High underactuated space manipulator trajectory optimization method

Abstract

The embodiment of the application provides a high under-actuated space manipulator trajectory optimization method, comprising the following steps: constructing a high under-actuated space manipulator direction dynamics operability and dynamics condition number index according to a coupling relationship between a high under-actuated space manipulator active joint torque and end acceleration; constructing a high under-actuated space manipulator trajectory optimization objective function according to the high under-actuated space manipulator direction dynamics operability and dynamics condition number index; and performing trajectory optimization on the high under-actuated space manipulator by using a gradient projection method according to a high under-actuated space manipulator kinematic coupling relationship and the high under-actuated space manipulator trajectory optimization objective function.

Description

[Technical Field]

[0001] This invention relates to a trajectory optimization method for a highly underactuated space robotic arm, belonging to the field of fault-tolerant trajectory optimization technology for space robotic arms. [Background Technology]

[0002] Many on-orbit missions on the space station rely on space robotic arms with strong operational capabilities, high mobility, and strong environmental adaptability. This places high demands on the reliability and safety of these robotic arms. If a joint of the space robotic arm experiences a free-swinging failure and cannot be repaired in time, the robotic arm may be unable to complete its mission on schedule. Joints experiencing free-swinging failures lose their torque output capability and can only indirectly control their movement through coupling with the active joints. In this case, the underactuated units of the space robotic arm, including the base and passive joints, exhibit high underactuation characteristics. Even with high underactuation, the space robotic arm can still perform end-effector trajectory tracking tasks based on its own kinematic coupling characteristics and optimize joint trajectories using non-holonomic redundancy. Therefore, trajectory optimization for high underactuated space robotic arms to achieve excellent motion capabilities is of great significance for further improving the on-orbit reliability of space robotic arms.

[0003] Existing methods for trajectory optimization of highly underactuated space manipulators mainly utilize directional dynamics manipulation or dynamic condition number to establish the trajectory optimization objective function. Directional dynamics manipulation reflects the acceleration capability of the active joint torque on the end effector along the task direction; a larger value indicates stronger acceleration. Dynamic condition number reflects the anisotropy of the acceleration capability of the active joint torque on the end effector; a larger value indicates greater differences in acceleration capability across different directions. However, the trajectory optimization objective function based on directional dynamics manipulation only considers the end effector acceleration capability along the task direction, neglecting acceleration capabilities in other directions. Similarly, the trajectory optimization objective function based on dynamic condition number only considers optimizing the isotropic effect of the end effector acceleration capability, ignoring acceleration capabilities along the task direction. Therefore, it is necessary to comprehensively consider the end effector acceleration capabilities along the task direction and other directions to construct a trajectory optimization objective function for highly underactuated space manipulators. [Summary of the Invention]

[0004] In view of this, embodiments of the present invention provide a trajectory optimization method for a highly underactuated space manipulator. By establishing the coupling relationship between the active joint torque and the end-effector acceleration of the highly underactuated space manipulator, the directional dynamics operability and dynamics condition number indices of the highly underactuated space manipulator are constructed. Then, the trajectory optimization objective function of the highly underactuated space manipulator is constructed, and the trajectory of the highly underactuated space manipulator is optimized using the gradient projection method.

[0005] This invention provides a method for optimizing the trajectory of a highly underactuated space robot, comprising:

[0006] Based on the coupling relationship between the active joint torque and the end-effector acceleration of a highly underactuated space manipulator, the directional dynamics operability and dynamic condition number indices of the highly underactuated space manipulator are constructed.

[0007] Based on the directional dynamics operability and dynamics condition number indices of the high underactuated space manipulator, a trajectory optimization objective function for the high underactuated space manipulator is constructed.

[0008] Based on the kinematic coupling relationship of the high-underactuated space manipulator and the trajectory optimization objective function of the high-underactuated space manipulator, the trajectory of the high-underactuated space manipulator is optimized using the gradient projection method.

[0009] In the above method, based on the coupling relationship between the active joint torque and the end effector acceleration of the highly underactuated space manipulator, the directional dynamics operability and dynamic condition number indices of the highly underactuated space manipulator are constructed, including:

[0010] The coupling relationship between the active joint torque and the end effector acceleration of a high-degree-of-freedom, underactuated space manipulator is as follows:

[0011]

[0012] In the formula, For terminal acceleration, The coupled inertia matrix characterizing the mapping of active joint torque to end-effector acceleration, where a is the number of active joints, J eA M is the Jacobian matrix mapping the active joint to the end-effector velocity. τA Let τ be the self-coupling inertial matrix of active joint acceleration and torque. A ∈R a×1 For active joint torque, C eτ This is a nonlinear term representing the coupling relationship between the active joint torque and the end-effector acceleration.

