A method for planning an energy-optimal trajectory of a panel installation robot

Abstract

This invention presents an energy-optimal trajectory planning method for a sheet metal assembly robot. First, the gripping and mounting points in the robot's workspace are converted into points in Cartesian space, and interpolation is performed between the gripping and mounting points. Then, the inverse kinematics of the robot is solved, and the solution is optimized as an individual component of a swarm intelligence algorithm to obtain the angles of each joint at each interpolation point. A quintic B-spline curve is used to fit all interpolation points in the joint space, and the derivative of the fitted curve is obtained to obtain the angular velocity and angular acceleration of each joint. Finally, an objective function for the overall energy consumption of the robot is constructed, using the jump time between two adjacent interpolation points as the optimization object, and the objective function for the overall energy consumption of each robot is optimized and solved. A quintic B-spline curve is used to fit the interpolation points to obtain the energy-optimal motion trajectory. This method selects the optimal solution based on the energy-optimal joint motion, and the energy consumption modeling process considers the work done by the drive load, joint friction losses, and joint motor heat losses.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of industrial robot trajectory planning, and particularly relates to a plate installation robot energy-optimal trajectory planning method. BACKGROUND

[0002] The building robot is a multi-joint manipulator or a multi-degree-of-freedom mechanical device for the building field, and can complete various tasks such as surveying, building, maintaining and demolishing. The plate installation robot is an important branch of the building robot, and is widely used in building glass, curtain wall, ceiling and other scenes. The plate installation robot has replaced manual installation of the plate, avoided the disadvantages of manual installation, and improved installation efficiency and precision.

[0003] The trajectory planning is to plan a motion trajectory according to the task requirements, and is an important prerequisite for the robot to complete the task as expected. The trajectory planning of the plate installation robot is usually to optimize the joint space trajectory according to some key points in the plate installation process. In the process of executing the installation task by the robot, the energy utilization is unreasonable, resulting in a large amount of energy waste. Reducing the energy consumption of the motion trajectory can reduce the power consumption of the robot, and has important significance for reducing the installation cost.

[0004] At present, in the robot trajectory planning based on energy consumption, the square of the robot joint torque is usually taken as the basis, that is, only the energy consumption of the driving load work is considered. Since the plate installation robot belongs to a heavy robot, the joint friction and motor heating loss are large during the plate carrying process, and this part of the energy consumption cannot be ignored. In addition, when the trajectory is optimized to save energy, only the joint space trajectory is usually planned, resulting in that the trajectory in the Cartesian space is completely unpredictable. When the joint space key points are solved according to the Cartesian space key points, the solution is selected by taking the square sum of the angles of each joint as the minimum. Since the influence of the same angle of each joint on the energy consumption is different during the plate carrying process of the plate installation robot, this way of selecting the key point ignores the influence of the rotation of different joints on the energy consumption. SUMMARY

[0005] In view of the deficiencies of the prior art, the technical problem to be solved by the application is to provide a plate installation robot energy-optimal trajectory planning method.

[0006] The technical solution adopted by the application to solve the technical problem is as follows:

[0007] A plate installation robot energy-optimal trajectory planning method, characterized by comprising the following steps:

[0008] Step S1, converting the grasping point and mounting point in the robot workspace into points in the Cartesian space, interpolating between the grasping point and the mounting point;

[0009] Step S2, solving the inverse kinematics of the robot, optimizing the solution as an individual of the swarm intelligence algorithm to obtain the angles of each joint at each interpolation point; fitting all interpolation points in the joint space using a quintic B-spline curve, and deriving the fitted curve to obtain the angular velocity and angular acceleration of each joint of the robot;

[0010] Step S3, solving the motor driving torque of each joint of the robot;

[0011]

[0012]

[0013] In the formula, represents the friction torque of joint i, respectively represent the viscous friction torque and the Coulomb friction torque at joint i, respectively represent the angular velocity and the angular acceleration of joint i, represents the motor driving torque of joint i, τ i represents the driving torque of joint i;

