arXiv subjects

Claus Danielson

Publications and source records attributed to Claus Danielson.

13 recordsLinked to original sources

arXiv2025

Learning Control Barrier Functions with Deterministic Safety Guarantees

Barrier functions (BFs) characterize safe sets of dynamical systems, where hard constraints are never violated as the system evolves over time. Computing a valid safe set and BF for a nonlinear (and potentially unmodeled), non-autonomous dynamical system is a difficult task. This work explores the design of BFs using data to obtain safe sets with deterministic assurances of control invariance. We leverage ReLU neural networks (NNs) to create continuous piecewise affine (CPA) BFs with deterministic safety guarantees for Lipschitz continuous, discrete-time dynamical system using sampled one-step trajectories. The CPA structure admits a novel classifier term to create a relaxed \ac{bf} condition and construction via a data driven constrained optimization. We use iterative convex overbounding (ICO) to solve this nonconvex optimization problem through a series of convex optimization steps. We then demonstrate our method's efficacy on two-dimensional autonomous and non-autonomous dynamical systems.

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arXiv2025

Data-driven certificates of constraint enforcement and stability for unmodeled, discrete dynamical systems using tree data structures

This paper addresses the critical challenge of developing data-driven certificates for the stability and safety of unmodeled dynamical systems by leveraging a tree data structure and an upper bound of the system's Lipschitz constant. Previously, an invariant set was synthesized by iteratively expanding an initial invariant set. In contrast, this work iteratively prunes the constraint set to synthesize an invariant set -- eliminating the need for a known, initial invariant set. Furthermore, we provide stability assurances by characterizing the asymptotic stability of the system relative to an invariant approximation of the minimal positive invariant set through synthesis of a discontinuous piecewise affine Lyapunov function over the computed invariant set. The proposed method takes inspiration from subdivision techniques and requires no prior system knowledge beyond Lipschitz continuity.

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arXiv2025

Data driven synthesis of provable invariant sets via stochastically sampled data

Positive invariant (PI) sets are essential for ensuring safety, i.e. constraint adherence, of dynamical systems. With the increasing availability of sampled data from complex (and often unmodeled) systems, it is advantageous to leverage these data sets for PI set synthesis. This paper uses data driven geometric conditions of invariance to synthesize PI sets from data. Where previous data driven, set-based approaches to PI set synthesis used deterministic sampling schemes, this work instead synthesizes PI sets from any pre-collected data sets. Beyond a data set and Lipschitz continuity, no additional information about the system is needed. A tree data structure is used to partition the space and select samples used to construct the PI set, while Lipschitz continuity is used to provide deterministic guarantees of invariance. Finally, probabilistic bounds are given on the number of samples needed for the algorithm to determine of a certain volume.

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arXiv2025

Safe On-Orbit Dislodging of Deployable Structures via Robust Adaptive MPC

This paper proposes a novel robust adaptive model predictive controller for on-orbit dislodging. We study orbit dislodging where a servicing spacecraft uses a robotic arm to free a jammed and unactuated solar panel mounted on a hybrid hinge that acts as a time-varying client on a space station. Our method couples online set-membership identification with a robust adaptive MPC to enforce safety under bounded disturbances. The controller explicitly balances exploration to excite the system and shrink uncertainty and exploitation to improve control performance through a dual-mode cost. The feasibility of the developed robust adaptive MPC method is also examined through dislodging simulations and hardware experiments in freefall and terrestrial laboratory environments, respectively. In addition, the advantages of our method are shown through comparison experiments with several state-of-the-art control schemes for both accuracy of parameter estimation and control performance.

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arXiv2024

Adaptive Robot Detumbling of a Non-Rigid Satellite

The challenge of satellite stabilization, particularly those with uncertain flexible dynamics, has become a pressing concern in control and robotics. These uncertainties, especially the dynamics of a third-party client satellite, significantly complicate the stabilization task. This paper introduces a novel adaptive detumbling method to handle non-rigid satellites with unknown motion dynamics (translation and rotation). The distinctive feature of our approach is that we model the non-rigid tumbling satellite as a two-link serial chain with unknown stiffness and damping in contrast to previous detumbling research works which consider the satellite a rigid body. We develop a novel adaptive robotics approach to detumble the satellite by using two space tugs as servicer despite the uncertain dynamics in the post-capture case. Notably, the stiffness properties and other physical parameters, including the mass and inertia of the two links, remain unknown to the servicer. Our proposed method addresses the challenges in detumbling tasks and paves the way for advanced manipulation of non-rigid satellites with uncertain dynamics.

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arXiv2024

Decentralized Adaptive Aerospace Transportation of Unknown Loads Using A Team of Robots

Transportation missions in aerospace are limited to the capability of each aerospace robot and the properties of the target transported object, such as mass, inertia, and grasping locations. We present a novel decentralized adaptive controller design for multiple robots that can be implemented in different kinds of aerospace robots. Our controller adapts to unknown objects in different gravity environments. We validate our method in an aerial scenario using multiple fully actuated hexarotors with grasping capabilities, and a space scenario using a group of space tugs. In both scenarios, the robots transport a payload cooperatively through desired three-dimensional trajectories. We show that our method can adapt to unexpected changes that include the loss of robots during the transportation mission.

