Target-oriented space robot fixed-time impedance control method

Abstract

The application discloses a kind of space robot fixed time impedance control methods for target grasping, first in turn constructs the contact kinematics model and dynamics model of space robot and the dynamics model and kinematics model of target satellite, then constructs the contact force model of the end effector of space robot and target satellite, including normal pressure and tangential friction force, finally based on fixed time theory constructs impedance controller, to ensure that when contact with target, the compliant control of space robot system can be quickly realized, realize the fixed time impedance control of space robot.The kinematics model of space robot constructed by the application considers the translational effect of contact force on space robot system, more accurately describes the motion state of space robot after contact occurs, and when designing the impedance controller, the impedance relationship is converted into the form of first-order filter, which can quickly realize the desired impedance relationship and achieve compliant control.

Description

Technical Field

[0001] This invention belongs to the field of space robot control, specifically relating to a fixed-time impedance control method for a target-oriented grasping space robot. Background Technology

[0002] As humanity's exploration of space deepens, a large number of artificial satellites are launched into space every year. Most of these satellites become space debris due to natural failure or accidents, and if not properly managed, they pose a serious threat to the safe operation of satellites in orbit and space stations. Considering economic efficiency, it is impossible to destroy all failed satellites; however, some depleted or repairable satellites can be recovered. In the harsh conditions of outer space—microgravity, high vacuum, strong radiation, and large temperature differences—relying solely on astronauts to complete satellite capture missions is extremely risky. Therefore, research on the safe capture and control of space robots has significant theoretical and engineering application value.

[0003] Scholars both domestically and internationally have conducted some research on the control of space robot capture. However, these studies generally focus on the attitude control of the space robot or combined spacecraft during and after capture, while research on compliant control of the space robot's contact with the target satellite is often neglected. If the space robot lacks compliance during capture, the collision may generate contact forces exceeding the equipment's tolerance, leading to equipment damage. Therefore, compliant control of the space robot is a necessary strategy to ensure the successful completion of the capture process. Currently, compliant control is mostly applied to ground robots, and the control strategies in related studies generally suffer from slow convergence speeds. Furthermore, existing research on space robot contact often only considers normal pressure in its analysis of contact forces, ignoring tangential friction, which inevitably leads to distortion. In addition, scholars often overlook the impact of contact force impulse on the kinematic model of the space robot system, which is also unreasonable.

[0004] There is an urgent need to establish complete contact kinematics and contact dynamics models for space robots during target capture, and a capture control method is required to enable space robots to achieve compliant control quickly during collisions with targets. However, there are currently no relevant descriptions in existing technologies. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide a fixed-time impedance control method for a space robot that grasps targets, thereby ensuring compliant control of the space robot system can be achieved quickly upon contact with the target.

[0006] The specific technical solution for achieving the purpose of this invention is as follows:

[0007] A fixed-time impedance control method for a target-grabbing space robot includes the following steps:

[0008] Step 1: Construct the contact kinematics and dynamics model of the space robot;

[0009] Step 2: Construct the dynamic and kinematic models of the target satellite;

[0010] Step 3: Construct a contact force model between the end effector of the space robot and the target satellite;

[0011] Step 4: Construct an impedance controller based on fixed-time theory to realize fixed-time impedance control of the space robot.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0013] (1) This invention constructs a contact kinematics and contact dynamics model of a rigid free-flying space robot during target capture, and constructs a dynamics model and kinematics model of the target satellite, thereby constructing an impedance controller for capture control based on fixed-time theory to ensure that the compliant control of the space robot system can be quickly realized when in contact with the target.

[0014] (2) The kinematic model of the space robot constructed in this invention takes into account the translational effect of the contact force on the space robot system, and describes the motion state of the space robot more accurately after contact occurs.

[0015] (3) The analysis of the capture process in this invention takes into account the specific shape of the end effector. The contact mechanics model constructed includes normal pressure and also considers the friction introduced by the tangential motion trend between the actuator and the target, making it more realistic.

[0016] (4) The present invention transforms the impedance relationship into the form of a first-order filter. Based on this, the fixed-time impedance controller designed can quickly realize the desired impedance relationship, achieve compliant control, and the convergence time is independent of the initial state of the system. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the steps of the fixed-time impedance control method for target-oriented grasping space robots according to the present invention.

