Duality-based Convex Optimization for Real-time Obstacle Avoidance between Polytopes with Control Barrier Functions

Thirugnanam, Akshay; Zeng, Jun; Sreenath, Koushil

doi:10.23919/acc53348.2022.9867246

Cited by 10 publications

(9 citation statements)

References 41 publications

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“…Preliminary results of this work were published in [1], which focused on obstacle avoidance between polytopes. We further elaborate on the results of this work and also provide a method for obstacle avoidance between strictly convex regions.…”

Section: Contributionsmentioning

confidence: 99%

“…We repeat this procedure for polytopes in the next two sections. We follow the outline of our previous paper [1]. In this section, we detail the continuity and differentiability properties for polytopes, which will then be used to derive the NCBF formulation for polytopes in the next section.…”

Section: Smoothness Properties For Polytopes With Dual Analysismentioning

confidence: 99%

“…The minimum distance functions for these constraints are smooth and differentiable when the shapes of the robots and the obstacles are considered lines, planes, circles, ellipses, hyper-ellipses, etc. However, the smoothness and the differentiability are no longer valid when the robots or the obstacles are considered as general convex regions, such as polytopes [1]. To handle this issue, polytopic obstacle avoidance can be reformulated into smooth constraints with dual variables within model predictive control for discrete-time systems.…”

Section: Introduction a Motivationmentioning

confidence: 99%

“…ODEs of the form of (1), where the RHS is a continuous function, are guaranteed to have a solution, but the solution might be non-unique. Although restricting the functions f i , g i , and u i in (1) to be Lipschitz continuous functions would guarantee uniqueness of solutions, imposing Lipschitz continuity on u i is too restrictive.…”

Section: Introductionmentioning

confidence: 99%

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Safety-Critical Control and Planning for Obstacle Avoidance between Polytopes with Control Barrier Functions

Thirugnanam¹,

Zeng²,

Sreenath³

2022

2022 International Conference on Robotics and Automation (ICRA)

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In this paper, we focus on non-conservative obstacle avoidance between robots with control affine dynamics with strictly convex and polytopic shapes. The core challenge for this obstacle avoidance problem is that the minimum distance between strictly convex regions or polytopes is generally implicit and non-smooth, such that distance constraints cannot be enforced directly in the optimization problem. To handle this challenge, we employ non-smooth control barrier functions to reformulate the avoidance problem in the dual space, with the positivity of the minimum distance between robots equivalently expressed using a quadratic program. Our approach is proven to guarantee system safety. We theoretically analyze the smoothness properties of the minimum distance quadratic program and its KKT conditions. We validate our approach by demonstrating computationally-efficient obstacle avoidance for multi-agent robotic systems with strictly convex and polytopic shapes. To our best knowledge, this is the first time a real-time QP problem can be formulated for general non-conservative avoidance between strictly convex shapes and polytopes.

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Section: Contributionsmentioning

confidence: 99%

Section: Smoothness Properties For Polytopes With Dual Analysismentioning

confidence: 99%

Section: Introduction a Motivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Safety-Critical Control and Planning for Obstacle Avoidance between Polytopes with Control Barrier Functions

Thirugnanam¹,

Zeng²,

Sreenath³

2022

2022 International Conference on Robotics and Automation (ICRA)

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“…Thus, the task is a polytopic obstacle avoidance task. To deal with this task, work has been done using discrete-time-CBF-based MPC [22] and finding a conservative kinematic controller [23]. In this example, we learn a CBF-based dynamic controller to solve this task.…”

Section: B Two-link Armmentioning

confidence: 99%

Learning a Better Control Barrier Function

Dai

Krishnamurthy

Khorrami

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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Control barrier functions (CBFs) have been widely used for synthesizing controllers in safety-critical applications. When used as a safety filter, it provides a simple and computationally efficient way to obtain safe controls from a possibly unsafe performance controller. Despite its conceptual simplicity, constructing a valid CBF is well known to be challenging, especially for high-relative degree systems under nonconvex constraints. Recently, work has been done to learn a valid CBF from data based on a handcrafted CBF (HCBF). Even though the HCBF gives a good initialization point, it still requires a large amount of data to train the CBF network. In this work, we propose a new method to learn more efficiently from the collected data through a novel prioritized data sampling strategy. A priority score is computed from the loss value of each data point. Then, a probability distribution based on the priority score of the data points is used to sample data and update the learned CBF. Using our proposed approach, we can learn a valid CBF that recovers a larger portion of the true safe set using a smaller amount of data. The effectiveness of our method is demonstrated in simulation on a unicycle and a two-link arm.

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Collision Avoidance Control for Distributed Multi-Robot Systems Using Collision Cones and CBF-Based Constraints

Palani,

Fukushima,

Izuhara

2024

2024 IEEE Conference on Control Technology and Applications (CCTA)

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Duality-based Convex Optimization for Real-time Obstacle Avoidance between Polytopes with Control Barrier Functions

Cited by 10 publications

References 41 publications

Safety-Critical Control and Planning for Obstacle Avoidance between Polytopes with Control Barrier Functions

Safety-Critical Control and Planning for Obstacle Avoidance between Polytopes with Control Barrier Functions

Learning a Better Control Barrier Function

Collision Avoidance Control for Distributed Multi-Robot Systems Using Collision Cones and CBF-Based Constraints

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