CN105353790A - Tethered space robot complex stable control method after target capture - Google Patents

Abstract

The invention discloses a method for stabilizing a complex after a space tethered robot captures a target, comprising the following steps: 1) establishing a complex dynamic equation after a space tethered robot captures a target; 2) calculating a virtual control input _ξ2c ; 3) Calculate the expected system state quantity ξ _2d ; 4) Estimate the uncertainty of the post-capture complex model ; 5) Calculate the stable control force and control torque Q of the complex after capture. The invention considers the limit of the speed of the tethered rope, and uses the instruction filtering method to design the controller, so as to ensure the stability of the controller. The invention designs an adaptive law, estimates the uncertainty of the complex, and compensates in the controller, thereby improving the control precision. The invention limits the control input through the filter, thereby improving the stability of the controller.

Description

A stability control method for the complex after target capture by a space tethered robot

【Technical field】

The invention belongs to the research field of spacecraft control technology, and in particular relates to a method for stabilizing a complex after a space tether robot captures a target.

【Background technique】

Due to its flexibility, safety, and low fuel consumption, space tethered robots have a wide range of roles in space on-orbit services, and can perform operations such as rescue of failed satellites, space junk cleaning, and auxiliary orbit changes.

According to the task flow of the space tethered robot, it can be divided into five stages: release, approaching the target, target capture, target capture post-capture stabilization, and target post-capture operation. One of the main studies.

After the space tethered robot captures the target, due to the collision and the spin of the target, the attitude of the captured complex is unstable. If no control is applied, unfavorable situations such as tether entanglement will occur, and the tension of the tether will greatly interfere with the platform itself. , therefore, the posture control of the post-capture complex is required. Due to the limited control torque of the space robot itself, when the complex is stably controlled after capture, the input saturation of the thruster will be limited, which will have a great impact on the control performance of the complex. In addition, due to the limitation of the rope release mechanism and the consideration of safety factors, the tether retraction speed is limited. Therefore, it is necessary to design a suitable control strategy to ensure the stability of the attitude control of the complex when the tether retraction speed is limited.

The stability of the complex after target capture is one of the important tasks of the space tethered robot. The stability control of the complex after the target capture directly affects the smooth progress of the subsequent dragging orbit change or recovery operation tasks, and it has become the research focus in the field of space tethered robots. .

The Chinese patent application number: 201310018221.7 proposes a method for controlling the complex after the space tethered robot captures, using thrusters and tethers to achieve stable control of the complex; the Chinese patent application number: 201410341562.2 proposes using the tether tension Combined with the configuration change of the space tethered manipulator, the required control moment is generated, so as to achieve the attitude stability of the complex. The above patents only consider the stable control of the attitude of the complex, and the stable control of the complex also requires the stable control of the position, which limits the use of these two control methods to a certain extent.

【Content of invention】

The purpose of the present invention is to solve the above problems and provide a method for stabilizing the complex after the target is captured by the space tethered robot. The method can realize the stable control of the pose of the complex after the target is captured.

In order to achieve the above object, the present invention adopts the following technical solutions to achieve:

A method for controlling the stability of a complex after a space tether robot target is captured, comprising the following steps:

1) Establish the dynamic equation of the complex after the space tethered robot captures the target;

2) Calculate the virtual control input ξ _2c ;

3) Calculate the expected system state quantity ξ _2d ;

4) Estimating Post-Catch Complex Model Uncertainties

5) Calculate the stable control force and control torque Q of the complex after capture.

The further improvement of the present invention is:

In the described step 1), the space tether robot target capture dynamics equation is:

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;\&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Q</span>}$

in: l is the length of the space tether; α is the interior angle of the space tether; β is the exterior angle of the space tether; θ and ψ are the attitude angles of the complex; M is the system inertia matrix; N is the nonlinear velocity related item; G is the gravity related item; Q is the space tethered robot control force and control torque.

In the described step 2), according to Calculate the virtual control input ξ _2c , where K ₁ is the designed positive definite matrix; ξ _1e = ξ ₁ -ξ _1d , where ξ ₁ = ξ, ξ _1d is the expected value of ξ ₁ , is the derivative of ξ _1e with respect to time.

