Confidence-weighted constrained torque allocation for fault-tolerant control of robotic manipulators: A convex projection-based framework

The paper proposes a confidence-weighted constrained torque allocation model of fault-tolerant control (FTC) of robotic manipulators in the presence of actuator degradation and sensor uncertainty. The presented approach develops the redistribution of the torque into a strictly convex quadratic programming (QP) problem including explicit torque magnitude and rate constraints and obtains a global minimum at every sampling instant. The adaptive positive-definite weighting matrix incorporates actuator effectiveness estimation and a smoothed version of the normalized innovation squared (NIS)-based confidence mechanism, which is used to form the geometry of allocation in real-time. The resulting control law admits a projection-based interpretation, in which the allocated torque is a weighted projection onto a time-varying convex feasible set. Lyapunov analysis has been used to determine uniform ultimate boundedness of the tracking error in the presence of degradation by modeling the projection-induced deviation as a bounded disturbance. The Monte Carlo simulations of a 6-degree-of-freedom (DOF) manipulator operated under moderate and severe constraints activated scenarios indicate that the unconstrained methods can reach slightly smaller Root Mean Square Error (RMSE) but with the proposed framework in this paper, strict feasibility, bounded tracking, moderate energy usage, and measurable constraint engagement are ensured. The findings of this paper validate the theory of feasible optimality rather than unconstrained optimality and offer a mathematically transparent and stability-preserving FTC strategy for manipulators operating under actuator and sensor faults.