Differential-Flatness and Control of Quadrotor(s) with a Payload Suspended through Flexible Cable(s)

摘要

We present the coordinate-free dynamics of three different quadrotor systems: (a) single quadrotor with a point-mass payload suspended through a flexiblecable; (b) multiple quadrotors with a shared point-mass payload suspendedthrough flexible cables; and (c) multiple quadrotors with a shared rigid-bodypayload suspended through flexible cables. We model the flexible cable(s) as afinite series of links with spherical joints with mass concentrated at the endof each link. The resulting systems are thus high-dimensional with highdegree-of-underactuation. For each of these systems, we show that the dynamicsare differentially-flat, enabling planning of dynamically feasibletrajectories. For the single quadrotor with a point-mass payload suspendedthrough a flexible cable with five links (16 degrees-of-freedom and 12degrees-of-underactuation), we use the coordinate-free dynamics to develop ageometric variation-based linearized equations of motion about a desiredtrajectory. We show that a finite-horizon linear quadratic regulator can beused to track a desired trajectory with a relatively large region ofattraction.