Systems and methods for a transformable unmanned aerial vehicle with coplanar and omnidirectional features

A transformable Unmanned Aerial Vehicle (UAV), can operate as a coplanar hexacopter or as an omnidirectional multirotor based on different operation modes. The UAV has 100% force efficiency for launching or landing tasks in the coplanar mode. In the omnidirectional mode, the UAV is fully actuated in the air for agile mobility in six degrees of freedom (DOFs). Models and control design are developed to characterize the motion of the transformable UAV. Simulation results are presented to validate the transformable UAV design and the enhanced UAV performance, compared with a fixed structure.

FIELD

The present disclosure generally relates to unmanned aerial vehicles, and in particular, to a system and associated method for a transformable unmanned aerial vehicle with both coplanar and omnidirectional Features.

BACKGROUND

Industrial and agricultural unmanned aerial vehicles (UAVs) have been widely used for long-distance flight applications such as aerial photography, mapping, package transportation, inspection, and pesticide spraying during the last several decades. Typically, coplanar multirotor UAVs, such as quadcopters and hexacopters, are applied to perform these tasks because of their carrying capacity and mechanical simplicity. These UAVs primarily work at near-hovering equilibriums with the thrust vectors limited to a single direction. The coupled translational and rotational kinematics indicate dependent position and orientation control. However, independent control of all six degrees of freedom (DOFs) for new challenges in difficult tasks, such as complex aerial movement and manipulation, may require full actuation with more actuators onboard.

Various tilted arms were added to common multirotors to achieve full even over actuation. Over-actuation could potentially enhance the overall system energy efficiency by optimizing control allocation on different actuators, which was demonstrated on ground vehicles. In some previous works, servo motors were added to rotate UAV arms independently around their main axes either radially or tangentially, and thus thrust vectors could be adjusted within certain limited angles in one plane to make the platform over-actuated. However, those platforms have low energy-efficiency issues for most movements due to internal force/torque cancellation. On the other hand, each arm of a quadcopter is typically designed to rotate in2with two servo motors, which caused a problem of short flight time by using eight additional motors to tilt four arms. Furthermore, in one example, a coupled tiltable mechanism controlled by two servos was added to adjust directions of thrust vectors. Unlike the four-servo and the eight-servo solutions, these platforms could reduce or avoid energy dissipation issues. Due to the limitation of mechanical design and actuator constraints, although the platforms with tiltable arms increased force or energy efficiency with over-actuation, they cannot achieve omnidirectional motions.

DETAILED DESCRIPTION

Omnidirectional UAVs demonstrate advantages of aerial interaction, uninhibited observation, and better capability for complex aerial manipulation missions, compared with common coplanar UAVs. Towards omnidirectional flight capability, platforms with fixed-motor configuration (and no tilt-arm servos) were developed based on optimization of static thrust and torque analysis in previous works. The force envelops must be larger than gravity in all directions with additional increments to maintain a hovering status. Hence, omnidirectional UAVs require at least six rotors allocated on at least three different planes are required. These platforms can exploit decoupled translational and rotational kinematics but suffer significant energy dissipation. By combining tiltrotor and omnidirectional fixed motor configurations, previous UAVs could hover in a given orientation while maintaining efficient flight configurations. However, these platforms are still heavy and suffer from short flight time without a power tether due to being equipped with six tilt-arm servos and twelve rotors (two on each arm with opposite direction to generate bi-directional thrusts). As such, these omnidirectional UAVs generally advance full-state flight capability but exhibit inherent limitations, such as overweight or significant energy dissipation. To achieve desired design weight and optimal energy efficiency with omnidirectional mobility, the number of the UAV actuators should be minimized.

Because coplanar UAVs typically have high energy efficiency, but with under-actuated configurations, a new trend of UAV design is to combine features of coplanar UAVs with full actuation. Although previous platforms could transit between an under-actuated coplanar mode and a fully actuated non-coplanar mode with one servo motor, which reduced energy consumption and design weight, these UAVs lacked the capability of omnidirectional motions and extended manipulation capability based on omnidirectional motions.

Motivated by the combined advantages of coplanar and omnidirectional UAVs, which can enable a broader range of applications, the present disclosure outlines a transformable UAV (hereinafter, “vehicle100” shown inFIGS.1A-1G) that integrates both coplanar and omnidirectional motion features. The vehicle100includes reversible motors with little nonlinearity influence (dead zone and delay at zero crossing) to generate bidirectional thrusts instead of dual motors placed in an opposite direction with heavier weights. Further, the vehicle100includes a transformation mechanism120(FIGS.2A-2C and3A-3C) that can use a single servo motor with a driving mechanism to transform the vehicle100between a coplanar (under-actuated) mode shown inFIG.1Aand an omnidirectional (fully-actuated) mode shown inFIG.1C. In another aspect, the vehicle100can be modeled and controlled with improved mobility performance. A controller200of the vehicle100is outlined inFIGS.6A and6B. When the vehicle100is in the coplanar mode ofFIG.1A, the vehicle100can operate in3as an under-actuated hexacopter without energy dissipation. When the vehicle100is in the omnidirectional mode ofFIG.1C, the vehicle100can track a full pose trajectory in3×SO(3) as a fully actuated system. As such, the vehicle100can arbitrarily transform for the required missions, e.g., long-range agile flight or complicated aerial manipulation.

