Differential-Flatness and Control of Quadrotor(s) with a Payload Suspended through Flexible Cable(s)
For researchers in aerial robotics, this work provides a theoretical framework for planning and control of quadrotors with flexible cable-suspended payloads, addressing a high-dimensional underactuated problem.
This paper presents coordinate-free dynamics for quadrotor systems with payloads suspended through flexible cables modeled as multiple links, proves differential flatness for trajectory planning, and demonstrates tracking control with a finite-horizon LQR for a 16-DOF system.
We present the coordinate-free dynamics of three different quadrotor systems : (a) single quadrotor with a point-mass payload suspended through a flexible cable; (b) multiple quadrotors with a shared point-mass payload suspended through flexible cables; and (c) multiple quadrotors with a shared rigid-body payload suspended through flexible cables. We model the flexible cable(s) as a finite series of links with spherical joints with mass concentrated at the end of each link. The resulting systems are thus high-dimensional with high degree-of-underactuation. For each of these systems, we show that the dynamics are differentially-flat, enabling planning of dynamically feasible trajectories. For the single quadrotor with a point-mass payload suspended through a flexible cable with five links (16 degrees-of-freedom and 12 degrees-of-underactuation), we use the coordinate-free dynamics to develop a geometric variation-based linearized equations of motion about a desired trajectory. We show that a finite-horizon linear quadratic regulator can be used to track a desired trajectory with a relatively large region of attraction.