[0014] Step S4, constructing the objective function of the overall energy consumption of the robot, represented as:

[0015]

[0016]

[0017] In the formula, W t represents the overall energy consumption of the robot, j represents the interpolation point number, represents the energy consumption of joint i, represents the motor energy consumption at joint i, represents the motor heat loss at joint i, K i represents the torque constant of the motor at joint i, R i represents the equivalent resistance of the motor at joint i, t0 and t1 represent the starting time and the cutoff time of the motor operation, respectively;

[0018] Step S5, parameterizing the time points of the quintic B-spline curve, taking the jump time between two adjacent interpolation points as the optimization object, and optimizing and solving with the overall energy consumption of the robot as the objective function; fitting the interpolation points using the quintic B-spline curve to obtain the optimal energy consumption motion trajectory.

[0019] Further, in step S2, the fitness function of the swarm intelligence algorithm is represented as:

[0020]

[0021] In the formula, (x,y,z) represents the endpoint of the trajectory obtained by the swarm intelligence algorithm, (x * ,y * ,z * ) represents the set trajectory endpoint, λ represents the penalty factor, and θ i This represents the angle of joint i when the robot's end effector reaches the end point of its trajectory. w represents the initial angle of joint i. i represents the energy consumption weight of joint i, and n represents the number of joints in the robot.

[0022] Furthermore, in step S2, the average value of the torque of each joint is obtained by conducting multiple experiments on the same motion trajectory; all average values ​​are normalized to obtain the energy consumption weight of each joint.

[0023] Compared with the prior art, the beneficial effects of the present invention are:

[0024] 1. Since there are multiple solutions when transforming Cartesian space to joint space for inverse kinematics of a robot, this invention selects the optimal solution based on the optimal energy consumption of joint movement, so that the joints near the base move as little as possible, thereby reducing energy consumption.

[0025] 2. Due to the large load of the sheet metal installation robot, the energy consumption from joint friction and joint motor heat also accounts for a large proportion. Therefore, the joint energy consumption of this invention includes three parts: the work done by the driving load, the joint friction loss, and the joint motor heat loss. The simulated annealing algorithm is used to optimize the objective function, avoid getting trapped in local optima, and ensure the optimal energy consumption of the entire trajectory. Attached Figure Description

[0026] Figure 1 This is an overall flowchart of the present invention;

[0027] Figure 2 This is a flowchart of the particle swarm optimization algorithm of the present invention;

[0028] Figure 3 This is a flowchart of the simulated annealing algorithm of the present invention;

[0029] Figure 4 This is a curve showing the angle of the second joint of the sheet metal mounting robot adjacent to the base of the present invention. Detailed Implementation

[0030] Specific embodiments are given below with reference to the accompanying drawings. These specific embodiments are only used to describe the technical solutions of the present invention in detail, but are not intended to limit the scope of protection of this application.

[0031] The application discloses a kind of plate installation robot energy optimal trajectory planning method (referred to as method, see Figures 1-4 ), comprising the following steps:

[0032] Step S1, the grabbing point and the installation point in the plate installation robot workspace are converted into points in Cartesian space, interpolation is carried out between the grabbing point and the installation point in Cartesian space, and the number of interpolation points is v is the moving speed of the end of the mechanical arm, Δt is the interpolation period, and l is the interpolation distance, i.e. the straight-line distance between the grabbing point and the installation point;

[0033] Step S2, inverse solution is solved for the kinematics of the plate installation robot, the solution is used as an individual of a swarm intelligence algorithm, optimization is carried out by the swarm intelligence algorithm, and the angle of each joint at each interpolation point is obtained;Swarm intelligence algorithm is one of particle swarm algorithm, ant colony algorithm and the like, and particle swarm algorithm is used in the embodiment, and its flow is referred to in Figure 2 ;

[0034] Since the load of the plate installation robot is large, the difference between the torques of each joint is large during the plate carrying process, the energy consumption of different joints is different when rotating the same angle, and therefore the energy consumption function of the joint movement of the robot is designed as