This disclosure is structured as follows. The design and mathematical models for the vehicle100are introduced in Section II with reference toFIGS.1A-5. A full-pose geometry control scheme in3×SO(3) for the vehicle100is presented in Section III with additional reference toFIGS.6A and6B. Simulation results show the design validity and control performance in Section IV.

II. Modeling of the Transformable UAV

Section II.A outlines mechanical design of the vehicle100with reference toFIGS.1A-3C. Section II.B introduces an actuator model and analysis of the efficiency index. Section II.C presents a rigid body model and force efficiency.

FIGS.1A-1Crespectively show the vehicle100in a coplanar mode, a transitional mode, and an omnidirectional mode. As shown, the vehicle100includes a body102having a first arm104, a second arm106, and a third arm108that can be actuated between the coplanar mode ofFIG.1Aand the omnidirectional mode ofFIG.1C.

With additional reference toFIGS.1D-1G, the vehicle100includes six reversible rotor assemblies positioned along respective free ends of the first arm104, the second arm106, and the third arm108(e.g., where the first arm104includes a first rotor assembly144A and a second rotor assembly144B, the second arm106includes a third rotor assembly164A and a fourth rotor assembly164B, and the third arm108includes a fifth rotor assembly184A and a sixth rotor assembly184B). In the coplanar mode ofFIG.1A, these rotor assemblies generate thrusts normal to a common plane shared by the first arm104, the second arm106, and the third arm108. In the coplanar mode ofFIG.1A, an inertial reference frame is denoted asw=Ow{xw, yw, zw} and a body frame is denoted asb=Ob, {xb, yb, zb}. Obcorresponds to a center of the body frame and a center of mass.

In the coplanar mode ofFIG.1A, all six rotor assemblies are positioned along the same plane, and all rotor disk (e.g., propeller) norms are parallel to the zbaxis.FIG.1Ashows a first position of the second arm106and a first position of the third arm108associated with the coplanar mode. The second arm106and third arm108are coplanar with one another and with the first arm104, with the first arm104and the second arm106being mutually perpendicular with one another and with the third arm108being oriented at a 45 degree angle relative to the first arm104and the second arm106. Further, when in the coplanar mode ofFIG.1A, the third arm108can be oriented such that the fifth rotor assembly184A and sixth rotor assembly184B of the third arm108are oriented 180 degrees relative to the first rotor assembly144A and the second rotor assembly144B of the first arm104and the third rotor assembly164A and the fourth rotor assembly164B of the second arm106.

During the transitional mode ofFIG.1B, the second arm106(with third rotor assembly164A and fourth rotor assembly164B, also denoted by 3, 4) and the third arm108(with fifth rotor assembly184A and sixth rotor assembly184B, also denoted by 5, 6) rotate around the center of the first arm104(with first rotor assembly144A and second rotor assembly144B, also denoted by 1, 2) with a direction change of xb(in the body frame).FIG.1Bshows transitioning the second arm106and the third arm108between the first positions associated with the coplanar mode and second positions associated with the omnidirectional mode. When in the transitional mode ofFIG.1B, the second arm106rotates about a fulcrum that coincides with an axis of elongation of the first arm104to be mutually perpendicular with the first arm104and parallel with the vertical axis. Simultaneously, the third arm108rotates about a vertical axis (e.g., normal to the plane shared by the first arm104, second arm106, and third arm108in the coplanar mode ofFIG.1A) to be mutually perpendicular with the first arm104and the second arm106while remaining coplanar with the first arm104. During this motion, the third arm108also rotates about an axis of elongation of the third arm108such that the fifth rotor assembly184A and sixth rotor assembly184B of the third arm108are oriented 90 degrees relative to the first rotor assembly144A and the second rotor assembly144B of the first arm104.

In the omnidirectional mode ofFIG.1C, the six rotor assemblies are located at the vertices of a regular octahedron.FIG.1Cshows a second position of the second arm106and a second position of the third arm108associated with the omnidirectional mode. As shown, the second arm106is parallel with a vertical axis and is mutually perpendicular with the first arm104and the third arm108. The third rotor assembly164A and the fourth rotor assembly164B of the second arm106are shown having been rotated 90 degrees about an axis of elongation of the first arm104to a position that is mutually perpendicular with the first rotor assembly144A and the second rotor assembly144B of the first arm104and the fifth rotor assembly184A and sixth rotor assembly184B of the third arm108. Further, in the omnidirectional mode ofFIG.1C, the third arm108is mutually perpendicular with the first arm104and the second arm106and coplanar with the first arm104. Note that the first arm104does not necessarily rotate independently from the body102, and the third arm108rotates to form a 90 degree angle with the first arm104. In this mode, the third arm108has also been rotated 90 degrees about an axis of elongation of the third arm108such that the fifth rotor assembly184A and sixth rotor assembly184B of the third arm108are mutually perpendicular with the first rotor assembly144A and the second rotor assembly144B of the first arm104and the third rotor assembly164A and the fourth rotor assembly164B of the second arm106.

