Passivity-Based Control of Multiple Quadrotors Carrying a Cable-Suspended Payload
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abstract
This thesis proposes several motion controllers to allow multiple quad-copters cooperatively
carry a cable-suspended payload. The problem is motivated by a desire for
developing a resilient scalable delivery vehicle that can be easily customized to its
payload. The control problem poses a number of challenges that complicate its design.
These include the quad-copter under-actuation, non-rigidity of the cables that
connect the payload to the copters, external disturbances, potential for inter-drone
collisions, and communication time-delay among the quad-copters. Simple robust
controllers with guaranteed stability are highly desirable in such safety critical applications. In this thesis, the energetic passivity property of the multi-body system combining
the quad-copters, cables and payload is employed to design novel motion controllers
for the system. These controllers make no assumption about the tension status of
the cables since this property holds whether the cables are in tension or not. The
design and stability analysis of the controllers rely on storage functions inspired by
the physical energy of the system. Quad-copters are able to produce thrust force
only along their propellers' axis. This under-actuation prevents direct application of
passivity-based controllers to the system under study. A cascade control structure
with an outer-loop position control and an inner-loop attitude control is employed to deal with the under-actuation. The first proposed controller assumes that the cables are attached to the quadcopters center of masses (COMs). This helps decouple the angular dynamics of the
quad-copters from the rest of the dynamics. As a result, the inner-loop attitude controllers
can be designed independently. First, angular controllers with exponentially
stable tracking errors are considered. While this produces nice theoretical results,
it requires measurements of linear acceleration and jerk, limiting its practical use.
Then, a modified cascade control structure is proposed that takes into account the
under-actuation and only needs measurements that are typically available in such
systems. Semi-global stability of the closed-loop system is shown, where the region
of attraction can be made arbitrary large by proper choice of control gains. An energy
observer/compensator is proposed to estimate perturbation-induced energy and
dissipate it through time-varying dampers. This helps suppress disturbance-induced
oscillations in the system response. The proposed controller is further revised to allow the cables be attached to the quad-copters and the payload at arbitrary points. This controller is augmented with an inter-drone collision avoidance term to prevent potential collisions among the drones. Another variation of the controller is developed by introducing inter-drone
coupling terms meant to improve the controller ability to preserve the formation shape
of the quad-copters. These coupling terms could potentially introduce time delay into
some of the feedback signal paths. An analysis is carried out to establish conditions
that the controller gains must satisfy in order to ensure closed-loop stability in the
presence of these time delays. The final contribution of this thesis focuses on the design of the reference positions for the quad-copters for the use in the controllers introduced earlier. In the proposed approach, the user specifies the desired position and orientation for the
payload. Given this desired pose, an optimization problem is formulated to find a
set of reference positions for the quad-copters that would minimize the total power
consumed under quasi-static conditions. The proposed controllers have been successfully evaluated in an indoor laboratory setting using measurements from a motion capture system and on-board IMUs. Results of the experiments are provided throughout the thesis.
