CN117872762A - Self-adaptive three-dimensional track tracking control method of six-degree-of-freedom under-actuated unmanned surface vessel - Google Patents

Abstract

The self-adaptive three-dimensional track tracking control method for the six-degree-of-freedom under-actuated unmanned surface vessel is provided, and can ensure that the unmanned surface vessel can track a given sea surface track under the condition that unknown hydrodynamics and external disturbance exist in an under-actuated unmanned surface vessel system, and comprises the following steps: establishing a six-degree-of-freedom unmanned surface vessel kinematics and dynamics model; defining a tracking error vector and virtual error coordinate transformation; constructing a virtual control law which is also called as a kinematic guidance law; establishing an auxiliary signal, an unknown hydrodynamics and an external disturbance compensation signal; the compensated input signal and the actual under-actuated input signal are constructed. According to the invention, the three-dimensional motion trail of the time-varying sea surface can be defined according to task requirements, and the motion trail of the unmanned surface vessel can be dynamically adjusted.

Description

Self-adaptive three-dimensional track tracking control method of six-degree-of-freedom under-actuated unmanned surface vessel

Technical Field

The invention relates to an unmanned surface vessel tracking control method, in particular to a self-adaptive three-dimensional track tracking control method considering six degrees of freedom, underactuated input, hydrodynamics and unknown environmental disturbance.

Background

Due to the wide application background in the ocean fields of ocean data collection, autonomous path cruising, sea surface collaborative combat and the like, the unmanned surface vessel (Unmanned Surface Vessel, USV) system control method has received wide attention of a plurality of scholars in recent years. The development of the control method of the six-degree-of-freedom unmanned surface vessel has important significance for enhancing the control precision, dynamic stability and task completion efficiency of an unmanned surface vessel system.

In an actual operating scenario, most unmanned surface vessel systems have no engines in the lateral and vertical directions and cannot provide thrust to their own lateral and vertical movements. Therefore, the underactuated performance of the unmanned surface vessel is considered, and the method has important theoretical significance and application value for the control method of the unmanned surface vessel in actual situations. However, because the motion characteristics of the six-degree-of-freedom unmanned surface vessel have complex coupling characteristics, the existing control method (S.L.Dai, S.He, H.Cai, and C.Yang, "Adaptive leader-follower formation control of underactuated surface vehicles with guaranteed performance," IEEE Transactions on Systems, man, and Cybernetics: systems, vol.52, no.3, pp.1997-2008,2020.) of the underactuated unmanned surface vessel is all directed against the three-degree-of-freedom unmanned surface vessel and cannot be applied to the control problem of the six-degree-of-freedom underactuated unmanned surface vessel.

In addition, existing unmanned surface vessel control methods (B.S.Park, J.W.Kwon, and H.Kim, "real network-based output feedback control for reference tracking of underactuated surface vessels," Automation, vol.77, pp.353-359,2017.) (Z.zheng, "Moving path following control for a surface vessel with error constraint," Automation, vol.118, p.109040, 2020.) all assume that the hydrodynamics of unmanned surface vessels are known or exist in a tight collection. However, in practical and complex marine formation tasks, the hydrodynamics and external environmental disturbances are generally unknown and there is no guarantee that the hydrodynamics always exist in close-coupled sets.

The actual modeled unmanned surface vessel system often contains six degrees of freedom and under-actuated motion features and faces a complex marine environment during task execution. Therefore, a self-adaptive control algorithm is constructed for the six-degree-of-freedom under-actuated surface unmanned ship with unknown hydrodynamics and external disturbance, and the self-adaptive control algorithm has very important theoretical significance and application value for improving the control precision and robustness of the unmanned surface ship system in actual operation.