FIG.1Dalso shows a top plate112and a bottom plate114of the body102.FIGS.1E-1Grespectively show the first arm104, the second arm106and the third arm108.

As shown inFIG.1E, the first arm104(which does not need to rotate between the coplanar mode ofFIG.1Aand the omnidirectional mode ofFIG.1C) includes a first portion142A associated with the first rotor assembly144A and a second portion142B associated with the second rotor assembly144B. The first portion142A can include a first connection point141A and the second portion142B can include a second connection point141B that couple with the body102of the vehicle100. Further, the first rotor assembly144A is shown having a first motor146A in operative association with a first propeller148A. Likewise, the second rotor assembly144B is shown having a second motor146B in operative association with a second propeller148B.

As shown inFIG.1F, the second arm106(which needs to pivot as shown between the coplanar mode ofFIG.1Aand the omnidirectional mode ofFIG.1C) includes a first portion162A associated with the third rotor assembly164A and a second portion162B associated with the fourth rotor assembly164B. The first portion162A and the second portion162B can be linked at a fulcrum161that couples with the transformation mechanism120of the vehicle100as discussed further herein. The third rotor assembly164A is shown having a third motor166A in operative association with a third propeller168A. Likewise, the fourth rotor assembly164B is shown having a fourth motor166B in operative association with a fourth propeller168B.

As shown inFIG.1G, the third arm108(which needs to rotate about a direction of elongation of the third arm108as shown between the coplanar mode ofFIG.1Aand the omnidirectional mode ofFIG.1C) includes a first portion182A associated with the fifth rotor assembly184A and a second portion182B associated with the sixth rotor assembly184B. The first portion182A and the second portion182B can be linked at a receptacle181having a pivot point183that receives part of the transformation mechanism120of the vehicle100as discussed further herein. The fifth rotor assembly184A is shown having a fifth motor186A in operative association with a fifth propeller188A. Likewise, the sixth rotor assembly184B is shown having a sixth motor186B in operative association with a sixth propeller188B.

The three canonical rotation matrices in SO(3) are denoted with Rx, Ryand Rz, and the operating mode of the transformable UAV with μ∈[0, 1]. μ=0 is defined for the coplanar mode ofFIG.1A, μ∈(0, 1) for the transition state ofFIG.1B, and μ=1 for the omnidirectional mode ofFIG.1C. The position and disk normal of all six motors are given by:

The transformation mechanism120of the vehicle100is shown inFIGS.2A-3Cthat transitions the second arm106between the first position associated with the coplanar mode and the second position associated with the omnidirectional mode and simultaneously transitions the third arm108between the first position associated with the coplanar mode and the second position associated with the omnidirectional mode. To transform from the coplanar mode to the omnidirectional mode, the second arm106needs to rotate 90 degrees about the fulcrum161. Concurrently, the third arm108needs to rotate 90 degrees about a direction of elongation of the third arm108. The transformation mechanism120facilitates this motion. As shown inFIGS.2A-2C, the transformation mechanism120includes a servo motor122that couples with and directly rotates the second arm106about the fulcrum161(which can be coaxial with an axis of elongation of the first arm104) between the first position and the second position as shown. The servo motor122can rotate the second arm106upon receipt of an actuation signal from a computing device300(FIG.6A) of the vehicle100.

The transformation mechanism120further includes a helical gear set124, including a first helical gear component126that couples and rotates with the second arm106at the fulcrum161and a second helical gear component128that couples with the receptacle181of the third arm108. The transformation mechanism120includes a linkage assembly130that allows rotation of the third arm108about an axis of elongation of the third arm108concurrently with rotation of the second arm106about the fulcrum161. The linkage assembly130can include a first joint component132A that extends from the second arm106at the first helical gear component126as shown, and a second joint component132B that connects with the pivot point183of the third arm108. The first joint component132A connects with the second joint component132B by linkages134as shown inFIGS.2B and2C.

