arXiv subjects

Kristin Y. Pettersen

Publications and source records attributed to Kristin Y. Pettersen.

12 recordsLinked to original sources

arXiv2026

Expressiveness, Equivalence, and Uncertainty in Velocity Obstacles and Closest Point of Approach Metrics

Time to Closest Point of Approach (TCPA), Distance to Closest Point of Approach (DCPA), and Velocity Obstacles (VOs), are widely used to assess and mitigate collision risk in autonomous navigation, yet their relationship and behavior under uncertainty remain largely unexplored. Assuming perfect state information, we establish a relationship between these representations over finite and infinite prediction horizons and derive conditions under which they provide equivalent characterizations of collision risk. Under bounded uncertainty, we extend the Closest Point of Approach (CPA) metrics and VO to convex relative-state sets. We show that in this setting, independently computed TCPA and DCPA bounds lose the joint relationship required for VO membership, while uncertainty-aware VOs preserve this relationship through a set-valued representation of collision-inducing velocities.

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arXiv2026

Tendon-Actuated Robots with a Tapered, Flexible Polymer Backbone: Design, Fabrication, and Modeling

This paper presents the design, modeling, and fabrication of 3D-printed, tendon-actuated continuum robots featuring a flexible, tapered backbone constructed from thermoplastic polyurethane (TPU). Our scalable design incorporates an integrated electronics base housing that enables direct tendon tension control and sensing via actuators and compression load cells. Unlike many continuum robots that are single-purpose and costly, the proposed design prioritizes customizability, rapid assembly, and low cost while enabling high curvature and enhanced distal compliance through geometric tapering, thereby supporting a broad range of compliant robotic inspection and manipulation tasks. We develop a generalized forward kinetostatic model of the tapered backbone based on Cosserat rod theory using a Newtonian approach, extending existing tendon-actuated Cosserat rod formulations to explicitly account for spatially varying backbone cross-sectional geometry. The model captures the graded stiffness profile induced by the tapering and enables systematic exploration of the configuration space as a function of the geometric design parameters. Specifically, we analyze how the backbone taper angle influences the robot's configuration space and manipulability. The model is validated against motion capture data, achieving centimeter-level shape prediction accuracy after calibrating Young's modulus via a line search that minimizes modeling error. We further demonstrate teleoperated grasping using an endoscopic gripper routed along the continuum robot, mounted on a 6-DoF robotic arm. Parameterized iLogic/CAD scripts are provided for rapid geometry generation and scaling. The presented framework establishes a simple, rapid, and reproducible pathway from parametric design to controlled tendon actuation for tapered, tendon-driven continuum robots manufactured using fused deposition modeling 3D printers.

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arXiv2026

The Quadruped Soft Tail: Compliant Grasping and Swabbing for Contamination Surveys in Harsh Environments

Beryllium contamination surveys in radioactive areas are challenging for robots in environments cluttered with cables and electronics. To address this problem, we have developed a novel quadruped system augmentation: A lightweight, soft, and compliant tendon-actuated robotic tail mounted on a quadruped robot. The tail features a hollow, flexible backbone and a tendon-actuated soft gripper that enables the robot to pick up sampling tissues, swab contaminated surfaces, and release the tissues at designated collection locations for subsequent beryllium analysis. To enable intuitive teleoperation, a closed-form kinematic model and a singularity-robust task-space controller are developed. Experimental results demonstrate that gripper actuation has a negligible effect on robot shape, while common-mode tendon actuation provides an effective mechanism for stiffness modulation and preload control. Furthermore, experimental validation indicates that the proposed kinematic model provides a suitable basis for real-time task-space control. The proposed system combines the agility of legged locomotion with the compliance of soft robotic manipulation, enabling the complete contamination-survey procedure to be performed without human exposure. While motivated by beryllium contamination surveys at CERN, the proposed quadruped soft-tail concept is broadly applicable to legged robots operating in cluttered, confined, or hazardous environments where conventional rigid-link manipulators are undesirable.

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arXiv2026

Data-Driven Dynamic Modeling of a Tendon-Actuated Continuum Robot

Developing dynamic models for tendon-driven continuum robots is challenging due to their nonlinear, high-dimensional, and friction-dominated dynamics. This paper presents a comparative study of data-driven system identification methods, including N4SID, ARX, and SINDYc, for modeling a tendon-actuated continuum robot with rolling joints developed at CERN. Despite the high number of joints of the robot, experimental analysis reveals that a two-degree-of-freedom dynamic model can accurately capture the system dynamics, owing to strong kinematic dependencies between the joints. The models are validated against experimental data, and used in the design of a model predictive controller, demonstrating their feasibility for real-time control.

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arXiv2025

Hybrid Control Barrier Functions for Nonholonomic Multi-Agent Systems

This paper addresses the problem of guaranteeing safety of multiple coordinated agents moving in dynamic environments. It has recently been shown that this problem can be efficiently solved through the notion of Control Barrier Functions (CBFs). However, for nonholonomic vehicles that are required to keep positive speeds, existing CBFs lose their validity. To overcome this limitation, we propose a hybrid formulation based on synergistic CBFs (SCBFs), which leverages a discrete switching mechanism to avoid configurations that would render the CBF invalid. Unlike existing approaches, our method ensures safety in the presence of moving obstacles and inter-agent interactions while respecting nonzero speed restrictions. We formally analyze the feasibility of the constraints with respect to actuation limits, and the efficacy of the solution is demonstrated in simulation of a multi-agent coordination problem in the presence of moving obstacles.

