Physical Parameter Uncertainty in Robotic Manipulators: A Fuzzy Modeling Approach

Uncertain masses, dimensions, and friction coefficients can cause a robot’s motion to differ from predictions based on nominal parameters. This study examines how these uncertainties affect joint trajectories and which parameters deserve closer characterization. Ten physical parameters of a planar two-degree-of-freedom manipulator are represented by triangular fuzzy numbers, defined by lower, nominal, and upper values. Their α-cuts form nested parameter intervals, whose vertices are propagated through the nonlinear rigid-body equations to approximate the range of joint responses. Numerical tests use sinusoidal and step torques, different initial conditions, Monte Carlo sampling, and sensitivity analysis. Verification with 50,000 samples per tested domain reveals a small second-joint exceedance under baseline sinusoidal excitation and larger exceedances under step torques; the alternative sinusoidal configuration retains complete sampled containment. Under the baseline sinusoidal excitation, the individual parameter ranking remains unchanged at the four nondegenerate α levels tested; the link length l1, second-joint friction b2, and first-link mass m1 have the largest effects. A reduced-order surrogate also lowers the cost of repeated model evaluation within the tested domain. The contribution is an integrated workflow for assessing response dispersion and prioritizing parameter characterization before controller design or hardware testing. Its envelopes support preliminary model assessment rather than guaranteed response bounds.