The first helical gear component126can be a beveled helical gear that engages with the second helical gear component128, which in turn rotates perpendicular to and concurrently with the first helical gear component126as shown. The second helical gear component128is positioned within the receptacle181of the third arm108and engages the pivot point183to connect the second arm106with the third arm108. The second helical gear component128includes a gear portion that engages the first helical gear component126, and rotates the third arm108about a vertical axis that is normal to the “shared” plane of the first arm104, the second arm106and the third arm108associated with the coplanar mode. This rotation causes the third arm108to transition between the first position and the second position (e.g., rotating the third arm108by 45 degrees in a first direction to become mutually perpendicular with the first arm104when transitioning the third arm108from the first position to the second position, or rotating the third arm108by 45 degrees in a second direction to transition the third arm108from the second position to the first position). Simultaneously, the linkage assembly130allows concurrent rotation of the third arm108by 90 degrees about the axis of elongation of the third arm108between the first position and the second position of the third arm108as the second arm106rotates about the fulcrum161between the first position and the second position of the second arm106.

FIGS.3A-3Cshow an example sequence of the transformation mechanism120between the coplanar mode (FIG.3A) and omnidirectional mode (FIG.3C) corresponding toFIGS.1A-1Cwith the transitional mode (FIG.3B) therebetween. As the servo motor122rotates the second arm106in a first rotational direction Q about the fulcrum161, the first helical gear component126and first joint component132A similarly rotate about the fulcrum161in the first rotational direction Q. Rotation of the first helical gear component126causes the second helical gear component128and third arm108to rotate in the second rotational direction R about a (vertical) axis that is normal to a plane shared by the first arm104and the third arm108as shown. Simultaneously, rotation of the first joint component132A causes the second joint component132B and the third arm108to rotate in a third rotational direction S about the axis of elongation of the third arm108. While the examples shown inFIGS.3A-3Cshow transitioning from the coplanar mode to the omnidirectional mode with rotational directions Q, R and S, the sequence and rotational directions can be reversed to transition from the omnidirectional mode to the coplanar mode.

During the transition, the angle between the heading axis xband the first arm104varies from 0 to 45 degree. A swift transition will be limited to avoid introducing unnecessary disturbances, and further discussions are given in subsections B and C. The transition time is designed within two seconds. The vehicle100will operate in either the coplanar or the omnidirectional mode.

B. Actuator Model & Efficiency Analysis

Most UAVs use unreversible motors plus ESCs, in which one single rotor thrust is constrained to:
0<frotor,min≤frotor≤frotor,max.  (3)

To generate a bi-directional thrust, two motors are placed in an opposite direction in some omnidirectional design, which causes large weight and energy loss. To overcome this issue, each rotor assembly (e.g., discussed above with reference toFIGS.1E-1G) of the vehicle100includes well-designed reversible motors with symmetric propellers, giving one single rotor-propeller thrust constrained to:
−frotor,max=frotor,min≤frotor≤frotor,max.  (4)

The dead zone effect can be ignored since min(|frotor|)<0.01N. With reversible motors, symmetric propellers, and suitable total weight, the omnidirectional flight of the vehicle100is achievable with two motors supplying most of the thrust to overcome the gravity. The thrust rotor and inverse torque rotor of each rotor are introduced and simplified as:

frotor,i=sgn⁢(ωi)⁢kf⁢ωi2τrotor,i=kτ-f⁢frotor,i⁢i=1,2⁢…6.(5)where ω is the rotor speed, and kfand kτ-fare aerodynamic factors of the rotors and the surrounding air, respectively. To simplify the actuator dynamics, the transfer function between the desired thrust frotor,desand actual thrust frotorcan be modeled as a first-order low-pass filter.

The total thrust F3×1and torque T3×1is given by:

For different μ that correspond to different modes or transition:

After the actuators are modeled, the rotor electrical power consumption is evaluated. An experiment using a reversible motor with a5045symmetric propeller was conducted. The rotor thrust vs. electrical power curve fitting is shown inFIG.4. A cubic polynomial model was developed in (10).

It is worth noting that {dot over (P)}rotor>0 for any reasonable frotor≥0. Thus, more energy will be cost if fewer actuators are selected to generate the same total thrust, which indicates the omni-mode costs more power than the coplanar mode at hovering.

In the coplanar mode, disk norms of six rotors are all collinear. The vehicle100works as an underactuated hexacopter with internal forces equal to zero during hovering. Yaw movement relies on the drag moment of each rotor. The vehicle100is fully actuated with internal forces determined by the current hovering orientation and transition state in the transition and omnidirectional mode. The force efficiency index is:

Clearly, γ(μ=0, frotor)=1 corresponds to the maximum force or energy efficiency.

