Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2507.04846

Dynamics and multi-stability of a rotor-actuated Twistcar robot with passive steering joint

Anna Zigelman·Zitao Yu·Rom Levy·Yizhar Or
View original source ↗Read source document ↗Export metadata ↓

Abstract

The nonlinear dynamics of many under-actuated wheeled platforms are governed by nonholonomic constraints of no-skid for passively rolling wheels, coupled with momentum balance. In most of theoretical models, the shape variables, i.e. joint angles, are directly prescribed as periodic inputs, such as steering angle of the Twistcar. In this work, we study a variant of the Twistcar model where the actuation input is periodic oscillations of an inertial rotor attached to the main body, while the steering joint is passively free to rotate. Remarkably, the dynamics of this model is extremely rich, and includes multiplicity of periodic solutions, both symmetric and asymmetric, as well as stability transitions and bifurcations. We conduct numerical simulations as well as asymptotic analysis of the vehicle's reduced equations of motion. We use perturbation expansion in order to obtain leading-order dynamics under symmetric periodic solution. Then, we utilize harmonic balance and further scaling assumptions in order to approximate the conditions for symmetry-breaking pitchfork bifurcation and stability transition of the symmetric periodic solution, as a function of actuation frequency and structural parameters. The asymptotic results show good agreement with numerical simulations. The results highlight the role of passive shape variables in generating multi-stable periodic solutions for nonholonomic systems of robotic locomotion.

Explore related subjects

cs.RO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Anna Zigelman, Zitao Yu, Rom Levy, Yizhar Or. 2025-07-08. Dynamics and multi-stability of a rotor-actuated Twistcar robot with passive steering joint. https://arxiv.org/abs/2507.04846

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

J-PARSE: Jacobian-based Projection Algorithm for Resolving Singularities Effectively in Inverse Kinematic Control of Serial Manipulators

J-PARSE is an algorithm for smooth first-order inverse kinematic control of a serial manipulator near kinematic singularities. The commanded end-effector velocity is interpreted component-wise, according to the available mobility in each dimension of the task space. First, a substitute ''Safety'' Jacobian matrix is created, keeping the aspect ratio of the manipulability ellipsoid above a threshold value. The desired velocity is then projected onto non-singular and singular directions, and the latter projection scaled down by a factor informed by the altered mobility. A right-inverse of the non-singular Safety Jacobian is applied to the modified command. In the absence of joint limits and collisions, this ensures safe transition into and out of low-mobility configurations, guaranteeing locally stable reaching behavior towards target poses within, on the boundary of, and outside the workspace. The behavior is further guaranteed to be locally asymptotically stable if the starting and target configurations are not exactly singular, even if they are nearly singular. Velocity control with J-PARSE is benchmarked against approaches from the literature, illustrating its use of a single tuning parameter to simultaneously achieve high reaching accuracy and stable behavior. Applications in teleoperation, servoing, and learning are demonstrated. Videos and code are available at https://jparse-manip.github.io/.

cs.RO↗
arXiv2026

Spatiotemporal Calibration of Doppler Velocity Logs for Underwater Robots

The calibration of extrinsic parameters and clock offsets between sensors for high-accuracy performance in underwater SLAM systems remains insufficiently explored. Existing methods for Doppler Velocity Log (DVL) calibration are either constrained to specific sensor configurations or rely on oversimplified assumptions, and none jointly estimate translational extrinsics and time offsets. We propose a Unified Iterative Calibration (UIC) framework for general DVL sensor setups, formulated as a Maximum A Posteriori (MAP) estimation with a Gaussian Process (GP) motion prior for high-fidelity motion interpolation. UIC alternates between efficient GP-based motion state updates and gradient-based calibration variable updates, supported by a provably statistically consistent sequential initialization scheme. The proposed UIC can be applied to IMU, cameras and other modalities as co-sensors. We release an open-source DVL-camera calibration toolbox. Beyond underwater applications, several aspects of UIC-such as the integration of GP priors for MAP-based calibration and the design of provably reliable initialization procedures-are broadly applicable to other multi-sensor calibration problems. Finally, simulations and real-world tests validate our approach.

cs.RO↗
arXiv2026

HazardArena: Evaluating Semantic Safety in Vision-Language-Action Models

Vision-Language-Action (VLA) models inherit rich world knowledge from vision-language backbones and acquire executable skills via action demonstrations. However, existing evaluations largely focus on action execution success, leaving action policies loosely coupled with visual-linguistic semantics. This decoupling exposes a systematic vulnerability whereby correct action execution may induce unsafe outcomes under semantic risk. To expose this vulnerability, we introduce HazardArena, a benchmark designed to evaluate semantic safety in VLAs under controlled yet risk-bearing contexts. HazardArena is constructed from safe/unsafe twin scenarios that share matched objects, layouts, and action requirements, differing only in the semantic context that determines whether an action is unsafe. We find that VLA models trained exclusively on safe scenarios often fail to behave safely when evaluated in their corresponding unsafe counterparts. HazardArena includes over 2,000 assets and 40 risk-sensitive tasks spanning 7 real-world risk categories grounded in established robotic safety standards. To mitigate this vulnerability, we propose a training-free Safety Option Layer that constrains action execution using semantic attributes or a vision-language judge, substantially reducing unsafe behaviors with minimal impact on task performance. We hope that HazardArena highlights the need to rethink how semantic safety is evaluated and enforced in VLAs as they scale toward real-world deployment. Code released at https://github.com/HazardArena-Team/HazardArena ; updated code availability information.

cs.RO↗