Adapting The Servo-Constraints Model Inversion Method For Robotic Cable Manipulation

Robotic Deformable Object Manipulation (DOM) is a research area of high practical relevance in various settings. While previous feedback-based, model-free solutions are effective, they can suffer from various limitations due to underlying assumption, such as quasi-static motions. To address this, we investigate a model-based trajectory tracking approach for manipulating cables, modeled as flexible multibody systems.

We adopt a two-stage strategy where a planner first generates a desired trajectory $z_d(t)$, then a trajectory tracking module computes the necessary control inputs $u(t)$ via inverse dynamics. Since DOM is an heavily underactuated problem, standard methods like computed torque are inapplicable. Consequently, we compare two alternatives: Optimal Control (OC) and the Servo-Constraints (SC) approach.

A significant challenge in applying standard SC to DOM is the requirement that the number of outputs equals the number of inputs ($n_z = n_u$). With deformable objects, the shape representation typically results in $n_z \gg n_u$. In addition, path planners relying on simplified models may generate physically infeasible trajectories, making the original SC approach ill-suited. To resolve this, we propose modifying the SC using a projection operator $P$, formulating the constraint as $P(z(t) - z_d(t)) = 0$. This projects the tracking error into a lower-dimensional space, ignoring orthogonal components that the system cannot physically correct. This modification enables valid inverse dynamics solutions even when $n_u < n_z$. The study compares this modified SC method against OC approaches in practical cable manipulation tasks.