The thrust vector coincides zbwithout any remnant in xband ybdirections. Hence, the vehicle100has four controllable degrees of freedom (3D position plus yaw angle). The force index maps corresponding to different μ∈(0,1] are shown inFIG.5. The vehicle100is fully actuated but can only enter the omnidirectional mode after the transformation. All three subplots have γ=1 at zbin the positive direction. When μ is small, most of the efficiency index map is smaller than 0.5. Two main points are discussed as follows. 1) The vehicle100should not generate any force in the direction of xband ybas the efficiency index is too low. The vehicle100needs to maintain low speed in transition and adds saturation on control inputs of rotors 3-6 at the early stage of transition. 2) To enter the omnidirectional mode or vice versa, the transition time is smooth enough to avoid unnecessary mechanical disturbances. As μ increases, the overall efficiency index keeps increasing. When μ=1, the vehicle100fully enters the omnidirectional mode. The efficiency index is between 57.7% and 100%. It reaches 100% (no internal forces) at each axis, corresponding to the maximum power efficiency matching six sets of roll-pitch angles during flight. Such orientations should be applied during hovering to maximize the flight time in the omni-mode.

C. Rigid Body Model

The rigid body kinematic model of the vehicle100is derived by considering the aerodynamic effects (interference) between rotors as disturbances. The inertial frame and the body frame are defined in subsection A. The translational dynamics of the vehicle100are described by the position p=[pxpypz]T and the velocity v=[vxvyvz]T. g=[0 0 g]Tis the gravity vector, and F, T are defined in (8). Based on, R is the rotation matrix maps from the body frame to the inertial frame, and ω=[ωxωyωz]Tdenotes the vehicle body angular velocity with the A operator converting ω into ω∧. Then the translational (force) and rotational (torque) aerodynamic drag equations are denoted as:

Cv, Cωare drag coefficients. τsrepresents the inverse torque generated from the mechanical structure in transition. The center of gravity is not essentially changed since the transformation mechanism120is located in the center of the body102, and all modules are placed symmetrically. Summing all torque and thrust contributions and using the Newton-Euler approach, the equation of motion of the vehicle100is expressed as:

{p˙=νn⁢ν˙=-m⁢g+RF-FvR˙=R⁢ω∧=R[0-ωzωyωz0-ωx-ωyωx0]J⁢ω˙=-ω×J⁢ω+T-τω-τs,(13)where m is the mass of the vehicle100and J is the 3×3 inertia tensor matrix. Then Jarm 3-4, Jarm 5-6, Jrestand rest are the inertia tensor matrices of the green arm, blue arm, and the rest of the body parts, respectively. Jarm 3-4,0, Jarm 5-6,0, Jrest,0are inertia tensor matrices of all these body parts when μ=0. Thus:

Based on (8) and (13), the equation of acceleration and rotation can be compactly rewritten as:

where B has the same rank as A. Unlike prior works, the vehicle100performs tasks either as a coplanar underactuated hexacopter or as an omnidirectional multirotor with rotors located at the vertices of a regular octahedron.

III. Control Design

In this section, a switching control structure on SO(3) is introduced for the vehicle100in Section II.FIGS.6A and6Bshow electrical components including a control architecture of a controller200of the vehicle100.

As shown inFIG.6A, the vehicle100can include a computing device300that implements functionalities of the controller200, including applying actuation signals to various motors of the vehicle100. These motors include: the servo motor122of the transformation mechanism120, the first motor146A of the first rotor assembly144A, the second motor146B of the second rotor assembly144B, the third motor166A of the third rotor assembly164A, the fourth motor166B of the fourth rotor assembly164B, the fifth motor186A of the fifth rotor assembly184A, and the sixth motor186B of the sixth rotor assembly184B. In particular, the computing device300can apply actuation signal(s) to the servo motor122to transition the second arm106between the first position and the second position of the second arm106, which causes the third arm108to concurrently transition between the first position and the second position of the third arm108. The computing device300can also apply actuation signal(s) to one or more of the first rotor assembly144A, the second rotor assembly144B, the third rotor assembly164A, the fourth rotor assembly164B, the fifth rotor assembly184A, and the sixth rotor assembly184B for propulsion and steering of the vehicle. In some examples, the vehicle100can include one or more sensor(s)118for data capture as well as position and attitude control. Examples include, but not limited to, an inertial measurement unit, an accelerometer, a global positioning system, a LiDAR unit, and/or an image capture device.FIG.6Aalso shows a power assembly116that can be coupled along the vehicle100and can include power source(s), connection elements, and other components that provide and/or regulate power delivery to the motors, computing device300, and sensor(s)118.

FIG.6Bshows a control architecture of the controller200for implementation of various functionalities of the vehicle100. The controller200includes a position controller and an attitude controller, and each have different characterizations depending on the mode of the vehicle100(e.g., coplanar mode or omnidirectional mode).

To avoid low force efficiency along x,y axis as μ≤0.5, the controller switching is performed at μ=μ0>0.5. In the coplanar mode, translational and rotational dynamics are coupled. Heading direction (yaw angle) and position tracking are achieved in a coupled loop. First, the position controller of the controller200calculates desired rotation matrix and a total thrust at zb. The attitude controller of the controller200subsequently outputs desired torques. Finally, the rotor thrust is chosen. In the transition state and omnidirectional mode, translational and rotational dynamics are decoupled, and hence the orientation and position are tracked in two separate loops. in one example implementation, the position controller and attitude controller of the controller200are designed with cascade PI/PD architecture.