Disclosure of Invention

Aiming at the problems existing in the prior art, the invention provides a self-adaptive three-dimensional track tracking control method considering six-degree-of-freedom under-actuated unmanned surface vessel, which comprises the following specific steps:

step 1: aiming at an unmanned surface vessel in actual operation, a ground coordinate system and a hull coordinate system are established, and a kinematic and dynamic model of the six-degree-of-freedom underactuated unmanned surface vessel is obtained as follows:

wherein: for the subsequent arbitrary matrix or vector X, the symbols areA derivative representing a matrix or vector X; p= [ eta ] ^T ,Φ ^T ] ^T Is the position coordinate eta= [ x, y, z ] of the ground coordinate system of the unmanned surface vessel] ^T Euler angle vector of ship coordinate systemThe upper corner mark T represents the transposition of the matrix, and x, y and z represent the x-axis, y-axis and z-axis coordinates of the origin of the hull coordinate system of the unmanned surface vessel relative to the ground coordinate system respectively>Representing roll angle, pitch angle and bow angle, respectively,)>Is the linear velocity vector v= [ u, v, w ] of the unmanned surface vessel under the hull coordinate system] ^T And angular velocity vector ω= [ p, q, r] ^T A second composite vector matrix of u, v, w representing the roll, heave and heave velocities, p, q, r representing the roll, pitch and yaw angular velocities, respectively, pi _E Is an unknown disturbance vector generated by environmental phenomena such as wind, surge and the like, and pi= [ pi ] _u ,0,0,π _p ,π _q ,π _r ] ^T Is an under-actuated input vector limited by actual conditions, pi _u Driving force pi representing the direction of swaying _p ,π _q ,π _r Driving moments respectively representing roll, pitch and yaw, R (phi) represents an Euler rotation matrix, M is a system inertia matrix,representing a coriolis centripetal matrix, ++>Is a damping matrix, and BETA (P) represents gravity and buoyancy vectors;

setting parameterized three-dimensional coordinates of virtual leader unmanned ship as eta _d ＝[x _d ,y _d ,z _d ] ^T The Euler angle vector is expected to bex _d ,y _d Sea surface path representing mission demand in a ground coordinate system, where x _d ,y _d Respectively representing the expected x-axis and y-axis coordinates of the origin of the ship body coordinate system relative to the fixed coordinate system, z _d Is the expected heave displacement of the unmanned surface vessel,representing desired roll, pitch and yaw angles, respectively; to simplify the representation of the virtual leader unmanned ship, the three-dimensional motion characteristics of the virtual leader unmanned ship are expressed as +.>

Step 2: respectively define tracking error vectors xi ₁ Virtual error coordinate transformation ζ ₂ Is that

Wherein: alpha ₁ Is a virtual controller under a back-step recursive framework, and eta (ρ) is an under-actuated compensation vector in the form of eta (ρ) = [0, eta ₁ (ρ ₁ ),η ₂ (ρ ₂ ),η ₃ (ρ),η ₄ (ρ),η ₅ (ρ)] ^T ，ρ＝[ρ ₁ ,ρ ₂ ] ^T Is an auxiliary vector ρ ₁ 、ρ ₂ Auxiliary variables, η, representing the direction of the sway and the direction of the heave, respectively ₁ (ρ ₁ )、η ₂ (ρ ₂ )、η ₃ (ρ)、η ₄ (ρ)、η ₅ (ρ) is a transverse function of form η _i (ρ _i )＝k _i (cos ³ (ρ _i )sin(ρ _i )-sin ³ (ρ _i )cos(ρ _i ) Where subscript i=1 or 2, k) _i Is a constant that can be adjusted so that,wherein subscript j=3, 4 or 5, k _j Is an adjustable constant;

step 3: construction of virtual controller alpha ₁ Is that

Wherein: c ₁ Is an adjustable positive constant lambda _R ＝λ _max (R(Φ)R ^T (Φ)) means the rotation matrix R (Φ) multiplied by its own transpose R ^T Maximum eigenvalue of (Φ), λ _max (. Cndot.) represents the maximum eigenvalue of the matrix;

step 4: construction of auxiliary messagesNumber (number)And unknown hydrodynamic and external disturbance compensation signals +.>Is that

