# Omni-copter

Omnicopters are six-degrees of freedom multi-rotor aerial vehicles whose dynamical properties are almost independent of the vehicle orientation and that are able to hover and accelerate in any direction at any altitude. Its omni-directionality allows the vehicle to fully exploit its decoupled translational and rotational dynamics with smooth possible maneuvers.

Generally, multi-rotor vehicles like quadcopters and helicopters are used due to their agility , size and mechanical simplicity. But these Aerial Systems are under-actuated. Most multi rotor vehicles such as quadcopters have a preferred direction in which substantially more thrust can be produced than in others in order to increase performance criteria such as flight duration, robustness, or payload.They are unable to independently control their thrust and torque in all three dimensions. The translation dynamics are coupled with the rotational dynamics of the systems.

Fig 1: All the rotors (actuators) are aligned in the same plane for a quadcopter. To move from Point A to Point B (Translational motion) the system needs to rotate to generate a horizontal component of the thrust and accelerate in the horizontal direction.

The eight-rotor configuration of the omni-copter maximise the agility in any direction and possesses full force and torque authority in all three dimensions. It can generate thrust in any direction and its translational properties are decoupled with the rotational dynamics of the systems. Let the state variables with respect to the center of mass of the body be represented as 𝛃 and the state variables of the system with respect to initial frame be represented as 𝞐. When the rotational and translational dynamics are coupled, then we define the Rotational Matrix (R) to relate the two state variables as,

S(𝛃) = R . S(𝞐) - Eq-1

Considering the inertia Tensor of the system , by eq-1 , it reduces to the multiple of the Identity matrix (to satisfy S(𝛃) = S(𝞐) ). From [1], Points which satisfy this are the vertices of regular solids of which the smallest three sets of points are the vertices of a regular tetrahedron (N = 4), the vertices of a regular octahedron (N = 6) and the vertices two arbitrary aligned regular tetrahedra whose centers coincide (N = 8).

Fig 2: Solving the optimisation problem and from [1], the for the sake of realisability, this activator configuration is found out to be the better configuration.

A control strategy that allows for exploiting the vehicle’s decoupled translational and rotational dynamics is required to attain a novel set of maneuvers. Considering the Ƥ being the desired position vector of the system, feeding this to the PID controller as depicted in fig 3, the force that is required to be generated by each of the actuators can be derived. The IMU of the System calculates the real time data of the System and is used as a feedback to calculate the Error in position, velocity or acceleration to drive the controller. The P, D gains of the system can be tuned through the multiple stages of the experiment. The force output from the controller needs to be converted to propellor thrust. There may be multiple values of propeller thrusts possible for the same values of force and torque, the propeller thrust is generated by pseudo-inverse.

Fig 3, PID controller.

Because of the non-planar configuration and tight arrangement of rotors, complex aerodynamic effects such as interference between rotors or induced velocity are likely to have a substantial effect on the vehicle dynamics for non-steady flight. Further study needs to be done which enables such designs to overcome the aerodynamic effects and to be used for various real life applications.

References:

- P. K. Aravind, “A comment on the moment of inertia of symmetrical solids,” American Journal of Physics, vol. 60, pp. 754–755, Aug. 1992.
- 2016 IEEE International Conference on Robotics and Automation (ICRA) Stockholm, Sweden, May 16-21, 2016, Design, Modeling and

Written by - Sai Ashwin , Nisarg Chaudhari , Raghavendra K