Pose estimation for underactuated cable-driven parallel robots

This PhD thesis addresses pose estimation for underactuated cable-driven parallel robots using proprioceptive sensing. In underactuated architectures, the geometric mapping from cable lengths to end-effector pose is intrinsically underdetermined: geometry alone does not yield a unique configuration, and the physically attained pose requires additional constraints such as static equilibrium. Classical geometrico-static formulations close the problem by enforcing equilibrium, but introduce dependencies on mass/inertia parameters and may admit multiple equilibria. The main objective is to obtain accurate pose estimates without explicitly enforcing equilibrium, by exploiting redundant proprioceptive measurements and a unified geometric/differential-kinematic modeling framework covering both spatial and planar cases. The model includes routing effects induced by swivel pulleys through explicit angle variables, and differential kinematics provides the analytic Jacobians required by iterative solvers. Building on these foundations, the thesis develops a sensor-fusion direct-kinematics method formulated as a weighted nonlinear least-squares problem. A flexible residual set is constructed by stacking heterogeneous pose-dependent quantities: cable lengths, pulley angles, and directly measured pose components (e.g., orientation from an inclinometer). The problem is solved via Gauss–Newton iterations with inverse-error weights. Since residual components are heterogeneous (meters and radians), component-wise termination conditions are defined, enforcing physically interpretable bounds separately on translation and orientation, preventing premature acceptances. The estimator is further extended with a tension-aware procedure: measurement uncertainties are modeled as functions of cable tensions, identified offline via density-aware fitting using linear or inverse models. Online, these models adapt both the weighting matrix and the termination thresholds according to configuration-dependent reliability. Experimental validations on two platforms — a planar 2-cable prototype and a spatial 4-cable 6-DoF prototype — show that appropriate redundancy improves observability, component-wise termination achieves accuracy comparable to stricter norm-based rules with lower runtimes, and the tension-aware formulation markedly reduces computational cost and iteration counts, often converging in a single Gauss–Newton update.