arXiv subjects

Shankar Deka

Publications and source records attributed to Shankar Deka.

3 recordsLinked to original sources

arXiv2026

Barrier Certificate Synthesis for Non-Polynomial Robotic Dynamics via Polynomial Lifting

Safe operation of robotic systems requires trajectories to remain within a prescribed safe set under admissible control inputs. Barrier certificates provide such guarantees by certifying a controlled-invariant region within that set. Sum-of-squares optimization offers a systematic way to synthesize such certificates, but its direct application requires polynomial dynamics, excluding common robotic nonlinearities, including trigonometric terms. We address this limitation using exact polynomial lifting, which replaces non-polynomial dynamics with polynomial-augmented dynamics subject to lifting-induced algebraic constraints, preserving nonlinear geometry without approximation. We formulate lifted-domain joint barrier synthesis that computes a certificate with a state-feedback control witness and develop a sampled-data safety filter for zero-order-hold implementation. To assess whether the benefits of lifting persist across synthesis frameworks, we also adapt a sample-guided successive-barrier method to the lifted representation. On coordinated-turn and planar multirotor models, exact lifting improves certified coverage in both methods: at matched sample sizes, lifted successive-barrier synthesis achieves higher coverage with fewer barriers and lower computational cost, while lifted joint barrier synthesis provides higher coverage and lower computational cost than the finest tested piecewise resolution. In closed-loop experiments, the safety filter maintains feasibility and safety across all evaluated trajectories, reduces spatial conservativeness, and requires less intervention for both models.

cs.RO↗

arXiv2026

Uncertainty Quantification via Invariant-Measure Conformal Prediction

Uncertainty quantification for learned stochastic dynamical systems is essential in safety-critical tasks such as control and monitoring. Standard conformal prediction provides finite-sample coverage guarantees under exchangeability, but this assumption is typically violated in dynamical systems because trajectory data are temporally dependent, state distributions evolve, and recursive prediction errors accumulate. This paper proposes an invariant-measure conformal prediction (imCP) framework that calibrates uncertainty using independent samples from an invariant measure of the Markov process induced by the dynamics. This aligns calibration with the stationary operating regime and restores the statistical symmetry needed for rolling one-step split conformal guarantees. For recursive multi-step prediction, imCP combines conformal calibration with Lipschitz error propagation through the learned predictor to obtain explicit horizon-dependent bounds.These pre-deployment uncertainty tubes are suitable for rolling and receding-horizon applications, such as self-triggered control and fault detection, where uncertainty bounds must be computed before future residuals are observed. Numerical experiments show that imCP yields reliable bounds, while non-invariant calibration can become misaligned during deployment.

eess.SY↗

arXiv2026

Minimal Intervention Shared Control with Guaranteed Safety under Non-Convex Constraints

Shared control combines human intention with autonomous decision-making. At the low level, the primary goal is to maintain safety regardless of the user's input to the system. However, existing shared control methods-based on, e.g., Model Predictive Control, Control Barrier Functions, or learning-based control-often face challenges with feasibility, scalability, and mixed constraints. To address these challenges, we propose a Constraint-Aware Assistive Controller that computes control actions online while ensuring recursive feasibility, strict constraint satisfaction, and minimal deviation from the user's intent. It also accommodates a structured class of non-convex constraints common in real-world settings. We leverage Robust Controlled Invariant Sets for recursive feasibility and a Mixed-Integer Quadratic Programming formulation to handle non-convex constraints. We validate the approach through a large-scale user study with 66 participants-one of the most extensive in shared control research-using a simulated environment to assess task load, trust, and perceived control, in addition to performance. The results show consistent improvements across all these aspects without compromising safety and user intent. Additionally, a real-world experiment on a robotic manipulator demonstrates the framework's applicability under bounded disturbances, ensuring safety and collision-free operation.

cs.RO↗