Indoor experimental validation of MPC-based trajectory tracking for a quadcopter via a flat mapping approach

LP-Generated Control Lyapunov Functions With Application to Multicopter Control

“…Besides, the image of the constraint ( 24) via ( 25) can be characterized as a convex set of u pos ≜ [u x , u y , u z ] ⊤ ∈ R 3 as in [29]:…”

“…with ϵ max ≜ min(ϕ max , θ max ). The set U pos is convex since it is the intersection of two convex sets: a ball of radius T max centered at −ge 3 and a convex cone defined with ϵ max and g. A detailed characterization of U pos as in ( 27) can be found in [29]. With the dynamics (26), one can consider this linearized system as either three independent double integrators in R 2 tangled by the constraint (27) or one system in R 6 and the input constraint u pos ∈ U pos .…”

“…where ζ ≜ p x p y p z ∈ R 6 and u pos denote the state and the input vector as in (27), respectively. u pos ∈ U p as in (29),…”

“…Values Tmax as in (27) 1.45g ≈ 14.22 m/s 2 θmax = ϕmax = ϵmax as in ( 24), (27) 0.1745 rad ūx, ūy, ūz as in (28) 0.8154, 0.8154, 3.27 S 1 , S 2 as in (29) 7, 3…”

“…In this subsection, the formulation of the CLFs for ( 26) and (30) subject to (28) and (29), respectively, will be discussed. With these functions come two ways of controlling the drone, as the following.…”