[0018] Figure 2 This is a schematic diagram of the space robot structure of the present invention.

[0019] Figure 3 This is a schematic diagram of the target satellite structure in this invention.

[0020] Figure 4This is a schematic diagram of a three-dimensional scene and two-dimensional analysis of a space robot capturing the handle of a target satellite in an embodiment of the present invention.

[0021] Figure 5 This is a schematic diagram of the space robot structure in an embodiment of the present invention.

[0022] Figure 6 This is a schematic diagram of the simulation results of the contact force experienced by the end effector of the space robot in an embodiment of the present invention.

[0023] Figure 7 This is a graph showing the change in the intermediate vector of impedance error in an embodiment of the present invention.

[0024] Figure 8 This is a graph showing the changes in the base and joint angles of the space robot in an embodiment of the present invention. Detailed Implementation

[0025] Combination Figure 1 and Figure 2 A fixed-time impedance control method for a target-grabbing space robot includes the following steps:

[0026] Step 1: Construct a contact kinematics model and a dynamics model for a class of space robots, specifically as follows:

[0027] Step 1-1: Construct a contact kinematics model for the space robot:

[0028] The position vector of the end effector of the space robot in the inertial coordinate system is:

[0029]

[0030] Where n represents the number of links in the space robot, r0 represents the position vector of the space robot's base center of mass in the inertial coordinate system, and l0 is the length from the base center of mass to joint 1. i (i = 1, 2, ..., n) represents the length of link i, and the variable e i Representing the y-axis of the space robot's body. i Unit vector on:

[0031]

[0032] q0 represents the rotation angle of the space robot's base, q i (i = 1, 2, ... n) represents the rotation angle of joint i of the space robot;

[0033] Differentiating the position vector formula with respect to time, the velocity of the end effector in the inertial coordinate system is expressed as:

[0034]

[0035] According to the momentum theorem, from the initial moment 0 to time t during the capture, the space robot satisfies the following equation:

[0036]

[0037] Where m0 represents the mass of the space robot's base, m i (i = 1, 2, ..., n) represents the mass of link i of the space robot, r i (i = 1, 2, ..., n) represents the position vector of the center of mass of link i in the inertial coordinate system, P0 is the initial linear momentum of the space robot system, and f e This represents the contact force experienced by the end effector of the space robot.

[0038] Considering that the velocity of the center of mass of link i satisfies the following relationship:

[0039]

[0040] Among them, a i This represents the distance from the center of mass of link i to joint i;

[0041] Then, by rearranging, we get:

[0042]

[0043] in, This indicates the total mass of the space robot;

[0044] The velocity of the end effector in the inertial coordinate system can then be expressed as:

[0045]

[0046] Where q = [q0, q1, ..., q n ] T ∈R n Let J(q) ∈ R represent the rotation vectors of the space robot's base and joints. 2×n Let Jacobian matrix be the distance from joint space to Cartesian space for a space robot. The elements of the matrix are represented as follows:

[0047]

[0048]

[0049]

[0050]

[0051] Steps 1-2: Construct a dynamic model of the space robot based on the Lagrange energy modeling method:

[0052] The total kinetic energy of the space robot system is:

[0053]

[0054] Where I0 represents the moment of inertia of the base about its own center of mass, I i (i = 1, 2…n) represents the moment of inertia of link i about its own center of mass. Neglecting potential energy, according to the Lagrange equation:

[0055]

[0056] Where L=T represents the Lagrange energy function and Q represents the generalized force;

[0057] Based on this, the dynamic equations of the space robot are obtained as follows:

[0058]

[0059] Where M(q)∈R n×n Let the inertia matrix of this rigid free-flying space robot system be... Let R be the matrix of Coriolis force and centripetal force, τ∈R n For the input control torque, τ e ∈R n The equivalent torque of the contact force at the actuator end in the joint space satisfies:

[0060] τ e =J(q) T f e

[0061] Where M(q)∈R n×n Let the inertia matrix of this rigid free-flying space robot system be... Let R be the matrix of Coriolis force and centripetal force, τ∈R n For the input control torque, τ e ∈R n Let q = [q0, q1, ..., q] be the equivalent torque of the contact force acting on the actuator end effector in the joint space. n ] T ∈R n Let f represent the base and joint rotation vectors of the space robot, J(q) be the Jacobian matrix of the space robot from joint space to Cartesian space, and f be the joint rotation vectors of the space robot. e This represents the contact force experienced by the end effector of a space robot.