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arXiv2023

Safety-Critical Control of Nonholonomic Vehicles in Dynamic Environments using Velocity Obstacles

This paper considers collision avoidance for vehicles with first-order nonholonomic constraints maintaining nonzero forward speeds, moving within dynamic environments. We leverage the concept of control barrier functions (CBFs) to synthesize control inputs that prioritize safety, where the safety criteria are derived from the velocity obstacle principle. Existing instantiations of CBFs for collision avoidance, e.g., based on maintaining a minimal distance, can result in control inputs that make the vehicle stop or even reverse. The proposed formulation effectively separates speed control from steering, allowing the vehicle to maintain a forward motion without compromising safety. This is beneficial for ensuring that the vehicle advances towards its desired destination, and it is moreover an underlying requirement for certain vehicles such as marine vessels and fixed-wing UAVs. Theoretical safety guarantees are provided, and numerical simulations demonstrate the efficiency of the strategy in environments containing moving obstacles.

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arXiv2023

Singularity-free Formation Path Following of Underactuated AUVs: Extended Version

This paper proposes a method for formation path following control of a fleet of underactuated autonomous underwater vehicles. The proposed method combines several hierarchic tasks in a null space-based behavioral algorithm to safely guide the vehicles. Compared to the existing literature, the algorithm includes both inter-vehicle and obstacle collision avoidance, and employs a scheme that keeps the vehicles within given operation limits. The algorithm is applied to a six degree-of-freedom model, using rotation matrices to describe the attitude to avoid singularities. Using the results of cascaded systems theory, we prove that the closed-loop system is uniformly semiglobally exponentially stable. We use numerical simulations to validate the results.

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arXiv2022

Formation Path Following Control of Underactuated AUVs -- With Proofs

This paper proposes a novel method for formation path following of multiple underactuated autonomous underwater vehicles. The method combines line-of-sight guidance with null-space-based behavioral control, allowing the vehicles to follow curved paths while maintaining the desired formation. We investigate the dynamics of the path-following error using cascaded systems theory, and show that the closed-loop system is uniformly semi-globally exponentially stable. We validate the theoretical results through numerical simulations.

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arXiv2021

Task-Priority Control of Redundant Robotic Systems using Control Lyapunov and Control Barrier Function based Quadratic Programs

This paper presents a novel task-priority control framework for redundant robotic systems based on a hierarchy of control Lyapunov function (CLF) and control barrier function (CBF) based quadratic programs (QPs). The proposed method guarantees strict priority among different groups of tasks such as safety-related, operational and optimization tasks. Moreover, a soft priority measure in the form of penalty parameters can be employed to prioritize tasks at the same priority level. As opposed to kinematic control schemes, the proposed framework is a holistic approach to control of redundant robotic systems, which solves the redundancy resolution, dynamic control and control allocation problems simultaneously. Numerical simulations of a hyper-redundant articulated intervention autonomous underwater vehicle (AIAUV) is presented to validate the proposed framework.

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arXiv2020

Economic model predictive control for snake robot locomotion

In this work, the control of snake robot locomotion via economic model predictive control (MPC) is studied. Only very few examples of applications of MPC to snake robots exist and rigorous proofs for recursive feasibility and convergence are missing. We propose an economic MPC algorithm that maximizes the robot's forward velocity and integrates the choice of the gait pattern into the closed loop. We show recursive feasibility of the MPC optimization problem, where some of the developed techniques are also applicable for the analysis of a more general class of system. Besides, we provide performance results and illustrate the achieved performance by numerical simulations. We thereby show that the economic MPC algorithm outperforms a standard lateral undulation controller and achieves constraint satisfaction. Surprisingly, a gait pattern different to lateral undulation results from the optimization.

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arXiv2017

Observer Based Path Following for Underactuated Marine Vessels in the Presence of Ocean Currents: A Local Approach - With proofs

In this article a solution to the problem of following a curved path in the presence of a constant unknown ocean current disturbance is presented. The path is parametrised by a path variable that is used to propagate a path-tangential reference frame. The update law for the path variable is chosen such that the motion of the path-tangential frame ensures that the vessel remains on the normal of the path-tangential reference frame. As shown in the seminal work [20] such a parametrisation is only possible locally. A tube is defined in which the aforementioned parametrisation is valid and the path-following problem is solved within this tube. The size of the tube is proportional to the maximum curvature of the path. It is shown that within this tube, the closed-loop system of the proposed controller, guidance law, and the ocean current observer provides exponential stability of the path-following error dynamics. The sway velocity dynamics are analysed taking into account couplings previously overlooked in the literature, and is shown to remain bounded. Simulation results are presented.

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arXiv2016

Set-based Control for Autonomous Spray Painting

In this paper, a method is presented for lowering the energy consumption and/or increasing the speed of a standard manipulator spray painting a surface. The approach is based on the observation that a small angle between the spray direction and the surface normal does not affect the quality of the paint job. Recent results in set-based kinematic control are utilized to develop a switched control system, where this angle is defined as a set-based task with a maximum allowed limit. Four different set-based methods are implemented and tested on a UR5 manipulator from Universal Robots. Experimental results verify the correctness of the method, and demonstrate that the set-based approaches can substantially lower the paint time and energy consumption compared to the current standard solution.

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