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This paper develops a control-theoretic framework for contact-persistent full actuation in unmanned aerial vehicles (UAVs), addressing the limitations of traditional certification methods that overlook the impact of sustained contact on available control forces. By integrating a rigid-body model with a morphology-dependent wrench map, the authors define feasible and residual wrench sets that account for actuator limits and task loading. The key finding reveals that effective contact-persistent actuation is characterized by the interiority of the task wrench within the feasible wrench polytope, highlighting the importance of maintaining residual authority during aerial interactions.
Contact-persistent full actuation reveals that traditional rank conditions may mislead UAV performance in physical interactions, emphasizing the critical role of residual authority in control.
Fully actuated unmanned aerial vehicles (UAVs) are usually certified through rank conditions on a control-allocation matrix or through free-flight tracking performance. For aerial physical interaction, this certification may be incomplete. During sustained contact, part of the available wrench is consumed by the interaction task, and only the residual wrench remains available for stabilization, disturbance rejection, and maneuvering. This paper introduces a control-theoretic framework for \emph{contact-persistent full actuation}. A rigid-body model on $\R^{3}\times\SO\left(3\right)$ is combined with a morphology-dependent wrench map that captures fixed-tilt, variable-tilt, coaxial, and overactuated multirotor architectures. We define feasible wrench sets under actuator limits, residual wrench sets under task loading, and residual authority margins that strengthen the usual rank-based notion of full actuation. The main result shows that contact-persistent full actuation is equivalent to interiority of the task wrench in the constrained feasible wrench polytope, and that the residual authority radius is exactly the distance to the polytope boundary. We further introduce a signed residual-margin certificate for infeasible and boundary cases, a slack-maximizing allocation certificate, and a robust implementability condition that can be used as a margin-aware safety filter. Numerical evaluation on an abstract tilted hexarotor shows that full row rank alone does not imply feasible contact operation. Intermediate tilt angles preserve residual authority during pushing, whereas small or excessive tilts fail because of lateral-force deficiency or hover-margin loss.