[0062] Step 2, Combining Figure 3 A dynamic and kinematic model of a target satellite with a cylindrical handle is constructed, specifically as follows:

[0063] Step 2-1: Construct a dynamic model for a target satellite with a cylindrical handle:

[0064] The target satellite is a freely floating rigid body in space. Based on the Newton-Euler method, a dynamic model of the target satellite is constructed:

[0065]

[0066]

[0067] Where m t The mass r of the target satellite is indicated by its mass. t Let I be the position vector of the target satellite's center of mass in the inertial coordinate system. t Let be the inertia matrix of the target satellite in its principal axis coordinate system. Let ρ be the angular velocity of the target satellite, and ρ represent the position vector of the contact point relative to the center of mass of the target satellite in the inertial coordinate system, taking into account the radius R of the cylindrical handle. h The contact force is much smaller than |ρ|, so the contact force on the target satellite can be approximated as acting on the center C of the handle. h Place, that is:

[0068] ρ=r h -r t

[0069] Where r h C h Position vector in the inertial coordinate system;

[0070] Step 2-2: Construct the kinematic model of the target satellite:

[0071]

[0072] Step 3, Combining Figure 4 A contact force model between the end effector of the space robot and the target satellite is constructed, specifically as follows:

[0073] Step 3-1: Based on the specific capture method, i.e., the end effector of the space robot uses a gripper for capture, the area enclosed by the gripper can be regarded as a capture circle with radius R(t) that contracts at a uniform speed, and the center of the circle is C. e Its position vector in the inertial coordinate system is:

[0074] r c =r e +R(t)e2

[0075] Before the capture begins, assume the handle is already within the circular area, i.e., surrounded by the grippers. As the grippers begin to close, the radius of the circular area decreases, causing a collision with the handle and generating a contact force. The capture circular area shrinks to the handle's radius R.h At this point, the space robot and the target satellite are fixedly connected, meaning there is no longer any contact force, thus completing the capture.

[0076] Step 3-2: Construct the normal pressure model for the end effector and the target satellite:

[0077]

[0078]

[0079]

[0080] Where δ represents the local intrusion amount of the handle and gripper in the plane, n is the unit vector along the common normal direction of the contact point, and F n K is the normal pressure exerted on the gripper. c and C c These are the stiffness coefficient and the damping coefficient, respectively.

[0081] Step 3-3: Construct a tangential friction model between the end effector and the target satellite:

[0082]

[0083] v t =Δv-(Δv T n)n

[0084]

[0085]

[0086]

[0087] Where Δv represents the velocity of the gripper relative to the handle at the point of contact, v t Let s(t) and s' be the tangential velocity of the gripper relative to the handle at the contact point. max (t) represent the average bristle offset vector and the maximum bristle offset at time t, respectively, where t0 is the initial moment of the collision, and μ k and μ s V represents the sliding friction coefficient and the static friction coefficient, respectively. d The critical speed for distinguishing between sliding friction and static friction is F. f k is the frictional force acting on the grippers. b and c b These represent the stiffness coefficient and damping coefficient of the bristles, respectively.

[0088] Steps 3-4: Construct a contact force model that includes normal pressure and tangential friction:

[0089] F r =Fn +F f

[0090] F t =-F r

[0091] In the formula, F r and F t These represent the contact forces experienced by the space robot and the target satellite, respectively.

[0092] Step 4: Construct an impedance controller based on fixed-time theory to ensure that the space robot can quickly achieve the desired impedance relationship upon collision with the target, thus realizing fixed-time impedance control of the space robot. Specifically:

[0093] Step 4-1: Construct the desired impedance model of the space robot joint space during the capture process:

[0094]

[0095] Among them, M d =diag(M d0 M d1 ,...,M dn ), C d =diag(C d0 C d1 ,...,C dn ) and K d =diag(K) d0 ,K d1 ,...,K dn ) are the desired inertia matrix, desired damping matrix, and desired stiffness matrix of the environment, respectively, q=[q0,q1,...,q n ] T ∈R n Let q represent the vector of the space robot's base and joint rotation angles. d =[q 0d ,q 1d ,...,q nd ] T τ represents the desired rotation vector between the base and the joint. e ∈R n This is the equivalent torque of the contact force at the actuator end in the joint space;