Wherein: χ is an adjustable positive constant, the upper-corner-1 represents the inverse of the matrix,

sign->Representing a transverse function eta ₁ For the auxiliary variable ρ ₁ Partial derivative, eta ₁ 、η ₂ 、η ₃ 、η ₄ 、η ₅ Respectively eta ₁ (ρ ₁ )、η ₂ (ρ ₂ )、η ₃ (ρ)、η ₄ (ρ)、η ₅ Shorthand for (ρ), pi ^* To compensate the input signal;

step 5: construction of the compensated input signal pi ^* And the actual underactuated input signal pi is

Wherein:and->Is equal to the value of the compensated input signal pi ^* Values of the second and third rows, c ₂ Is an adjustable normal number

Compared with the prior art, the invention has the advantages that:

(1) For a six-degree-of-freedom under-actuated unmanned surface vessel system, step 2 establishes a new coordinate transformation formula under a recursive frame by establishing a new transverse function vector. And 2, constructing a new transverse function form to reduce the burden of the self-adaptive controller caused by the traditional transverse function method.

(2) According to the invention, a new dynamic signal is established in control, unknown hydrodynamics and external disturbance in the six-degree-of-freedom under-actuated unmanned surface vessel are compensated, and the control performance of the six-degree-of-freedom under-actuated unmanned surface vessel is improved. Therefore, the controller built by the invention can not only cope with the influence of the actual unknown environmental characteristics on the six-degree-of-freedom unmanned surface vessel, but also can ensure that the six-degree-of-freedom unmanned surface vessel can track a given sea surface path under the underactuated characteristics.

Drawings

FIG. 1 shows a schematic diagram of a general control process;

FIG. 2 shows a three-dimensional view of a six degree of freedom unmanned surface vessel motion profile;

FIG. 3 shows a trace plot of the various Euler angle variables;

FIG. 4 shows a plot of the trajectory of the various linear velocity variables;

fig. 5 shows a running trace graph of each angular velocity variable;

FIG. 6 shows a trace plot of a path tracking error norm;

Detailed Description

The invention provides a self-adaptive control method of a six-degree-of-freedom under-actuated unmanned surface vessel, which can enable the six-degree-of-freedom under-actuated unmanned surface vessel to track a given three-dimensional sea surface path under the condition that unknown hydrodynamics and environmental disturbance exist in the six-degree-of-freedom under-actuated unmanned surface vessel. The technical idea of the method is as follows: firstly, under a back-step recursion frame, a novel coordinate transformation formula is established for a six-degree-of-freedom under-actuated unmanned surface vessel system to ensure the under-actuated requirement of the system; secondly, by establishing auxiliary variables, introducing dynamic signals, and compensating hydrodynamic and external disturbance brought by an unknown environment to the unmanned surface vessel; then, a virtual control law and an actual control input are constructed by means of an adaptive compensation strategy, forming an effective adaptive control scheme to achieve the desired system performance.

The method comprises the following specific steps:

step 1: aiming at an unmanned surface vessel in actual operation, a ground coordinate system and a hull coordinate system are established, and a kinematic and dynamic model of the six-degree-of-freedom underactuated unmanned surface vessel is obtained as follows:

