful satisfaction of control objectives, whereas an exponentially stabilizing low-level controller fails.Control Barrier Functions (CBFs)2020-12-20T12:35:00+00:002020-12-20T12:35:00+00:00http://www.rkcosner.com/blogs/Control-Barrier-Functions<p>** Coming Soon **</p>Ryan Cosner** Coming Soon **