[0096] To simplify impedance controller design, the impedance relationship is transformed into a first-order filter form:

[0097] Define augmented impedance error:

[0098]

[0099] Where, e = qqd , Λ and Γ are both diagonal matrices and satisfy the following conditions:

[0100] Define the impedance error intermediate vector:

[0101]

[0102] Construct an impedance model in the form of a first-order filter:

[0103]

[0104] Step 4-2: Construct an impedance controller based on fixed-time theory to achieve compliant movements of the space robot:

[0105] Define the angular velocity and angular acceleration of the reference rotation angle:

[0106]

[0107] The fixed-time impedance control law is:

[0108]

[0109] Where α>1, 0<β<1, sig γ (z)=[|z0| γ sign(z0),|z1| γ sign(z1),...,|z n | γ sign(z n )] T (γ=α,β), K1=diag(K 10 ,K 11 ,...,K 1n ), K2 = diag(K 20 ,K 21 ,...,K 2n And satisfy z T K1=k1sig α (z T ), z T K2=k2sig β (z T ), k1>0, e=qq d , Λ and Γ are both diagonal matrices and satisfy the following conditions:

[0110] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, performs the following steps:

[0111] Step 1: Construct the contact kinematics and dynamics model of the space robot;

[0112] Step 2: Construct the dynamic and kinematic models of the target satellite;

[0113] Step 3: Construct a contact force model between the end effector of the space robot and the target satellite;

[0114] Step 4: Construct an impedance controller based on fixed-time theory to realize fixed-time impedance control of the space robot.

[0115] A computer-storeable medium storing a computer program, characterized in that the following steps are implemented by a processor on the computer program:

[0116] Step 1: Construct the contact kinematics and dynamics model of the space robot;

[0117] Step 2: Construct the dynamic and kinematic models of the target satellite;

[0118] Step 3: Construct a contact force model between the end effector of the space robot and the target satellite;

[0119] Step 4: Construct an impedance controller based on fixed-time theory to realize fixed-time impedance control of the space robot.

[0120] Example

[0121] Combination Figure 5 This embodiment takes a two-link free-flying space robot as an example to illustrate the fixed-time impedance control method for target-oriented grasping space robots of the present invention, which includes the following steps:

[0122] Step 1: Construct a contact kinematics model and a dynamics model for a class of space robots, specifically as follows:

[0123] Step 1-1: Construct a contact kinematics model for the space robot:

[0124] The position vector of the end effector of the space robot in the inertial coordinate system is:

[0125] r e =r0+l0e0+l1e1+l2e2

[0126] Where r0 represents the position vector of the space robot's base center of mass in the inertial coordinate system, l0 is the length from the base center of mass to joint 1, and l1 and l2 represent the lengths of link 1 and link 2, respectively. Variables e0, e1, and e2 represent the unit vectors on axes y0, y1, and y0, respectively.

[0127] e0 = [sin(q0), cos(q0)] T

[0128] e1 = [sin(q0+q1),cos(q0+q1)] T

[0129] e2=[sin(q0+q1+q2),cos(q0+q1+q2)] T

[0130] q0, q1 and q2 represent the base rotation angle, joint 1 rotation angle and joint 2 rotation angle, respectively;

[0131] Differentiating the position vector formula with respect to time, the velocity of the end effector in the inertial coordinate system is expressed as:

[0132]

[0133] According to the momentum theorem, from the initial moment 0 to time t during the capture, the space robot satisfies the following equation:

[0134]

[0135] Where m0, m1, and m2 are the masses of the space robot's base, link 1, and link 2, respectively; r1 and r2 represent the position vectors of the centers of mass of link 1 and link 2 in the inertial coordinate system, respectively; P0 is the initial linear momentum of the space robot; and f e This represents the contact force experienced by the end effector of the space robot.