[0013] Based on the coupled inertia matrix M that maps the active joint torque to the end-effector acceleration in the above formula. eτ The directional dynamics operability and dynamic condition number indices of the highly underactuated space manipulator are as follows:

[0014]

[0015] In the formula, λ1 is the directional dynamic operability, r is the dynamic condition number, p is the unit vector along the mission direction, and L = diagτ 1max ,…,τ nmax Let τ be the torque normalization matrix, and diag denote the diagonal matrix. imaxLet σ1 and σ be the maximum allowable torque of joint i. m M respectively eτ The maximum and minimum singular values.

[0016] In the above method, based on the directional dynamics operability and dynamics condition number indices of the high-underactuated space manipulator, a trajectory optimization objective function for the high-underactuated space manipulator is constructed, including:

[0017] Based on the directional dynamics maneuverability and dynamics condition number indices of the highly underactuated space manipulator, the trajectory optimization objective function of the highly underactuated space manipulator is obtained as follows:

[0018]

[0019] In the formula, α>0 is a constant, and r max This is the threshold value for the set dynamic condition number. From the expression of the trajectory optimization objective function, it can be seen that when the anisotropy of the active joint torque on the end-effector acceleration capability is acceptable, r < r max ,but The joint trajectory will be optimized in the direction of increasing the dynamic maneuverability. When the anisotropy exceeds the threshold, r > r max ,but The joint trajectory will be optimized to reduce the dynamic condition number in order to weaken the anisotropy of active joint torque on end-effector acceleration capability.

[0020] In the above method, based on the kinematic coupling relationship of the high-underactuated space manipulator and the trajectory optimization objective function of the high-underactuated space manipulator, the gradient projection method is used to optimize the trajectory of the high-underactuated space manipulator, including:

[0021] The kinematic coupling relationship of the highly underactuated space manipulator is as follows:

[0022]

[0023] In the formula, v e ,ω e These are the terminal linear velocity and the terminal angular velocity, respectively. For active joint velocity;

[0024] The expression for the active joint velocity is obtained by utilizing the kinematic coupling relationship of the highly underactuated space manipulator:

[0025]

[0026] In the formula, Indicates the pseudo-inverse of a matrix;

[0027] The trajectory optimization objective function of the highly underactuated space manipulator is incorporated into the expression for the active joint velocity using the gradient projection method:

[0028]

[0029] In the formula, β is the optimization coefficient, and I is the identity matrix. Optimize the gradient of the objective function for the trajectory;

[0030] When performing trajectory planning, given the end velocity By using the above-mentioned expression for the active joint velocity, which introduces a trajectory optimization objective function, to solve for the active joint velocity, trajectory optimization of a highly underactuated space robot arm can be achieved.

[0031] As can be seen from the above technical solutions, the embodiments of the present invention have the following beneficial effects:

[0032] In the technical solution of this invention, based on the coupling relationship between the active joint torque and end-effector acceleration of a highly underactuated space manipulator, directional dynamics operability and dynamics condition number indices are established, a trajectory optimization objective function is constructed, and the trajectory optimization of the highly underactuated space manipulator is achieved using the gradient projection method. The proposed trajectory optimization objective function comprehensively considers directional dynamics operability and dynamics condition number, achieving strong end-effector acceleration along the mission direction while ensuring adequate acceleration in other directions, thus making the trajectory optimization of the highly underactuated space manipulator more aligned with the needs of space missions. This improved trajectory optimization method for underactuated space manipulators can provide a basis for the design of system trajectory optimization methods. [Attached Image Description]

[0033] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort or labor.

[0034] Figure 1 This is a flowchart illustrating the trajectory optimization method for a highly underactuated spatial robotic arm provided in an embodiment of the present invention.

[0035] Figure 2 This is a schematic diagram of a seven-degree-of-freedom spatial robotic arm model provided in an embodiment of the present invention;

[0036] Figure 3 This is a comparison chart of the directional dynamics operability indices of highly underactuated space manipulators;

[0037] Figure 4 This is a comparison chart of dynamic condition parameters for highly underactuated space manipulators;

[0038] Figure 5 This is a comparison chart of the joint angular velocities of a high-underactuated space robotic arm.