A. Attitude Control

Assume the measurements are well filtered, and the attitude controller has a high sampling frequency. The attitude controller has a high sampling frequency. The attitude controller is designed with a cascade geometric structure on SO(3) which gives a smooth movement trajectory to track. The inner loop uses ω as feedback to compute the reference torque based on feedback linearization as:
Tdes=−J(kp,ωeω+kd,ωėω)+ω×Jω,(16)which denotes a Proportional-Derivative (PD) controller to deal with dynamics of angular velocity acting like a first-order system brought by motor dynamics in the actuator model. kp,ω, kd,ωare positive gain matrices and eωis the angular rate error which is defined as

The reference angular velocity is chosen as
ωdes=−kp,ReR−ki,R∫eR,  (18)which is a proportional-integral (PI) controller. kp,R, ki,Rare positive gain matrices, and eRis the orientation tracking error on SO(3) defined as

∨ is the inverse operator of ∧ in Eqn. (13). This attitude controller has the same structure in both working modes (coplanar/omnidirectional). The geometric control law gives exponential stability when the attitude tracking error should be less than 180°. A low pass prefilter is added to the global attractiveness command signal.

Importantly, based on an output of the attitude controller of the controller200(e.g., implemented by the computing device300), the computing device300generates and applies actuation signals for application to one or more of the first rotor assembly144A, the second rotor assembly144B, the third rotor assembly164A, the fourth rotor assembly164B, the fifth rotor assembly184A, and the sixth rotor assembly184B for propulsion and steering of the vehicle.

B. Position Control

Similar to attitude controllers, the position controller of the controller200can be designed with a cascade structure. In coplanar mode, the position controller takes the yaw angle ψdesand pdesas the reference trajectory. In the omnidirectional mode, the position controller takes Rdesand pdes(full pose) as the reference trajectory. In both modes, the outer loop is defined as:
ep=p−pdes,  (20)
and proportional control is used to get the desired velocity:
vdes=−kp,pep−ki,p∫ep.  (21)

The velocity tracking error is defined as

The desired force vector in the inertial frame is defined as
Fdes,w=mg−(kp,vev+kd,vėv),  (23)
which needs to be converted to the body frame. kp,p, ki,p, kp,vand kd,vare all positive definite diagonal matrices. The body heading axis needs to be calculated in the coplanar mode given the desired yaw angle. Hence, the normalized thrust vector of the inertial frame should first be calculated:

n^=Fdes,w/Fdes,w=[n1,n2,n3]T,(24)
based on the expression of the rotation matrix defined in modeling. Here cos(sin−1(n1)) is denoted as n4which yields:

Let u=Rx,hRy,hRz(ψref)·[0,0,1]Tand û=u/∥u∥. Then denote û=n×u/∥n×u∥. Finally, the reference rotation matrix in coplanar mode is denoted as:
Rdes,c=[û{circumflex over (k)}{circumflex over (n)}].(27)

In the omnidirectional mode, Rdes,ois the reference input. Hence, the reference force in the body frame is given by:
Fdes=RTFdes,w,  (28)in both modes. Notice Fdes,o=[0 0 Fz,c]Tin the coplanar mode, and Fdes,o=[Fx,oFy,oFz,o]Tin the omnidirectional mode. The position control in both modes is asymptotically stable. Similarly, based on an output of the position controller of the controller200(e.g., implemented by the computing device300), the computing device300generates and applies actuation signals for application to one or more of the first rotor assembly144A, the second rotor assembly144B, the third rotor assembly164A, the fourth rotor assembly164B, the fifth rotor assembly184A, and the sixth rotor assembly184B for propulsion and steering of the vehicle.
C. Control Allocation

To obtain the unique relation for minimization of control effort, the reference force and torque are converted to rotor thrust with a pseudo-inverse of the allocation matrix, which is:
M=AT(AAT)−1.  (29)

Then, the reference rotor thrust can be computed by:

IV. Simulation Results and Discussions

This section presents simulation scenarios in MATLAB and results to illustrate the enhanced performance of the vehicle100. A list of chosen modeling parameters in simulation is shown in Table 1, and a list of controller parameters is shown in Table 2.

The most challenging and significant mission for the transformable UAV is the combined flight containing under-actuated long-range flight and omnidirectional motions in the air. The commanded trajectory consists of three phases, and the 2-second transitions happen between two phases.1) Phase 1 (0≤t<16 s): The vehicle100is first commanded to take off, accelerate, and fly to a long-distance set point as a coplanar hexacopter. The vehicle100decelerates as it approaches the destination, and the transition begins.2) Transition C→0 (16≤t<18 s): The vehicle100transforms from the coplanar mode to the omnidirectional mode at a suitable translational speed, and then the system becomes fully actuated.(3) Phase 2 (18≤t<42 s): The vehicle100enters the omnidirectional mode. In real applications, sinusoidal signals are used to generate reference 3D positional tracking with steer attitude (18≤t<30 s) and 3D rotational tracking with steer position (30≤t<42 s) separately, representing two different aerial tasks, such as aerial writing and inspection, respectively.(4) Transition O→C (42≤t<44 s): The vehicle100transforms from the omnidirectional mode back to the coplanar directional mode at a suitable translational speed, and the system becomes under actuated again.(5) Phase 3 (44≤t<60 s): The vehicle100accelerates and flies towards the landing area. As the vehicle100approaches the target area, the vehicle velocity reduces, and the vehicle100finally finishes the landing.