[0136] Considering that the velocities of the centers of mass of connecting rod 1 and connecting rod 2 satisfy the following relationship:

[0137]

[0138]

[0139] Where a1 and a2 represent the distance from the center of mass of link 1 to joint 1 and the distance from the center of mass of link 2 to joint 2, respectively;

[0140] Then, by rearranging, we get:

[0141]

[0142] Where M = m0 + m1 + m2 represents the total mass of the space robot;

[0143] The velocity of the end effector in the inertial coordinate system can then be expressed as:

[0144]

[0145] Where q = [q0, q1, q2]T ∈R 3 Let J(q) ∈ R represent the rotation vectors of the space robot's base and joints. 2×3 Let Jacobian matrix be the distance from joint space to Cartesian space for a space robot. The elements of the matrix are represented as follows:

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] Steps 1-2: Construct a dynamic model of the space robot based on the Lagrange energy modeling method:

[0153] The total kinetic energy of the space robot system is:

[0154]

[0155] Where I0 represents the moment of inertia of the base about its own center of mass, I i (i = 1, 2... n) represents the moment of inertia of link i about its own center of mass. Neglecting potential energy, according to the Lagrange equation:

[0156]

[0157] Where L=T represents the Lagrange energy function and Q represents the generalized force;

[0158] Based on this, the dynamic equations of the space robot are obtained as follows:

[0159]

[0160] Where M(q)∈R 3×3 Let the inertia matrix of this rigid free-flying space robot system be... Let R be the matrix of Coriolis force and centripetal force, τ∈R 3 For the input control torque, τ e ∈R 3 The equivalent torque of the contact force at the actuator end in the joint space satisfies:

[0161] τ e =J(q) T f e

[0162] For ease of representation, the following intermediate quantities are denoted as:

[0163]

[0164]

[0165]

[0166]

[0167] L4=m0G0G1+m1(G0+l0)(G1+a1)+m2(G0+l0)(G1+l1)

[0168] L5=m0G0G2+m1(G0+l0)G2+m2(G0+l0)(G2+a2)

[0169] L6=m0G1G2+m1(G1+a1)G2+m2(G1+l1)(G2+a2)

[0170] Where I0, I1, and I2 represent the moments of inertia of the space robot's base, link 1, and link 2 about their own centers of mass, respectively. Then, the elements of the inertia matrix M(q) can be represented as:

[0171] M 11 =2(L1+L2+L3+L4cos(q1)+L5cos(q1+q2)+L6cos(q2))

[0172] M 12 =M 21 =2(L2+L3+L6cos(q2))+L4cos(q1)+L5cos(q1+q2)

[0173] M 13 =M 31 = 2L3 + L5cos(q1 + q2) + L6cos(q2)

[0174] M 22 = 2(L2+L3+L6cos(q2))

[0175] M 23 =M 32 = 2L3 + L6cos(q2)

[0176] M 33 =2L3

[0177] Coriolis force and centripetal force matrix Each element in the expression can be represented as:

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185]

[0186] C 33 =0

[0187] In this embodiment, the parameters of the space robot are as follows:

[0188] m0=200kg, m1=8kg, m2=16kg, I0=100kg·m 2 I1 = 4.2 kg·m 2 I2 = 42 kg·m 2 Given a1 = 1m, a2 = 0.95m, l0 = 1m, l1 = 2m, l2 = 1m, the initial position vector and velocity vector of the base's center of mass in the inertial coordinate system are r0 = [0,0]. T and The initial angles, initial angular velocities, and initial angular accelerations of the base and joint are q0 = [0, 0.0655, 2.024]. T (rad / s)

[0189] Step 2: Construct a dynamic and kinematic model for a target satellite with a cylindrical handle, specifically as follows:

[0190] Step 2-1: Construct a dynamic model for a target satellite with a cylindrical handle:

[0191] The target satellite is a freely floating rigid body in space. Based on the Newton-Euler method, a dynamic model of the target satellite is constructed:

[0192]

[0193]

[0194] Where m t The mass r of the target satellite is indicated by its mass. tLet I be the position vector of the target satellite's center of mass in the inertial coordinate system. t Let be the inertia matrix of the target satellite in its principal axis coordinate system. Let ρ be the angular velocity of the target satellite, and ρ represent the position vector of the contact point relative to the center of mass of the target satellite in the inertial coordinate system, taking into account the radius R of the cylindrical handle. h The contact force is much smaller than |ρ|, so the contact force on the target satellite can be approximated as acting on the center C of the handle. h Place, that is:

[0195] ρ=r h -r t

[0196] Where r h C h Position vector in the inertial coordinate system;

[0197] Step 2-2: Construct the kinematic model of the target satellite:

[0198]

[0199] In this embodiment, the target satellite parameters are as follows:

[0200] m t =20kg, I t =10kg·m 2 The initial position vector and initial velocity vector of the satellite's center of mass in the inertial coordinate system are r and r, respectively. t0 =[2.087,2.450] T m, The satellite's initial attitude angle and angular velocity in the two-dimensional plane are q t0 =0 and (Vertical plane pointing outwards is positive), R h =0.02m, |ρ|=1, C h The initial position vector in the inertial coordinate system is r. h0 =r t0 -|ρ|=[1.087,2.450] T m.