[0035]

[0036] In the formula, θ i represents the angle of joint i when the end of the robot moves to the trajectory end point, represents the initial angle of joint i, and n represents the number of joints of the robot;w i represents the energy consumption weight of joint i, according to multiple experiments on the same movement trajectory, the average value of the torque of each joint is obtained, and all average values are normalized to obtain the energy consumption weight of each joint;

[0037] In the inverse solution process, the trajectory end point must meet the position requirement, and therefore the fitness function of the swarm intelligence algorithm is represented as

[0038]

[0039] In the formula, (x, y, z) represents the trajectory end point obtained by the swarm intelligence algorithm, (x * ,y * ,z * ) represents the set trajectory end point, and λ represents a penalty factor;

[0040] In the joint space of the robot, all interpolation points are fitted by using a quintic B-spline curve, the fitted curve is differentiated to obtain the angular velocity and angular acceleration of each joint of the robot;

[0041] Step S3, solving the motor driving torque of each joint of the robot;

[0042] According to the Lagrange dynamics equation and the robot rigid body kinematics equation, the driving torque matrix τ of the joint motion of the robot is expressed as:

[0043]

[0044] wherein D(θ) represents a joint inertia matrix, G(θ) represents a joint gravity parameter matrix, θ = [θ1, θ2, …, θ i ,…,θ n ] represents a joint angle matrix, ω(θ) represents a joint angular velocity matrix, α(θ) represents a joint angular acceleration matrix, respectively represent the angular velocity and angular acceleration of joint i;

[0045] A friction model of Coulomb friction and viscous friction is used to analyze the joint motion, and the friction torque of each joint is solved;

[0046]

[0047] wherein, τf,i represents the friction torque of joint i, respectively represent the viscous friction torque and Coulomb friction torque at joint i;

[0048] According to the Lagrange dynamics formula, the motor driving torque of each joint is obtained from the friction torque of the joint;

[0049]

[0050] wherein, τm,i represents the motor driving torque of joint i, τ i ∈τ represents the driving torque of joint i;

[0051] Step S4, the energy consumption of the joint of the robot is mainly divided into three parts, which are the joint motor heat loss, the joint friction loss and the motor driving load work;

[0052] The first part of the joint motor heat loss is expressed according to the Joule-Lenz law as:

[0053]

[0054] wherein, Im,i represents the motor heat loss at joint i, I i 、R i respectively represent the effective current and equivalent resistance of the motor at joint i, Ki represents the torque constant of the motor at joint i;

[0055] The second part of the joint friction loss refers to step S4;

[0056] The third part is the motor driving load work, the motor driving torque, according to the motor work is equal to the integral of the motor output power on the motor running time, combined with the joint angular velocity in the robot motion process, the motor energy consumption model is expressed as:

[0057]

[0058] In the formula, represents the motor energy consumption at joint i, t0, t1 respectively represent the starting time and the cutoff time of the motor running, P i represents the power of the motor at joint i;

[0059] The above three parts of the energy consumption are integrated to obtain the energy consumption function of each joint of the robot:

[0060]

[0061] In the formula, represents the energy consumption of joint i;

[0062] The above energy consumption analysis is for the energy consumption of the robot in the process of jumping between any two adjacent interpolation points, so the target function of the overall energy consumption of the robot is:

[0063]

[0064] In the formula, W t represents the overall energy consumption of the robot, j represents the interpolation point number;

[0065] Step S5, parameterize the time points of the quintic B-spline curve, expressed as [u0, u1], …, [u j-1 , j , N-1 , N , j , j-1 respectively represent the time corresponding to the jth and j-1th points; take the jumping time between the adjacent two interpolation points as the optimization object, solve the target function by using the simulated annealing algorithm, and then optimize the position of each interpolation point; use the quintic B-spline curve to fit the interpolation points to obtain the motion trajectory with optimal energy consumption;

[0066] The specific process of the simulated annealing algorithm is as follows:

[0067] First, set the initial temperature T0 as 100, start cooling from the initial temperature, the temperature T after cooling T=alphaT0, the cooling rate alpha is set as 0.95, the iteration number at each generation temperature is set as 200, and each jump time is taken as an initial solution;

[0068] Then, Metropolis criterion is used for sampling, the new solution u' is analyzed according to the size of the acceptance probability, the current fitness function f(u') is obtained according to the given objective function f(u), when the fitness increment Delta f(u)=f(u')-f(u) is greater than or equal to 0, the iteration process is accepted, otherwise, the new solution is accepted with a probability of exp(-Delta f(u) / T) when the control temperature is close to 0, Metropolis criterion is repeatedly used, Metropolis criterion is expressed as:

[0069]

[0070] In the above formula, T represents the current temperature, u represents the solution at the current temperature, u' represents the solution after one iteration at the current temperature, and f(u) represents the function of the problem to be optimized.

[0071] When the iteration number reaches the maximum number, the next generation cooling is carried out, when the simulated annealing does not reach the cooling state finally, the cooling operation is needed, when the cooling state is reached, the five B-spline curves under the lowest energy consumption are inversely solved according to the time between the interpolation points output by the algorithm, that is, the optimal energy consumption trajectory.

[0072] The simulated annealing algorithm is used to solve the objective function, which mainly achieves the traversal of all possible optimal values of the function by cooling the initial value T=alphaT0, and due to the use of Metropolis criterion, the simulated annealing algorithm is not easy to fall into the local optimal condition like the particle swarm algorithm, there is a small probability of entering a worse direction each time to get out of the local optimal condition.

[0073] The unmentioned part of the application is applicable to the prior art.

Claims

1. A method for optimal energy consumption trajectory planning of a panel installation robot, characterized in that, The method comprises the following steps: Step S1, converting the grasping point and the mounting point in the robot workspace into points in the Cartesian space, and interpolating between the grasping point and the mounting point; Step S2, solving the inverse kinematics of the robot, taking the solution as an individual of a swarm intelligence algorithm, and optimizing the individual to obtain the angles of each joint at each interpolation point; fitting all interpolation points in the joint space by using a quintic B-spline curve, deriving the fitted curve to obtain the angular velocity and angular acceleration of each joint of the robot; Step S3, solving the motor driving torque of each joint of the robot; wherein, denotes the friction torque of joint i, denotes the viscous and Coulomb friction torque at joint i, respectively, denotes the angular velocity and angular acceleration of joint i, respectively, denotes the motor driving torque of joint i, τ i denotes the driving torque of joint i; Step S4, constructing a target function of the overall energy consumption of the robot, and representing the target function as: wherein W t represents the overall energy consumption of the robot, j represents the interpolation point number, represents the energy consumption of joint i, represents the motor energy consumption at joint i, represents the motor heat loss at joint i, K i represents the torque constant of the motor at joint i, R i represents the equivalent resistance of the motor at joint i, t0 and t1 represent the start time and the end time of the motor operation, respectively; Step S5, parameterizing the time points of the quintic B-spline curve, taking the jump time between two adjacent interpolation points as an optimization object, and optimizing and solving the overall energy consumption of the robot as a target function; fitting the interpolation points by using a quintic B-spline curve to obtain an optimal energy consumption motion trajectory.

2. The method of claim 1, wherein, In step S2, the fitness function of the swarm intelligence algorithm is represented as: where (x, y, z) represents the trajectory end point obtained by the swarm intelligence algorithm, (x * , y * , z * ) represents the set trajectory end point, λ represents the penalty factor, θ i represents the angle of joint i when the robot end is moved to the trajectory end point, represents the initial angle of joint i, w i represents the energy consumption weight of joint i, and n represents the number of joints of the robot.

3. The method of claim 2, wherein the method further comprises: In step S2, according to multiple experiments on the same motion trajectory, the average values of the joint torques are obtained; and the average values are normalized to obtain the energy consumption weights of the joints.

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