arXiv subjects

Yvonne R. Stürz

Publications and source records attributed to Yvonne R. Stürz.

11 recordsLinked to original sources

arXiv2023

Control of Uncertain PWA Systems using Difference-of-Convex Decompositions

In this report, we analyze and design feedback policies for discrete-time Piecewise-Affine (PWA) systems with uncertainty in both the affine dynamics and the polytopic partition. The main idea is to utilise the Difference-of-Convex (DC) decomposition of continuous PWA systems to derive quadratic Lyapunov functions as stability certificates and stabilizing affine policies in a higher dimensional space. When projected back to the state space, we obtain time-varying PWQ Lyapunov functions and time-varying PWA feedback policies.

math.OC↗

arXiv2022

Safe Human-Robot Collaborative Transportation via Trust-Driven Role Adaptation

We study a human-robot collaborative transportation task in presence of obstacles. The task for each agent is to carry a rigid object to a common target position, while safely avoiding obstacles and satisfying the compliance and actuation constraints of the other agent. Human and robot do not share the local view of the environment. The human policy either assists the robot when they deem the robot actions safe based on their perception of the environment, or actively leads the task. Using estimated human inputs, the robot plans a trajectory for the transported object by solving a constrained finite time optimal control problem. Sensors on the robot measure the inputs applied by the human. The robot then appropriately applies a weighted combination of the human's applied and its own planned inputs, where the weights are chosen based on the robot's trust value on its estimates of the human's inputs. This allows for a dynamic leader-follower role adaptation of the robot throughout the task. Furthermore, under a low value of trust, if the robot approaches any obstacle potentially unknown to the human, it triggers a safe stopping policy, maintaining safety of the system and signaling a required change in the human's intent. With experimental results, we demonstrate the efficacy of the proposed approach.

cs.RO↗

arXiv2021

Learning Environment Constraints in Collaborative Robotics: A Decentralized Leader-Follower Approach

In this paper, we propose a leader-follower hierarchical strategy for two robots collaboratively transporting an object in a partially known environment with obstacles. Both robots sense the local surrounding environment and react to obstacles in their proximity. We consider no explicit communication, so the local environment information and the control actions are not shared between the robots. At any given time step, the leader solves a model predictive control (MPC) problem with its known set of obstacles and plans a feasible trajectory to complete the task. The follower estimates the inputs of the leader and uses a policy to assist the leader while reacting to obstacles in its proximity. The leader infers obstacles in the follower's vicinity by using the difference between the predicted and the real-time estimated follower control action. A method to switch the leader-follower roles is used to improve the control performance in tight environments. The efficacy of our approach is demonstrated with detailed comparisons to two alternative strategies, where it achieves the highest success rate, while completing the task fastest. See the link www.dropbox.com/s/hexadigqkvspaeh/IROS_Video.mp4?dl=0 for a descriptive video of the algorithm.

cs.RO↗

arXiv2021

A Simple Robust MPC for Linear Systems with Parametric and Additive Uncertainty

We propose a simple and computationally efficient approach for designing a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertainty is modeled as an additive disturbance and an additive error on the system dynamics matrices. Set based bounds for each component of the model uncertainty are assumed to be known. We separate the constraint tightening strategy into two parts, depending on the length of the MPC horizon. For a horizon length of one, the robust MPC problem is solved exactly, whereas for other horizon lengths, the model uncertainty is over-approximated with a net-additive component. The resulting MPC controller guarantees robust satisfaction of state and input constraints in closed-loop with the uncertain system. With appropriately designed terminal components and an adaptive horizon strategy, we prove the controller's recursive feasibility and stability of the origin. With numerical simulations, we demonstrate that our proposed approach gains up to 15x online computation speedup over a tube MPC strategy, while stabilizing about 98$\%$ of the latter's region of attraction.

eess.SY↗

arXiv2021

Collision Avoidance in Tightly-Constrained Environments without Coordination: a Hierarchical Control Approach

We present a hierarchical control approach for maneuvering an autonomous vehicle (AV) in tightly-constrained environments where other moving AVs and/or human driven vehicles are present. A two-level hierarchy is proposed: a high-level data-driven strategy predictor and a lower-level model-based feedback controller. The strategy predictor maps an encoding of a dynamic environment to a set of high-level strategies via a neural network. Depending on the selected strategy, a set of time-varying hyperplanes in the AV's position space is generated online and the corresponding halfspace constraints are included in a lower-level model-based receding horizon controller. These strategy-dependent constraints drive the vehicle towards areas where it is likely to remain feasible. Moreover, the predicted strategy also informs switching between a discrete set of policies, which allows for more conservative behavior when prediction confidence is low. We demonstrate the effectiveness of the proposed data-driven hierarchical control framework in a two-car collision avoidance scenario through simulations and experiments on a 1/10 scale autonomous car platform where the strategy-guided approach outperforms a model predictive control baseline in both cases.

cs.RO↗

arXiv2020

Parameter Identification for Digital Fabrication: A Gaussian Process Learning Approach

Tensioned cable nets can be used as supporting structures for the efficient construction of lightweight building elements, such as thin concrete shell structures. To guarantee important mechanical properties of the latter, the tolerances on deviations of the tensioned cable net geometry from the desired target form are very tight. Therefore, the form needs to be readjusted on the construction site. In order to employ model-based optimization techniques, the precise identification of important uncertain model parameters of the cable net system is required. This paper proposes the use of Gaussian process regression to learn the function that maps the cable net geometry to the uncertain parameters. In contrast to previously proposed methods, this approach requires only a single form measurement for the identification of the cable net model parameters. This is beneficial since measurements of the cable net form on the construction site are very expensive. For the training of the Gaussian processes, simulated data is efficiently computed via convex programming. The effectiveness of the proposed method and the impact of the precise identification of the parameters on the form of the cable net are demonstrated in numerical experiments on a quarter-scale prototype of a roof structure.

