This study focuses on Physical Human-Robot Interaction (pHRI) tasks that require a close coupling between safety constraints and compliance with human intentions. To address this, the authors propose a novel switched admittance controller for an n-link manipulator to comply with external forces while ensuring safety in the workspace. The controller switches between two reference models to generate a reference trajectory that maintains the safety constraints. Stability analysis of the switched reference model is performed by selecting an appropriate Common Quadratic Lyapunov Function (CQLF), which ensures the asymptotic convergence of the trajectory tracking error. The effectiveness of the proposed controller is demonstrated through simulation on a 4-DOF SCARA (RRPR) robot manipulator.
Chayan Kumar Paul, Neetish Patel, Bhabani Shankar Dey, and Indra Narayan Kar; "Adaptive Impedance Control: A Contraction Theory Approach", 2024 Eighth IFAC International Conference on Advances in Control and Optimization of Dynamical Systems (ACODS 2024).
This paper introduces an adaptive impedance control framework tailored for a rigid manipulator with n links, even in scenarios where the precise model is not known apriori. The framework utilizes a contraction theory-based virtual system, ensuring the exponential convergence of the actual trajectory towards the desired one. Within this framework, only the underlying structure of the matrices governing the manipulator's system dynamics is assumed to be known. By ensuring incremental stability of the virtual system dynamics, the framework guarantees exponential convergence of the tracking error. This primarily involves assessing the negative definiteness of the Jacobian, which governs the differential dynamics of the virtual system. To validate this approach, simulation results for a 2-link rigid manipulator are presented, offering empirical validation for the proposed method.
Neetish Patel, Chayan Kumar Paul, Indra Narayan Kar, and S. Mukherjee;"Finite-Time Adaptive Backstepping Control Approach for Quadrotors", 2024 Eighth IFAC International Conference on Advances in Control and Optimization of Dynamical Systems (ACODS 2024).
The adaptive finite-time backstepping control method, presented in this work enables a quadrotor to precisely track desired trajectories. We use a direct adaptive neural network to handle the effects of unknown nonlinearities in the quadrotor model. Our study, based on Lyapunov theory, establishes the weight adaption laws for the neural network in addition to ensuring overall system stability. The performance of the quadrotor system is assessed under recurring disturbances. The suggested controller exhibits outstanding tracking accuracy as well as resistance to uncertainities and external disturbances. The effectiveness of the proposed strategy, emphasizing stability and tracking performance, is supported by simulation results.
Chayan Kumar Paul, Indra Narayan Kar and Janardhanan Sivaramakrishnan;"Unknown Input Dynamic Observer for a class of Nonlinear Systems using Contraction Analysis", Submitted in International Journal of Systems and Science (under review).
This paper proposes a novel methodology to design an unknown-input dynamic observer for a class of nonlinear systems, grounded in contraction theory. The primary contributions include a contraction-based framework for handling unknown inputs and the development of a dynamic observer structure that enhances robustness and steady-state accuracy. Existence and stability conditions are established using contraction analysis, ensuring exponential convergence of the estimation error. These conditions are further expressed as simplified linear matrix inequalities (LMIs), enabling computationally efficient implementation despite system nonlinearities. The proposed observer is evaluated against existing methods through numerical simulations, demonstrating improved performance and practical applicability in the presence of different unknown input.