FIG.7shows the mode (μ) switching plot. To describe the servo and the rotational structure dynamics during the transition associated with μ, a saturated damping signal is selected by going through a first-order low pass filter

FIGS.8A-8Dinclude results for the position tracking p→pdes, the position error ep, the velocity tracking v→vdes, and the velocity error ev.

Ramping references are selected to represent a high-speed and long-distance motion in the coplanar mode. At the same time, the maximum position error reaches up to 0.49 m, and the maximum velocity error reaches up to 0.74 m/s. Sinusoidal references are designed for the position tracking reference of omni mode (18≤t<30 s). It is worth to note that a fast attitude tracking with steer reference position (30≤t<42 s) would cause relatively large tracking error. During each transition, the tracking errors are controlled in small ranges (ep<0.001 m, ev<0.02 m/s).

Moreover, the orientation tracking R→Rdes, the orientation tracking error

Ψ⁡(R,Rdes)=12⁢tr[I-RdesT⁢R],
the angular velocity tracking ω→ωdes, and the angular velocity error eωare shown inFIGS.9A-9D. In the coplanar mode, tracking error is relatively large (eR<0.044, eω<23 deg/s) when changing the heading direction to the targeting area. During 30≤t<42 s, the tracking errors (eR<0.77, eω<38 deg/s) are caused by the UAV fast rotations to adjust roll, pitch, and yaw angles simultaneously (aggressive references). Similar to position tracking, the orientation tracking errors are controlled in small ranges (eR<0.44, eω<0.2 deg/s) during each transition.
C. Rotor Thrust, Force Efficiency, and Disturbance

InFIGS.10A-10C, all rotors give thrusts within the constraints during the whole flight mission. In the coplanar mode (phases 1&3), γ=100% corresponds to upward heading directions of all rotors in the body frame. In phase 2, the fully actuated omnidirectional motions with lower force efficiency 57.7%≤γ≤100% requiring more thrust for each rotor, especially during the steer position part. Hence, the orientation trajectory should cover the red zone inFIG.5as much as possible. It is also worth noting that the internal disturbance torque (∥τ∥≤0.0053N·m) at the beginning and the end of each transition time has little influence on orientation tracking (eR<0.002, eω, <6.4 deg/s), which shows the effectiveness of the switching control design.

D. Comparison with Coplanar-Only and Omni-Only UAVs

Compared with coplanar-only UAVs, it is straightforward that the vehicle100has omnidirectional flight capability. The vehicle100does not require other robot arms for many aerial manipulation tasks or only needs less complicated modules to fulfill the same mission. To, the electrical power consumption of the vehicle100is calculated in Eq. (31) in comparison with omni-only UAVs. Ignoring the power cost of non-rotor modules (flight controller, servo, etc.), power consumption is denoted by:

An omni-only UAV with a fixed frame is modeled to do the same task as the simulation scenario above. The omni-only UAV flies with γ=100% (roll and pitch angles are zero) at phases 1 and 3.

InFIG.11, the omni-only UAV costs more electrical power during phases than the vehicle100while performing the same flight mission. The total energy cost of the omni-only UAV is 21134J, and that of the vehicle100is 17782J.

The vehicle100combines both coplanar and omnidirectional flight features. In particular, the vehicle100is capable of both under-actuated coplanar flight and fully actuated omnidirectional motions. The vehicle100includes the controller with a cascade structure on3×SO(3) to achieve flight capability via different modes with respect to disturbances.

FIG.12is a schematic block diagram showing the computing device300that may be used with one or more embodiments described herein, e.g., as a component of vehicle100ofFIGS.1A-3C and6Aand/or implementing the controller200shown inFIGS.6A and6B.

Computing device300comprises one or more network interfaces310(e.g., wired, wireless, PLC, etc.), at least one processor320, and a memory340interconnected by a system bus350, as well as a power supply360(e.g., battery, plug-in, etc.).

Network interface(s)310include the mechanical, electrical, and signaling circuitry for communicating data over the communication links coupled to a communication network. Network interfaces310are configured to transmit and/or receive data using a variety of different communication protocols. As illustrated, the box representing network interfaces310is shown for simplicity, and it is appreciated that such interfaces may represent different types of network connections such as wireless and wired (physical) connections. Network interfaces310are shown separately from power supply360, however it is appreciated that the interfaces that support PLC protocols may communicate through power supply360and/or may be an integral component coupled to power supply360.