In the described step 3), the method for calculating the expected system state quantity ξ _2d is: through the first-order filter $\mathrm{\&epsiv;}{\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_{2d}+{\mathrm{\&xi;}}_{2d}={\mathrm{\&xi;}}_{2c},{\mathrm{\&xi;}}_{2d}\left(0\right)={\mathrm{\&xi;}}_{2c}\left(0\right)$ Realization, where ε>0.

In the step 4), the complex model uncertainty Obtained by: Among them, a and ε _λ are positive numbers, η·η=(η ₁ η ₁ η ₂ η ₂ η ₃ η ₃ ) ^T , Proj(·) projection operator; η=ξ _2e -χ, χ passes through the filter Get; K ₂ and P are positive definite matrices.

In the described step 5), the stable control force and control torque Q of the complex after the calculation are captured: $Q_0=m_0{\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_{2d}+N_0{\mathrm{\&xi;}}_{2d}+G_0+(N_0-K_2)\mathrm{\&chi;}-{\mathrm{P\&xi;}}_{1e}-\frac{{\widehat{\mathrm{\&lambda;}}}_L\&Center\; Dot;\mathrm{\&eta;}}{\left|\mathrm{\&eta;}\right|+{\mathrm{\&epsiv;}}_{\mathrm{\&lambda;}}},$ Among them, Q is Q ₀ obtained through the saturation link, M ₀ is the nominal inertia matrix of the system; N ₀ is the nominal nonlinear velocity related item; G ₀ is the nominal gravity related item.

Compared with the prior art, the present invention has the following beneficial effects:

The method for controlling the stability of the complex after the target capture of the space tethered robot of the present invention considers the limitation of the speed of the tethered rope as a whole, and uses the command filtering method to design the controller to ensure the stability of the controller. The invention designs an adaptive law, estimates the uncertainty of the complex, and compensates in the controller, thereby improving the control precision. The invention limits the control input through the filter, thereby improving the stability of the controller.

【Description of drawings】

Figure 1 is a schematic diagram of target capture by a space tethered robot.

In the figure: 1. capture target; 2. space tethered robot; 3. space tether; 4. space platform; 5. earth; 6. post-capture complex.

【detailed description】

The present invention will be described in detail below in conjunction with the accompanying drawings. It should be noted that the described embodiments are only intended to facilitate the understanding of the present invention, and do not limit it in any way.

Referring to Fig. 1, the complex stability control method after the space tether robot target capture of the present invention comprises the following steps:

1) Establish the dynamic equation of the complex after the space tethered robot captures the target

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;\&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Q</span>}$

Among them, the system state where l, α and β are the length of the space tether, the interior angle of the space tether plane and the exterior angle of the space tether plane, respectively, θ and ψ are the attitude angles of the complex after capture; for generalized control.

2) Calculate the virtual control input ξ _2c

ξ ₁ = ξ, Taking _ξ1d as the expected value of _ξ1 , the tracking error can be expressed as:

ξ _1e = ξ ₁ -ξ _1d

Deriving both sides of ξ _1e can get:

${\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; d</span>}}$

Let ξ _2c be the dummy input of ξ ₂ , designed as:

${\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; d</span>}}$

Among them, K ₁ is a positive definite matrix.

3) Calculate the expected system state quantity ξ _2d

Considering that the tether release speed is limited, the system state _ξ2 is limited by command filtering method, the specific method is as follows:

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>$

Where ε>0.

4) Estimating Post-Catch Complex Model Uncertainties

The ξ _2e error dynamics equation can be expressed as:

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d</span>}}$

in, is the system uncertainty, which is mainly produced by the errors of parameters such as the mass of the complex, the moment of inertia, and the position of the tether connection point. Assuming that the system uncertainty is limited, there is an upper limit λ _L , that is, ||ρ(ΔM ₀ ,ΔN ₀ ,ΔG)||≤||λ _L ||. Design an adaptive law to estimate λ _L and get its estimated value

${\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; PR</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; )</span>$

Among them, a and ε _λ are positive numbers; η·η=(η ₁ η ₁ η ₂ η ₂ η ₃ η ₃ ) ^T ; Proj(·) projection operator; η is the corrected tracking error, and satisfies η=ξ _2e -χ, where χ is obtained by the following first-order filter:

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&chi;</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&chi;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}$

Among them, K ₂ is a positive definite matrix.

