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A Control Theoretic Study on Omnidirectional MAVs with Minimum Number of Actuators and No Internal Forces at Any Orientation

Ahmed Ali, Chiara Gabellieri, Antonio Franchi

Abstract

We propose a new multirotor aerial vehicle class of designs composed of a multi-body structure in which a main body is connected by passive joints to links equipped with propellers. We have investigated some instances of such class, some of which are shown to achieve omnidirectionality while having a minimum number of inputs equal to the main body Degrees of Freedom DoF's, only uni-directional positive thrust propellers, and no internal forces generated at steady state. After dynamics are derived following the Euler-Lagrange approach, an I/O dynamic feedback linearization strategy is then used to show the controllability of any desired pose with stable zero dynamics. We finally verify the developed controller with closed-loop simulations.

A Control Theoretic Study on Omnidirectional MAVs with Minimum Number of Actuators and No Internal Forces at Any Orientation

Abstract

We propose a new multirotor aerial vehicle class of designs composed of a multi-body structure in which a main body is connected by passive joints to links equipped with propellers. We have investigated some instances of such class, some of which are shown to achieve omnidirectionality while having a minimum number of inputs equal to the main body Degrees of Freedom DoF's, only uni-directional positive thrust propellers, and no internal forces generated at steady state. After dynamics are derived following the Euler-Lagrange approach, an I/O dynamic feedback linearization strategy is then used to show the controllability of any desired pose with stable zero dynamics. We finally verify the developed controller with closed-loop simulations.

Paper Structure

This paper contains 10 sections, 2 theorems, 30 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Dynamic Model
  3. Omnidirectionality analysis
  4. Controller Design
  5. Simulation Results
  6. Robustness Analysis of Trajectory Tracking Scenario
  7. Robustness against parametric uncertainty
  8. Robustness against external disturbance
  9. discussion
  10. Conclusion

Key Result

Proposition 1

At any equilibrium pose $\boldsymbol{q}^i_d \in \mathcal{D}^i_q$, Type 1 vehicle is not omnidirectional while Type 2 is fully omnidirectional.

Figures (5)

  • Figure 1: A schematic representation of instances in Type 1 and 2, where $N$=3 and $N$=2, respectively. The non-inertial body frames are attached to each body's CoM. $f_i$ is the thrust of the propeller $i$. $\tau_a$ is the servo torque while $\tau_{f_i}$ denotes the friction at joint $i$.
  • Figure 2: Evolution of states and control input is depicted. The initial state in Sim 1 (a,c,e) is another admissible equilibrium $\in \mathcal{D}^2_x$ while in Sim 2 (b,d,f) it is chosen randomly $\in \mathcal{L}_E$ in the vicinity of the desired equilibrium. Last row: zero dynamics evolution starts from a single initial condition (g) and multiple conditions (h).
  • Figure 3: Tracking errors of the orientation and position are shown for each maximum perturbation $\Delta p$ of each parameter in positive (a,c) and negative (b,d) magnitudes.
  • Figure 4: Evolution of the worst-case output error, within the uniformly sampled 1000 combined perturbations, is depicted.
  • Figure 5: Time evolution of output error is illustrated when disturbances having different frequencies enter the system output channels at the acceleration level.

Theorems & Definitions (5)

  • Definition : Omnidirectional MAV Understanding
  • Proposition 1
  • proof
  • Theorem 1
  • proof