Memory340includes a plurality of storage locations that are addressable by processor320and network interfaces310for storing software programs and data structures associated with the embodiments described herein. In some embodiments, device300may have limited memory or no memory (e.g., no memory for storage other than for programs/processes operating on the device and associated caches).

Processor320comprises hardware elements or logic adapted to execute the software programs (e.g., instructions) and manipulate data structures345. An operating system342, portions of which are typically resident in memory340and executed by the processor, functionally organizes computing device300by, inter alia, invoking operations in support of software processes and/or services executing on the device. These software processes and/or services may include transformable UAV processes/services390which can include a set of instructions within the memory340that implement aspects of controller200when executed by the processor320. Note that while transformable UAV processes/services390is illustrated in centralized memory340, alternative embodiments provide for the process to be operated within the network interfaces310, such as a component of a MAC layer, and/or as part of a distributed computing network environment.

It will be apparent to those skilled in the art that other processor and memory types, including various computer-readable media, may be used to store and execute program instructions pertaining to the techniques described herein. Also, while the description illustrates various processes, it is expressly contemplated that various processes may be embodied as modules or engines configured to operate in accordance with the techniques herein (e.g., according to the functionality of a similar process). In this context, the term module and engine may be interchangeable. In general, the term module or engine refers to model or an organization of interrelated software components/functions. Further, while the transformable UAV processes/services390is shown as a standalone process, those skilled in the art will appreciate that this process may be executed as a routine or module within other processes.

Methods

FIG.13shows a method400associated with the vehicle100outlined herein. The functions performed in the processes and methods may be implemented in differing order. Furthermore, the outlined steps and operations are provided as examples, and some of the steps and operations may be optional, combined into fewer steps and operations, or expanded into additional steps and operations without detracting from the essence of the disclosed embodiments.

As shown, step402of method400includes providing a vehicle including: a first arm in association with a body; a second arm in association with the body, the second arm being rotatable by a servo motor between a first position associated with a coplanar mode of the vehicle and a second position associated with an omnidirectional mode; and a third arm in association with the body, the third arm being rotatable between a first position associated with the coplanar mode of the vehicle and a second position associated with the omnidirectional mode, wherein rotation of the second arm between the first position and the second position of the second arm causes concurrent rotation of the third arm between the first position and the second position of the third arm. The second arm is oriented coplanar with the first arm when in the first position of the second arm, and the second arm is oriented mutually perpendicular with the first arm when in the second position of the second arm. The third arm is oriented coplanar with the first arm and the second arm and is oriented at a 45 degree angle relative to the first arm and the second arm when in the first position of the third arm. When in the second position of the third arm, the third arm is oriented mutually perpendicular with the first arm and the second arm. Step404of method400includes: applying, by a processor in communication with a memory and the servo motor, an actuation signal to the servo motor. Step406of method400includes rotating, by the servo motor, the second arm between the first position and the second position of the second arm. Step408of method400can occur concurrently with step406as a result of the rotation by the servo motor, and can include rotating the third arm about an axis that is normal to a shared plane of the first arm and the third arm and simultaneously rotating the third arm by 90 degrees about an axis of elongation of the third arm.

The first arm can include a first rotor assembly and a second rotor assembly, the second arm can include a third rotor assembly and a fourth rotor assembly and the third arm can include a fifth rotor assembly and a sixth rotor assembly. Step410of method400includes generating an actuation signal for application to one or more of the first rotor assembly, the second rotor assembly, the third rotor assembly, the fourth rotor assembly, the fifth rotor assembly, and the sixth rotor assembly for propulsion of the vehicle based on an output of a controller implemented at the processor. Step412can include applying, by the processor in communication with the memory, the actuation signal to one or more of the first rotor assembly, the second rotor assembly, the third rotor assembly, the fourth rotor assembly, the fifth rotor assembly, and the sixth rotor assembly for propulsion of the vehicle.

Importantly, the third rotor assembly and the fourth rotor assembly of the second arm are oriented coplanar with the first rotor assembly and the second rotor assembly of the first arm when the second arm is in the first position. The third rotor assembly and the fourth rotor assembly of the second arm are oriented 90 degrees relative to the first rotor assembly and the second rotor assembly of the first arm when the second arm is in the second position. The fifth rotor assembly and the sixth rotor assembly of the third arm are oriented 180 degrees relative to the first rotor assembly and the second rotor assembly of the first arm and the third rotor assembly and the fourth rotor assembly of the second arm when the third arm is in the first position. The fifth rotor assembly and the sixth rotor assembly of the third arm are oriented mutually perpendicular with the first rotor assembly and the second rotor assembly of the first arm and the third rotor assembly and the fourth rotor assembly of the second arm when the third arm is in the second position.