[0201] Step 3: Construct a contact force model between the end effector of the space robot and the target satellite, specifically as follows:

[0202] Step 3-1: Based on the specific capture method, i.e., the end effector of the space robot uses a gripper for capture, the area enclosed by the gripper can be regarded as a capture circle with radius R(t) that contracts at a uniform speed, and the center of the circle is C. e Its position vector in the inertial coordinate system is:

[0203] rc =r e +R(t)e2

[0204] Before the capture begins, assume the handle is already within the circular area, i.e., surrounded by the grippers. As the grippers begin to close, the radius of the circular area decreases, causing a collision with the handle and generating a contact force. The capture circular area shrinks to the handle's radius R. h At this point, the space robot and the target satellite are fixedly connected, meaning there is no longer any contact force, thus completing the capture.

[0205] In this embodiment, the radius of the circular area after the capture begins is R(t) = (0.1-0.01t)m.

[0206] Step 3-2: Construct the normal pressure model for the end effector and the target satellite:

[0207]

[0208]

[0209]

[0210] Where δ represents the local intrusion amount of the handle and gripper in the plane, n is the unit vector along the common normal direction of the contact point, and F n K is the normal pressure exerted on the gripper. c and C c These are the stiffness coefficient and the damping coefficient, respectively.

[0211] In this embodiment, the parameters of the normal pressure model are as follows:

[0212] K c =5×10 6 N / m, C c =0 Nm / s

[0213] Step 3-3: Construct a tangential friction model between the end effector and the target satellite:

[0214]

[0215] v t =Δv-(Δv T n)n

[0216]

[0217]

[0218]

[0219] Where Δv represents the velocity of the gripper relative to the handle at the point of contact, v tLet s(t) and s' be the tangential velocity of the gripper relative to the handle at the contact point. max (t) represent the average bristle offset vector and the maximum bristle offset at time t, respectively, where t0 is the initial moment of the collision, and μ k and μ s V represents the sliding friction coefficient and the static friction coefficient, respectively. d The critical speed for distinguishing between sliding friction and static friction is F. f k is the frictional force acting on the grippers. b and c b These represent the stiffness coefficient and damping coefficient of the bristles, respectively.

[0220] In this embodiment, the parameters of the tangential friction force model are as follows:

[0221] k b =5×10 4 N / m, c b =0 Nm / s, μ k =0.25, μ s =0.3, v d =10 -2 m / s

[0222] Steps 3-4: Construct a contact force model that includes normal pressure and tangential friction:

[0223] F r =F n +F f

[0224] F t =-F r

[0225] In the formula, F r and F t These represent the contact forces experienced by the space robot and the target satellite, respectively.

[0226] Step 4: Construct an impedance controller based on fixed-time theory to ensure that the space robot can quickly achieve the desired impedance relationship upon collision with the target, thus realizing fixed-time impedance control of the space robot. Specifically:

[0227] Step 4-1: Construct the desired impedance model of the space robot joint space during the capture process:

[0228]

[0229] Where q d , and Let M represent the desired rotation angle, desired angular velocity, and desired angular acceleration of the base and joint, respectively. d =diag(Md1 M d2 M d3 ), C d =diag(C d1 C d2 C d3 ) and K d =diag(K) d1 ,K d2 ,K d3 ) are the desired inertia matrix, desired damping matrix, and desired stiffness matrix of the environment, respectively;

[0230] In this embodiment, the desired rotation angle and desired impedance model parameters are as follows:

[0231] q d =[0.06,0.1355,1.974] T (rad / s) M d =diag(1,1,1), C d =diag(10,10,10), K d =diag(25,25,25);

[0232] To simplify impedance controller design, the impedance relationship is transformed into a first-order filter form:

[0233] Define augmented impedance error:

[0234]

[0235] Where e = qq d , Λ and Γ are both diagonal matrices and satisfy the following conditions:

[0236] Define the impedance error intermediate vector:

