Differential Flatness Transformations for Aggressive Quadrotor Flight

Aggressive maneuvering amongst obstacles could enable advanced capabilities for quadrotors in applications such as search and rescue, surveillance, inspection, and situations where rapid flight is required in cluttered environments. Previous works have treated quadrotors as differentially flat systems, and this property has been exploited widely to design simple algorithms that generate dynamically feasible trajectories and to enable hierarchical control. The differentially flat property allows the full state of the quadrotor to be extracted from the reduced dimensional space of x, y, z, yaw and their derivatives. This differential flatness transformation has a number of singularities, however, as well as stability issues when controlling near these singularities. Many methods have been described in the literature to address these; however, they all have limitations when exploring the full flight envelope of a quadrotor, including roll or pitch angles past 90°, and during inverted flight. In this paper, we review these existing methods and then introduce our method, which combines multiple methods to provide a highly-robust differential flatness transformation that addresses most of these issues. Our approach is demonstrated enabling highly-aggressive quadrotor flight in both simulations and real-world experiments.

Authors

• Benjamin Morrell
• Marc Rigter
• Gene B. Merewether
• Robert G. Reid
• Rohan Thakker
• Theodore Tzanetos
• Vinay Rajur
• Gregory E. Chamitoff

Keywords

• Trajectory
• Attitude control
• Standards
• Acceleration
• Aerospace electronics
• Australia
• Robustness
• Differential Transformation
• Differential Flatness
• Pitch Angle
• Roll Angle
• Standard Method
• Large Changes
• Cross-product
• Revolutions Per Minute
• Body Axis
• Sensitive Region
• Yaw Angle
• Standard Transformation
• Trajectory Planning
• Orthogonal Vectors
• Angle Of Approach
• Outer Control
• Flight Test
• Flat Space
• Trajectory Tracking Control
• Roll Rate
• Pitch Rate
• Flight Experiments
• Jump Discontinuities
• Singular Type
• Indoor Environments
• Yaw Rate
• Outer Position