eess.SY↗

arXiv2020

Trajectory Optimization for Nonlinear Multi-Agent Systems using Decentralized Learning Model Predictive Control

We present a decentralized minimum-time trajectory optimization scheme based on learning model predictive control for multi-agent systems with nonlinear decoupled dynamics and coupled state constraints. By performing the same task iteratively, data from previous task executions is used to construct and improve local time-varying safe sets and an approximate value function. These are used in a decoupled MPC problem as terminal sets and terminal cost functions. Our framework results in a decentralized controller, which requires no communication between agents over each iteration of task execution, and guarantees persistent feasibility, finite-time closed-loop convergence, and non-decreasing performance of the global system over task iterations. Numerical experiments of a multi-vehicle collision avoidance scenario demonstrate the effectiveness of the proposed scheme.

eess.SY↗

arXiv2020

Distributed Learning Model Predictive Control for Linear Systems

This paper presents a distributed learning model predictive control (DLMPC) scheme for distributed linear time invariant systems with coupled dynamics and state constraints. The proposed solution method is based on an online distributed optimization scheme with nearest-neighbor communication. If the control task is iterative and data from previous feasible iterations are available, local data are exploited by the subsystems in order to construct the local terminal set and terminal cost, which guarantee recursive feasibility and asymptotic stability, as well as performance improvement over iterations. In case a first feasible trajectory is difficult to obtain, or the task is non-iterative, we further propose an algorithm that efficiently explores the state-space and generates the data required for the construction of the terminal cost and terminal constraint in the MPC problem in a safe and distributed way. In contrast to other distributed MPC schemes which use structured positive invariant sets, the proposed approach involves a control invariant set as the terminal set, on which we do not impose any distributed structure. The proposed iterative scheme converges to the global optimal solution of the underlying infinite horizon optimal control problem under mild conditions. Numerical experiments demonstrate the effectiveness of the proposed DLMPC scheme.

eess.SY↗

arXiv2020

Distributed Control Design for Heterogeneous Interconnected Systems

This paper presents scalable controller synthesis methods for heterogeneous and partially heterogeneous systems. First, heterogeneous systems composed of different subsystems that are interconnected over a directed graph are considered. Techniques from robust and gain-scheduled controller synthesis are employed, in particular the full-block S-procedure, to deal with the decentralized system part in a nominal condition and with the interconnection part in a multiplier condition. Under some structural assumptions, we can decompose the synthesis conditions into conditions that are the size of the individual subsystems. To solve these decomposed synthesis conditions that are coupled only over neighboring subsystems, we propose a distributed method based on the alternating direction method of multipliers. It only requires nearest-neighbor communication and no central coordination is needed. Then, a new classification of systems is introduced that consists of groups of homogeneous subsystems with different interconnection types. This classification includes heterogeneous systems as the most general and homogeneous systems as the most specific case. Based on this classification, we show how the interconnected system model and the decomposed synthesis conditions can be formulated in a more compact way. The computational scalability of the presented methods with respect to a growing number of subsystems and interconnections is analyzed, and the results are demonstrated in numerical examples.

eess.SY↗

arXiv2019

Nonlinear Control of Quadcopters via Approximate Dynamic Programming

While Approximate Dynamic Programming has successfully been used in many applications involving discrete states and inputs such as playing the games of Tetris or chess, it has not been used in many continuous state and input space applications. In this paper, we combine Approximate Dynamic Programming techniques and apply them to the continuous, non-linear and high dimensional dynamics of a quadcopter vehicle. We use a polynomial approximation of the dynamics and sum-of-squares programming techniques to compute a family of polynomial value function approximations for different tuning parameters. The resulting approximations to the optimal value function are combined in a point-wise maximum approach, which is used to compute the online policy. The success of the method is demonstrated in both simulations and experiments on a quadcopter. The control performance is compared to a linear time-varying Model Predictive Controller. The two methods are then combined to keep the computational benefits of a short horizon MPC and the long term performance benefits of the Approximate Dynamic Programming value function as the terminal cost.

eess.SY↗

arXiv2018

Control of an Architectural Cable Net Geometry

Doubly curved thin concrete shells are very efficient building structures, suitable for light-weight construction because of their high structural stability. In the process of constructing such shells, an efficient innovative flexible formwork that is based on a cable network can be used instead of the costly conventional timber formwork. To guarantee the structural properties of such a shell, the desired form, that is designed and optimized in advance, needs to be precisely achieved. The sensitivity of the flexible cable net formwork to fabrication tolerances and uncertainties makes high accuracy challenging. We propose a new construction method where the form of the cable net structure is measured and controlled in a feedback loop during its construction. Two models based on a force and on an energy approach are reviewed and their equivalence is shown. An efficient control algorithm, which is based on a variant of Sequential Quadratic Programming, and which guarantees feasibility at every iteration, is derived. Based on mild assumptions on the cable net, global convergence to a stationary point is shown. For practical applicability, an extension of the control algorithm for computing sparse input vectors is given. Experimental results on a cable net formwork prototype for a shell roof structure are presented to demonstrate the control performance.

math.OC↗