[0237]

[0238] Construct an impedance model in the form of a first-order filter:

[0239]

[0240] Step 4-2: Construct an impedance controller based on fixed-time theory to achieve compliant movements of the space robot:

[0241] Define the angular velocity and angular acceleration of the reference rotation angle:

[0242]

[0243] The fixed-time impedance control law is:

[0244]

[0245] Where α>1, 0<β<1, sig γ (z)=[|z1| γ sign(z1),|z2| γ sign(z2),|z3| γ sign(z3)] T (γ=α,β), K1=diag(K 11 ,K 12 ,K 13 ), K2 = diag(K 21 ,K 22 ,K 23 And satisfy z T K1=k1sig α (z T ), z T K2=k2sig β (z T ), k1>0, k2>0.

[0246] In this embodiment, the parameters of the fixed-time impedance controller are as follows:

[0247] α=1.5, β=0.833, k1=1, k2=1.

[0248] The simulation results obtained based on MATLAB are as follows: Figures 6-8 As shown;

[0249] Simulation results show that the control algorithm designed in this invention can ensure that the space robot can quickly achieve the desired impedance relationship when colliding with the target during the capture process, thus realizing the compliant movement of the space robot; specifically, Figure 6 This describes the contact force experienced by the end effector during target capture; from Figure 7 It can be seen that after the capture begins, the fixed-time impedance controller enables the impedance error to converge to zero in approximately 2.5 seconds, achieving the desired impedance relationship; furthermore, Figure 8 This indicates that when there is no contact force at the end of a space robot, it will tend to move along the desired trajectory. If there is a contact force at the end, it can actively deviate from the desired trajectory to adapt to changes in the environment, thereby achieving compliant movements of the space robot.

[0250] This embodiment employs a compliant control method for space robots designed for target grasping. First, contact kinematics and dynamics models are established for a class of free-flying space robots and a target satellite, respectively. Then, based on the specific grasping method, a contact force model incorporating normal pressure and tangential friction is constructed to describe the contact behavior between the space robot and the target. Addressing the compliant motion requirements of the robotic arm in space target safe capture missions, the designed fixed-time impedance controller can quickly achieve the desired impedance relationship. The embodiment verifies the effectiveness of this invention.

[0251] The above embodiments illustrate and describe the basic principles and main features of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed.

Claims

1. A fixed-time impedance control method for a target-oriented grasping space robot, characterized in that, Includes the following steps: Step 1: Construct the contact kinematics and dynamics model of the space robot; Step 2: Construct the dynamic and kinematic models of the target satellite; Step 3: Construct a contact force model between the end effector of the space robot and the target satellite; Step 4: Construct an impedance controller based on fixed-time theory to achieve fixed-time impedance control of the space robot: Step 4-1: Construct the desired impedance model of the space robot joint space during the capture process: ； in, , and These represent the desired inertia matrix, desired damping matrix, and desired stiffness matrix of the environment, respectively. Represents the base and joint rotation vectors of the space robot, where This represents the rotation angle of the space robot's base, and n represents the number of joints in the space robot. This represents the desired rotation vector between the base and the joint. This is the equivalent torque of the contact force at the actuator end in the joint space; Define augmented impedance error: ； in, , , , and All are diagonal matrices and satisfy the following conditions: , , . Define the impedance error intermediate vector: ； Construct an impedance model in the form of a first-order filter: ； Step 4-2: Construct an impedance controller based on fixed-time theory to achieve compliant movements of the space robot: The impedance controller in step 4-2 is specifically as follows: ； ； ； ； in, , , , , And satisfy , , , , , , and All are diagonal matrices and satisfy the following conditions: , , , The inertia matrix of a rigid, free-flying space robot system. The matrix represents the Coriolis force and the centripetal force. To input control torque, Let be the desired angular velocity of the base and joint. The angular velocity is used as a reference angle.

2. The fixed-time impedance control method for a target-oriented grasping space robot according to claim 1, characterized in that, The construction of the contact kinematics and dynamics model of the space robot in step 1 specifically includes: Step 1-1: Construct a contact kinematics model for the space robot; Steps 1-2: Construct a dynamic model of the space robot.