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arXiv2024

Immersive Robot Programming Interface for Human-Guided Automation and Randomized Path Planning

Researchers are exploring Augmented Reality (AR) interfaces for online robot programming to streamline automation and user interaction in variable manufacturing environments. This study introduces an AR interface for online programming and data visualization that integrates the human in the randomized robot path planning, reducing the inherent randomness of the methods with human intervention. The interface uses holographic items which correspond to physical elements to interact with a redundant manipulator. Utilizing Rapidly Random Tree Star (RRT*) and Spherical Linear Interpolation (SLERP) algorithms, the interface achieves end-effector s progression through collision-free path with smooth rotation. Next, Sequential Quadratic Programming (SQP) achieve robot s configurations for this progression. The platform executes the RRT* algorithm in a loop, with each iteration independently exploring the shortest path through random sampling, leading to variations in the optimized paths produced. These paths are then demonstrated to AR users, who select the most appropriate path based on the environmental context and their intuition. The accuracy and effectiveness of the interface are validated through its implementation and testing with a seven Degree-OF-Freedom (DOF) manipulator, indicating its potential to advance current practices in robot programming. The validation of this paper include two implementations demonstrating the value of human-in-the-loop and context awareness in robotics.

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arXiv2023

Blameless and Optimal Control under Prioritized Safety Constraints

In many resource-limited optimal control problems, multiple constraints may be enforced that are jointly infeasible due to external factors such as subsystem failures, unexpected disturbances, or fuel limitations. In this manuscript, we introduce the concept of blameless optimality to characterize control actions that a) satisfy the highest prioritized and feasible constraints and b) remain optimal with respect to a mission objective. For a general optimal control problem with jointly infeasible constraints, we prove that a single optimization problem cannot find a blamelessly optimal control sequence. Instead, finding blamelessly optimal control actions requires sequentially solving at least two optimal control problems: one to determine the highest priority level of constraints that is feasible and another to determine the optimal control action with respect to these constraints. We apply our results to a rocket landing scenario in which violating at least one safety-induced landing constraint is unavoidable. Leveraging the concept of blameless optimality, we formulate blamelessly optimal controllers that can autonomously prioritize the constraints most critical to a mission.

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arXiv2023

Data-driven invariant set for nonlinear systems with application to command governors

This paper presents a novel approach to synthesize positive invariant sets for unmodeled nonlinear systems using direct data-driven techniques. The data-driven invariant sets are used to design a data-driven command governor that selects a command for the closed-loop system to enforce constraints. Using basis functions, we solve a semi-definite program to learn a sum-of-squares Lyapunov-like function whose unity level-set is a constraint admissible positive invariant set, which determines the constraint admissible states and input commands. Leveraging Lipschitz properties of the system, we prove that tightening the model-based design ensures robustness of the invariant set to the inherent plant uncertainty in a data-driven framework. To mitigate the curse-of-dimensionality, we repose the semi-definite program into a linear program. We validate our approach through two examples: First, we present an illustrative example where we can analytically compute the maximum positive invariant set and compare with the presented data-driven invariant set. Second, we present a practical autonomous driving scenario to demonstrate the utility of the presented method for nonlinear systems.

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arXiv2021

Extremum Seeking Control with an Adaptive Gain Based On Gradient Estimation Error

This paper presents an extremum seeking control algorithm with an adaptive step-size that adjusts the aggressiveness of the controller based on the quality of the gradient estimate. The adaptive step-size ensures that the integral-action produced by the gradient descent does not destabilize the closed-loop system. To quantify the quality of the gradient estimate, we present a batch least squares estimator with a novel weighting and show that it produces bounded estimation errors, where the uncertainty is due to the curvature of the unknown cost function. The adaptive step-size then maximizes the decrease of the combined plant and controller Lyapunov function for the worst-case estimation error. We prove that our ESC is input-to-state stable with respect to the dither signal. Finally, we demonstrate our proposed ESC through five numerical examples; one illustrative, one practical, and three benchmarks.

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arXiv2019

Approximate Dynamic Programming For Linear Systems with State and Input Constraints

Enforcing state and input constraints during reinforcement learning (RL) in continuous state spaces is an open but crucial problem which remains a roadblock to using RL in safety-critical applications. This paper leverages invariant sets to update control policies within an approximate dynamic programming (ADP) framework that guarantees constraint satisfaction for all time and converges to the optimal policy (in a linear quadratic regulator sense) asymptotically. An algorithm for implementing the proposed constrained ADP approach in a data-driven manner is provided. The potential of this formalism is demonstrated via numerical examples.

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arXiv2017

Path Planning using Positive Invariant Sets

We present an algorithm for steering the output of a linear system from a feasible initial condition to a desired target position, while satisfying input constraints and non-convex output constraints. The system input is generated by a collection of local linear state-feedback controllers. The path-planning algorithm selects the appropriate local controller using a graph search, where the nodes of the graph are the local controllers and the edges of the graph indicate when it is possible to transition from one local controller to another without violating input or output constraints. We present two methods for computing the local controllers. The first uses a fixed-gain controller and scales its positive invariant set to satisfy the input and output constraints. We provide a linear program for determining the scale-factor and a condition for when the linear program has a closed-form solution. The second method designs the local controllers using a semi-definite program that maximizes the volume of the positive invariant set that satisfies state and input constraints. We demonstrate our path-planning algorithm on docking of a spacecraft. The semi-definite programming based control design has better performance but requires more computation.

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arXiv2014

Optimality of certainty equivalence in expected value problems for uncertain linear systems

In this paper we study the optimality of the certainty equivalence approximation in robust finite-horizon optimization problems with expected cost. We provide an algorithm for determining the subset of the state-space for which the certainty equivalence technique is optimal. In the second part of the paper we show how patterns in the problem structure called symmetries can be used to reduce the computational complexity of the previous algorithm. Finally we demonstrate our technique through numerical examples. In particular we examine networked battery systems and radiant slab building control, for which we show the certainty equivalence controller is optimal over the entire operating range.

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