5) Calculate the stable control force and control torque Q of the complex after capture

according to $Q_0=m_0{\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_{2d}+N_0{\mathrm{\&xi;}}_{2d}+G_0+(N_0-K_2)\mathrm{\&chi;}-{\mathrm{P\&xi;}}_{1e}-\frac{{\widehat{\mathrm{\&lambda;}}}_L\&CenterDot;\mathrm{\&eta;}}{\left|\mathrm{\&eta;}\right|+{\mathrm{\&epsiv;}}_{\mathrm{\&lambda;}}}$ Get Q ₀ , and then input Q ₀ into the saturation link to get Q, Q is the actual input control force and control torque; M ₀ is the system nominal inertia matrix; N ₀ is the nominal nonlinear velocity related item; G ₀ is the nominal gravity related item.

The above content is only to illustrate the technical idea of the present invention, and cannot limit the protection scope of the present invention. Any changes made on the basis of the technical solution according to the technical idea proposed in the present invention, all fall into the scope of the claims of the present invention. within the scope of protection.

Claims (6)

1. A method for stabilizing the complex after a space tether robot target is captured, is characterized in that, comprises the following steps: 1) Establish the dynamic equation of the complex after the space tethered robot captures the target; 2) Calculate the virtual control input ξ _2c ; 3) Calculate the expected system state quantity ξ _2d ; 4) Estimating Post-Catch Complex Model Uncertainties 5) Calculate the stable control force and control torque Q of the complex after capture. 2. the complex stability control method after the space tethered robot target captures according to claim 1, it is characterized in that, in described step 1), the dynamic equation of the space tethered robot target capture is: $\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;\&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Q</span>}$ in: l is the length of the space tether; α is the interior angle of the space tether; β is the exterior angle of the space tether; θ and ψ are the attitude angles of the complex; M is the system inertia matrix; N is the nonlinear velocity related item; G is the gravity related item; Q is the space tethered robot control force and control torque. 3. the space tether robot target according to claim 1 captures complex body stability control method, it is characterized in that, in described step 2), according to Calculate the virtual control input ξ _2c , where K ₁ is the designed positive definite matrix; ξ _1e = ξ ₁ -ξ _1d , where ξ ₁ = ξ, ξ _1d is the expected value of ξ ₁ , is the derivative of ξ _1e with respect to time. 4. space tether robot object according to claim 1 captures complex body stability control method, it is characterized in that, in described step 3), calculate the method for expecting system state quantity ξ _2d to be: through first-order filtering $\mathrm{\&epsiv;}{\stackrel{\&Center\; Dot;}{\mathrm{\&xi;}}}_{2d}+{\mathrm{\&xi;}}_{2d}={\mathrm{\&xi;}}_{2c},{\mathrm{\&xi;}}_{2d}\left(0\right)={\mathrm{\&xi;}}_{2c}\left(0\right)$ Realization, where ε>0. 5. the complex stability control method after the space tether robot target captures according to claim 1, is characterized in that, in described step 4), the complex model uncertainty Obtained by: Among them, a and ε _λ are positive numbers, η·η=(η ₁ η ₁ η ₂ η ₂ η ₃ η ₃ ) ^T , Proj(·) projection operator; η=ξ _2e -χ, χ passes through the filter Get; K ₂ and P are positive definite matrices. 6. the space tether robot object according to claim 1 captures complex body stability control method, is characterized in that, in described step 5), calculates the complex body stability control force and control torque Q after capture: $Q_0=m_0{\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_{2d}+N_0{\mathrm{\&xi;}}_{2d}+G_0+(N_0-K_2)\mathrm{\&chi;}-{\mathrm{P\&xi;}}_{1e}-\frac{{\widehat{\mathrm{\&lambda;}}}_L\&Center\; Dot;\mathrm{\&eta;}}{\left|\mathrm{\&eta;}\right|+{\mathrm{\&epsiv;}}_{\mathrm{\&lambda;}}},$ Among them, Q is Q ₀ obtained through the saturation link, M ₀ is the nominal inertia matrix of the system; N ₀ is the nominal nonlinear velocity related item; G ₀ is the nominal gravity related item.