wherein: for any matrix or vector X, the symbols areRepresenting the derivative of the matrix or vector X, p= [ η ] ^T ,Φ ^T ] _T Is the position coordinate eta= [ x, y, z ] of the ground coordinate system of the unmanned surface vessel] ^T Euler angle vector of ship coordinate system>The upper corner mark T represents the transposition of the matrix, and x, y and z represent the x-axis, y-axis and z-axis coordinates of the origin of the hull coordinate system of the unmanned surface vessel relative to the ground coordinate system respectively>Representing roll angle, pitch angle and bow angle, respectively,)>Is the linear velocity vector v= [ u, v, w ] of the unmanned surface vessel under the hull coordinate system] ^T And angular velocity vector ω= [ p, q, r] ^T A second composite vector matrix consisting of u, v, w representing the yaw, pitch and heave velocities, p, q, r representing the roll, pitch and yaw angular velocities, respectively,/>Is the first derivative of ζ, pi _E Is an unknown disturbance vector generated by environmental phenomena such as wind, surge and the like, and pi= [ pi ] _u ,0,0,π _p ,π _q ,π _r ] ^T Is an under-actuated input vector limited by actual conditions, pi _u Driving force pi representing the direction of swaying _p ,π _q ,π _r Driving moments respectively representing roll, pitch and yaw, R (phi) represents Euler rotation matrix, M is system inertia matrix, < >>Representing a coriolis centripetal matrix, ++>Is a damping matrix, and beta (P) represents gravitational and buoyancy vectors (T.I. Fossen, handbook of marine craft hydrodynamics and motion control. John Wiley&Sons,2011.)。

Setting parameterized three-dimensional coordinates of virtual leader unmanned ship as eta _d ＝[x _d ,y _d ,z _d ] ^T The Euler angle vector is expected to bex _d ,y _d Sea surface path representing mission demand in a ground coordinate system, where x _d ,y _d Respectively representing the expected x-axis and y-axis coordinates of the origin of the ship body coordinate system relative to the fixed coordinate system, z _d Is the expected heave displacement of the unmanned surface vessel,representing the desired roll, pitch and yaw angles, respectively. Setting parameterized three-dimensional coordinates of virtual leader unmanned ship as eta _d The Euler angle is expected to be phi _d . In order to simplify the representation of the virtual leadership, the three-dimensional movement characteristics of the virtual leadership are expressed as +.>

Step 2: respectively define tracking error vectors xi ₁ Virtual error coordinate transformation ζ ₂ Is that

Wherein: alpha ₁ Is a virtual controller under a back-step recursive framework, and eta (ρ) is an under-actuated compensation vector in the form of eta (ρ) = [0, eta ₁ (ρ ₁ ),η ₂ (ρ ₂ ),η ₃ (ρ),η ₄ (ρ),η ₅ (ρ)] ^T ，ρ＝[ρ ₁ ,ρ ₂ ] ^T Is an auxiliary vector ρ ₁ 、ρ ₂ Auxiliary variables, η, representing the direction of the sway and the direction of the heave, respectively ₁ (ρ ₁ )、η ₂ (ρ ₂ )、η ₃ (ρ)、η ₄ (ρ)、η ₅ (ρ) is referred to as a transverse function in the form of η _i (ρ _i )＝k _i (cos ³ (ρ _i )sin(ρ _i )-sin ³ (ρ _i )cos(ρ _i ) Where subscript i=1 or 2, k) _i Is a constant that can be adjusted so that,wherein subscript j=3, 4 or 5, k _j Is an adjustable constant.

Step 3: establishing virtual controller alpha ₁ Is that

Wherein: c ₁ Is an adjustable positive constant lambda _R ＝λ _max (R(Φ)R ^T (Φ)) means the rotation matrix R (Φ) multiplied by its own transpose R ^T Maximum eigenvalue of (Φ), symbol λ _max (. Cndot.) represents the maximum eigenvalue of the matrix.

Step 4: construction of auxiliary signalsAnd unknown hydrodynamic and external disturbance compensation signals +.>Is that

Wherein: χ is an adjustable positive constant, the upper-corner-1 represents the inverse of the matrix,

sign->Representing a transverse function eta ₁ For the auxiliary variable ρ ₁ Partial derivative, eta ₁ 、η ₂ 、η ₃ 、η ₄ 、η ₅ Respectively eta ₁ (ρ ₁ )、η ₂ (ρ ₂ )、η ₃ (ρ)、η ₄ (ρ)、η ₅ Shorthand for (ρ), pi ^* To compensate the input signal, its form will be given in the next step.

Step 5: establishing a compensated input signal pi ^* And the actual underactuated input signal pi is

Wherein:and->Is equal to the value of the compensated input signal pi ^* Values of the second and third rows, c ₂ Is an adjustable positive constant.

DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION

According to the specific implementation steps of the technical scheme of the invention, the following embodiment is provided.

Step 1: and (3) establishing a six-degree-of-freedom unmanned surface vessel system model shown in the formula (1). Model parameters of the unmanned surface vessel are respectively as follows: m=61.5×10 ⁵ ,x _g ＝-2.3,z _g ＝-5.2,I _x ＝31.429×10 ⁸ ,I _y ＝4.2767×10 ⁸ ,I _z ＝16.6653×10 ⁸ ,I _xz ＝I _zx ＝1.9025×10 ⁸ , The other parameter value is taken as 0. Initial position state (x (0), y (0), z (0)) and initial Euler angle +.>Respectively set as [0.5, -0.1 ]] ^T And [ -0.6,0,0] ^T Define the sea surface parameterization path of the mission requirement as +.>To ensure stability and sailing efficiency of the unmanned surface vessel, the desired heave displacement is set to 0 and the desired euler angle is set to

Step 2: define a tracking error vector ζ of the form (2) ₁ Virtual error coordinate transformation ζ ₂ The parameters in the transverse function are selected to be k _j ＝10,(j＝1,2,3,4,5)。

Step 3: establishing a virtual control law in the form of a formula (3), wherein a virtual controller control parameter is selected as c ₁ ＝25。

Step 4: constructing auxiliary signals in the form of (4) and (5)And unknown hydrodynamic and external disturbance compensation signalsWhere the parameter is chosen as χ=0.5.

Step 5: building up compensated input signals pi in the form of (6) and (7) ^* And the actual underactuated input signal pi, wherein the parameter is selected as c ₂ ＝25。

Fig. 2 shows a three-dimensional view of the six degrees of freedom unmanned surface vessel motion trajectory, indicating that the desired sea surface trajectory tracking mode has been established. FIG. 3 is a graph showing the trajectory of each Euler angle variable, and it can be seen from the graph that the roll angle and pitch angle of the unmanned surface vessel do not exceedThe unmanned surface vessel meets the real navigation condition of the unmanned surface vessel. Fig. 4 and 5 show the trajectories of the linear velocity norms and the angular velocity norms, respectively, and it can be seen from fig. 4 and 5 that the respective linear velocity and angular velocity converge into a small neighborhood near the origin, i.e., the linear velocity and angular velocity are bounded.

In addition, as can be seen from fig. 6, the formation error finally converges to a small neighborhood of the origin, namely, the proposed control algorithm can enable the six-degree-of-freedom unmanned surface vessel system to meet the sea surface track tracking requirement.

The self-adaptive control scheme of the invention not only can ensure that the six-degree-of-freedom underactuated unmanned surface vessel can track a given three-dimensional sea surface path under the condition of unknown hydrodynamics and external environment disturbance, but also can ensure that the linear speed, the angular speed and the tracking error of the underactuated unmanned surface vessel can be converged in any small tight collection.

Claims (1)

1. A self-adaptive three-dimensional track tracking control method considering six-degree-of-freedom under-actuated unmanned surface vessel is characterized by comprising the following specific steps:

step 1: aiming at an unmanned surface vessel in actual operation, a ground coordinate system and a hull coordinate system are established, and a kinematic and dynamic model of the six-degree-of-freedom underactuated unmanned surface vessel is obtained as follows:

wherein: for the subsequent arbitrary matrix or vector X, the symbols areA derivative representing a matrix or vector X; p= [ eta ] ^T ,Φ ^T ] ^T Is the position coordinate eta= [ x, y, z ] of the ground coordinate system of the unmanned surface vessel] ^T Euler angle vector of ship coordinate system>The upper corner mark T represents the transposition of the matrix, and x, y and z represent the x-axis, y-axis and z-axis coordinates of the origin of the hull coordinate system of the unmanned surface vessel relative to the ground coordinate system respectively>Representing roll angle, pitch angle and bow angle, respectively,)>Is the linear velocity vector v= [ u, v, w ] of the unmanned surface vessel under the hull coordinate system] ^T And angular velocity vector ω= [ p, q, r] ^T A second composite vector matrix of u, v, w representing the roll, heave and heave velocities, p, q, r representing the roll, pitch and yaw angular velocities, respectively, pi _E Is an unknown disturbance vector generated by environmental phenomena such as wind, surge and the like, and pi= [ pi ] _u ,0,0,π _p ,π _q ,π _r ] ^T Is an under-actuated input vector limited by actual conditions, pi _u Driving force pi representing the direction of swaying _p ,π _q ,π _r Driving moments respectively representing roll, pitch and yaw, R (phi) represents Euler rotation matrix, M is system inertia matrix, < >>Representing a coriolis centripetal matrix, ++>Is a damping matrix, and BETA (P) represents gravity and buoyancy vectors;

setting parameterized three-dimensional coordinates of virtual leader unmanned ship as eta _d ＝[x _d ,y _d ,z _d ] ^T The Euler angle vector is expected to bex _d ,y _d Sea surface path representing mission demand in a ground coordinate system, where x _d ,y _d Respectively representing the expected x-axis and y-axis coordinates of the origin of the ship body coordinate system relative to the fixed coordinate system, z _d Is the expected heave displacement of the unmanned surface vessel,respectively representing periodsThe roll, pitch and yaw angles of the telescope; to simplify the representation of the virtual leader unmanned ship, the three-dimensional motion characteristics of the virtual leader unmanned ship are expressed as +.>

Step 2: respectively define tracking error vectors xi ₁ Virtual error coordinate transformation ζ ₂ Is that

Wherein: alpha ₁ Is a virtual controller under a back-step recursive framework, and eta (ρ) is an under-actuated compensation vector in the form of eta (ρ) = [0, eta ₁ (ρ ₁ ),η ₂ (ρ ₂ ),η ₃ (ρ),η ₄ (ρ),η ₅ (ρ)] ^T ，ρ＝[ρ ₁ ,ρ ₂ ] ^T Is an auxiliary vector ρ ₁ 、ρ ₂ Auxiliary variables, η, representing the direction of the sway and the direction of the heave, respectively ₁ (ρ ₁ )、η ₂ (ρ ₂ )、η ₃ (ρ)、η ₄ (ρ)、η ₅ (ρ) is a transverse function of form η _i (ρ _i )＝k _i (cos ³ (ρ _i )sin(ρ _i )-sin ³ (ρ _i )cos(ρ _i ) Where subscript i=1 or 2, k) _i Is a constant that can be adjusted so that,wherein subscript j=3, 4 or 5, k _j Is an adjustable constant;

step 3: construction of virtual controller alpha ₁ Is that

Wherein: c ₁ Is an adjustable positive constant lambda _R ＝λ _max (R(Φ)R ^T (Φ)) means the rotation matrix R (Φ) multiplied by its own transpose R ^T Maximum eigenvalue of (Φ), λ _max (. Cndot.) represents the maximum eigenvalue of the matrix;

step 4: construction of auxiliary signalsAnd unknown hydrodynamic and external disturbance compensation signals +.>Is that

Wherein: χ is an adjustable positive constant, the upper-corner-1 represents the inverse of the matrix,

sign->Representing a transverse function eta ₁ For the auxiliary variable ρ ₁ Partial derivative, eta ₁ 、η ₂ 、η ₃ 、η ₄ 、η ₅ Respectively eta ₁ (ρ ₁ )、η ₂ (ρ ₂ )、η ₃ (ρ)、η ₄ (ρ)、η ₅ Shorthand for (ρ), pi ^* To compensate the input signal;

step 5: construction of the compensated input signal pi ^* And the actual underactuated input signal pi is

Wherein:and->Is equal to the value of the compensated input signal pi ^* Values of the second and third rows, c ₂ Is an adjustable positive constant.