Detailed Implementation Methods

[0039] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0040] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0041] This invention provides a trajectory optimization method for a highly underactuated space robot arm. Please refer to [link / reference]. Figure 1 This is a flowchart illustrating the trajectory optimization method for a highly underactuated spatial manipulator provided in an embodiment of the present invention. The method includes the following steps:

[0042] Step 101: Based on the coupling relationship between the active joint torque and the end-effector acceleration of the high-underactuated space manipulator, construct the directional dynamics operability and dynamic condition number indices of the high-underactuated space manipulator.

[0043] Specifically, the coupling relationship between the active joint torque and the end effector acceleration of an n-DOF high-underactuated space manipulator is as follows:

[0044]

[0045] In the formula, For terminal acceleration, The coupled inertia matrix characterizing the mapping of active joint torque to end-effector acceleration, where a is the number of active joints, J eA M is the Jacobian matrix mapping the active joint to the end-effector velocity. τA Let τ be the self-coupling inertial matrix of active joint acceleration and torque. A ∈R a×1 For active joint torque, C eτ This is a nonlinear term representing the coupling relationship between the active joint torque and the end-effector acceleration.

[0046] Based on the coupled inertia matrix M that maps the active joint torque to the end-effector acceleration in the above formula. eτ The directional dynamics operability and dynamic condition number indices of the highly underactuated space manipulator are as follows:

[0047]

[0048] In the formula, λ1 is the directional dynamic operability, r is the dynamic condition number, p is the unit vector along the mission direction, and L = diagτ 1max ,…,τ nmax Let τ be the torque normalization matrix, and diag denote the diagonal matrix. imax Let σ1 and σ be the maximum allowable torque of joint i. m M respectively eτ The maximum and minimum singular values.

[0049] Step 102: Based on the directional dynamics operability and dynamics condition number indices of the high-underactuated space manipulator, construct the trajectory optimization objective function of the high-underactuated space manipulator.

[0050] Specifically, based on the directional dynamics maneuverability and dynamics condition number indices of the highly underactuated space manipulator, the trajectory optimization objective function of the highly underactuated space manipulator is obtained as follows:

[0051]

[0052] In the formula, α>0 is a constant, and r max It is the threshold number of the set dynamic conditions.

[0053] Step 103: Based on the kinematic coupling relationship of the high-underactuated space manipulator and the trajectory optimization objective function of the high-underactuated space manipulator, the trajectory of the high-underactuated space manipulator is optimized using the gradient projection method.

[0054] Specifically, the kinematic coupling relationship of the highly underactuated space manipulator is as follows:

[0055]

[0056] In the formula, v e ,ω e These are the terminal linear velocity and the terminal angular velocity, respectively. For active joint velocity;

[0057] The expression for the active joint velocity is obtained by utilizing the kinematic coupling relationship of the highly underactuated space manipulator:

[0058]

[0059] In the formula, Indicates the pseudo-inverse of a matrix;

[0060] The trajectory optimization objective function of the highly underactuated space manipulator is incorporated into the expression for the active joint velocity using the gradient projection method:

[0061]

[0062] In the formula, β is the optimization coefficient, and I is the identity matrix. Optimize the gradient of the objective function for the trajectory;

[0063] When performing trajectory planning, given the end velocity By using the above-mentioned expression for the active joint velocity, which introduces a trajectory optimization objective function, to solve for the active joint velocity, trajectory optimization of a highly underactuated space robot arm can be achieved.

[0064] Based on the method provided in the embodiments of the present invention, a simulation experiment was conducted on the trajectory optimization method for a highly underactuated spatial manipulator.

[0065] Please refer to Figure 2 This is a schematic diagram of a seven-degree-of-freedom spatial robotic arm model provided in an embodiment of the present invention. Its DH parameters are shown in Table 1, and its dynamic parameters are shown in Table 2.