3. The fixed-time impedance control method for a target-oriented grasping space robot according to claim 2, characterized in that, The construction of the contact kinematics model of the space robot in step 1-1 specifically involves: ； ； ； in, This represents the velocity vector of the end effector of a space robot in the inertial coordinate system. Indicates the number of links in a space robot. The length from the base's center of mass to joint 1. Representative link Length; Representing the coordinate axes of each part of the space robot unit vector on, Represents the joints of a space robot The corner; This represents the vectors of the space robot's base and joint rotation angles. Let Jacobian matrix be the distance from joint space to Cartesian space for a space robot. This represents the contact force experienced by the end effector of the space robot. m 0 Indicates the mass of the space robot's base. m i Indicates the linkage of a space robot i quality M This represents the total mass of the space robot. Indicates the link i Center of mass to joint i The distance.

4. The fixed-time impedance control method for a target-oriented grasping space robot according to claim 2, characterized in that, The construction of the dynamic model of the space robot in steps 1-2 is specifically as follows: ； ； in The inertia matrix of a rigid, free-flying space robot system. The matrix represents the Coriolis force and the centripetal force. To input control torque, This is the equivalent torque of the contact force acting on the actuator end in the joint space. This represents the vectors of the space robot's base and joint rotation angles. Let Jacobian matrix be the distance from joint space to Cartesian space for a space robot. This represents the contact force experienced by the end effector of a space robot.

5. The fixed-time impedance control method for a target-oriented grasping space robot according to claim 1, characterized in that, The construction of the dynamic and kinematic models of the target satellite in step 2 specifically includes: Step 2-1: Construct a dynamic model for a target satellite with a cylindrical handle: The target satellite is a freely floating rigid body in space. Based on the Newton-Euler method, a dynamic model of the target satellite is constructed: ； in Indicates the mass of the target satellite. Let be the inertia matrix of the target satellite in its principal axis coordinate system. The angular velocity of the target satellite, This represents the contact force experienced by the end effector of the space robot. The radius of the cylindrical handle represents the position vector of the contact point relative to the center of mass of the target satellite in the inertial coordinate system. Much smaller than The contact force acting on the target satellite is considered to act on the center of the handle. Place, that is: ； in for Position vector in the inertial coordinate system Let be the position vector of the target satellite's center of mass in the inertial coordinate system; Step 2-2: Construct the kinematic model of the target satellite: 。 6. The fixed-time impedance control method for a target-oriented grasping space robot according to claim 5, characterized in that, The contact force model between the end effector of the space robot and the target satellite in step 3 is specifically as follows: Step 3-1: The end effector of the space robot uses a gripper for grasping. The area enclosed by the gripper can be considered as a radius of... A uniformly contracting capture circle, with the center of the circle being... Its position vector in the inertial coordinate system is: ； This indicates the position of the end effector in the inertial coordinate system. In the inertial coordinate system Unit vector on; Before the capture begins, assume the handle is already within the circular area, i.e., surrounded by the grippers. As the grippers begin to close, the radius of the circular area decreases, causing it to collide with the handle and generate contact force. When the radius of the capture circular area shrinks to the radius of the handle... At this point, the space robot and the target satellite are fixedly connected, meaning there is no longer any contact force, thus completing the capture. Step 3-2: Construct the normal pressure model for the end effector and the target satellite: ； ； ； in, This indicates the local intrusion amount of the handle and gripper within the plane. Let be the unit vector along the direction of the common normal at the contact point. The normal pressure exerted on the grippers. and These are the stiffness coefficient and the damping coefficient, respectively. Step 3-3: Construct a tangential friction model between the end effector and the target satellite: ； ； ； ； ； in, This indicates the velocity of the gripper relative to the handle at the point of contact. Let be the tangential velocity of the gripper relative to the handle at the point of contact. and They represent The average bristle offset vector and the maximum bristle offset at time t. At the initial moment of the collision, and These represent the sliding friction coefficient and the static friction coefficient, respectively. The critical speed for distinguishing between sliding friction and static friction. The frictional force experienced by the grippers. and These represent the stiffness coefficient and damping coefficient of the bristles, respectively. Steps 3-4: Construct a contact force model that includes normal pressure and tangential friction: ； ； In the formula, and These represent the contact forces experienced by the space robot and the target satellite, respectively.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method steps as defined in any one of claims 1 to 6.

8. A computer-storeable medium storing a computer program, characterized in that, The method steps specified in any of 1 to 6 above are implemented by a processor in the computer program.

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