[0066] Table 1 DH Parameters of Space Robotic Arm

[0067]

[0068] Table 2 Dynamic parameters of the space robotic arm

[0069]

[0070] Please refer to Figure 3 , Figure 4 The figures show a comparison of the directional dynamics operability index and the dynamics condition number index of a highly underactuated space manipulator. Assuming joint 1 experiences a free swing failure, a straight path planning task is performed, with an initial configuration of [-50, -170, 150, -60, 130, 170, 10]° and a target pose of [6.5m, 3.84m, 5.4m, -1rad, -0.3rad, -2.4rad]. The optimization group employs the trajectory optimization method proposed in this invention, with α = 5, r... max =350, the control group does not undergo trajectory optimization, and the changes in directional dynamics operability and dynamics condition number during task execution can be obtained respectively. From Figure 2 It can be seen that the directional dynamics operability of the optimized group is better than that of the control group, indicating that the optimized group has stronger end-effector acceleration capability along the task direction. Figure 3 It can be seen that the number of kinetic conditions in the optimized group is less than that in the control group and less than r. max =350, indicating that the optimization group has good isotropic acceleration capability at the end of the curve, and the acceleration capability in other directions is not too weak. Please refer to... Figure 5 The figure shows a comparison of the joint angular velocities of the high-underactuated space manipulator. The joint angular velocity curves of the optimized group and the control group do not overlap, indicating that the improved trajectory optimization method for the high-underactuated space manipulator has played a role.

[0071] The trajectory optimization of a highly underactuated space robot arm was achieved using the method described above in the embodiments of the present invention.

[0072] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0073] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A trajectory optimization method for a highly underactuated spatial robotic arm, characterized in that, The method includes: Based on the coupling relationship between the active joint torque and the end-effector acceleration of a highly underactuated space manipulator, the directional dynamics operability and dynamic condition number indices of the highly underactuated space manipulator are constructed. Based on the directional dynamics operability and dynamics condition number indices of the high underactuated space manipulator, a trajectory optimization objective function for the high underactuated space manipulator is constructed. Based on the kinematic coupling relationship of the high-underactuated space manipulator and the trajectory optimization objective function of the high-underactuated space manipulator, the trajectory of the high-underactuated space manipulator is optimized using the gradient projection method. Based on the coupling relationship between the active joint torque and the end effector acceleration of the highly underactuated space manipulator, the directional dynamics operability and dynamic condition number indices of the highly underactuated space manipulator are constructed, including: The coupling relationship between the active joint torque and the end effector acceleration of a high-degree-of-freedom underactuated space manipulator is as follows: In the formula, For terminal acceleration, To characterize the coupled inertia matrix that maps active joint torque to end-effector acceleration, The number of active joints. The Jacobian matrix is ​​the mapping of the active joint to the end-effector velocity. This represents the self-coupled inertial matrix of active joint acceleration and torque. For active joint torque, This is a nonlinear term representing the coupling relationship between the active joint torque and the end-effector acceleration. Based on the coupled inertia matrix mapping the active joint torque to the end-effector acceleration in the above formula. The directional dynamic maneuverability and dynamic condition number indices of the highly underactuated space manipulator are as follows: In the formula, For directional dynamics operability, For the dynamic condition number, Let be the unit vector along the mission direction. This is the torque normalization matrix. Represents a diagonal matrix. for The maximum allowable torque of the joint They are respectively The maximum and minimum singular values.

2. The method according to claim 1, characterized in that, Based on the directional dynamics maneuverability and dynamics condition number indices of the highly underactuated space manipulator, a trajectory optimization objective function for the highly underactuated space manipulator is constructed, including: Based on the directional dynamics maneuverability and dynamics condition number indices of the highly underactuated space manipulator, the trajectory optimization objective function of the highly underactuated space manipulator is obtained as follows: In the formula, It is a constant. It is the set threshold for the number of dynamic conditions. For directional dynamics operability, is the dynamic condition number.

3. The method according to claim 1, characterized in that, Based on the kinematic coupling relationship of the highly underactuated space manipulator and its trajectory optimization objective function, the trajectory of the highly underactuated space manipulator is optimized using the gradient projection method, including: The kinematic coupling relationship of the highly underactuated space manipulator is as follows: In the formula, These are the terminal linear velocity and the terminal angular velocity, respectively. For active joint velocity; The expression for the active joint velocity is obtained by utilizing the kinematic coupling relationship of the highly underactuated space manipulator: In the formula, Indicates the pseudo-inverse of a matrix; By incorporating the trajectory optimization objective function of the highly underactuated spatial manipulator into the expression for the active joint velocity using the gradient projection method, we can obtain: In the formula, To optimize the coefficients, It is the identity matrix. Optimize the gradient of the objective function for the trajectory; When performing trajectory planning, given the end velocity By using the above-mentioned expression for the active joint velocity, which introduces a trajectory optimization objective function, to solve for the active joint velocity, the trajectory optimization of a highly underactuated space robot arm can be achieved.

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