CN108621165B - Optimal trajectory planning method for industrial robot dynamics performance in obstacle environment - Google Patents
Optimal trajectory planning method for industrial robot dynamics performance in obstacle environment Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
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- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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- G05B2219/40—Robotics, robotics mapping to robotics vision
- G05B2219/40519—Motion, trajectory planning
Abstract
The invention discloses a method for planning an optimal trajectory of the dynamic performance of an industrial robot in an obstacle environment, which comprises the following steps: s1, inputting an environment map and robot body information through an input layer, and outputting space-time information of a track through an output layer so as to drive the robot to complete a given task; s2, obtaining a collision-free path through a C space efficient RRT-Connect algorithm, and then pruning and smoothing the path; and S3, optimizing the path planned in the second stage into a dynamic executable track through a dynamic optimizer. In a complex obstacle environment, the trajectory planning method has high efficiency and practicability.
Description
Technical Field
The invention relates to the field of robot trajectory planning, in particular to a method for planning an optimal trajectory of an industrial robot in an obstacle environment.
Background
The planning of the dynamic trajectory of an industrial robot in an obstacle environment is complex because, when the robot completes a task, the robot body is required not to collide or penetrate with the outside world, but also to satisfy the kinematics/dynamic constraint of the intrinsic system of the robot.
At present, a static dynamics planning method is mainly adopted to solve the problem of trajectory planning under the conditions of kinematics, incompleteness and dynamics constraint, and two types of planning methods are available: one is decoupling and separating path planning from dynamic constraint, namely, path planning is carried out according to performance indexes of paths without considering dynamic factors in the traditional path planning. And after the path planning is finished, performing trajectory planning under the dynamic constraint, and finally planning an optimal trajectory. The method is widely applied to the fields of incomplete systems and humanoid robots; the second category is that path planning and dynamics constraint are considered together, at this time, robot trajectory planning becomes the problem of solving extreme values about the functional of the trajectory, namely, the variable is the trajectory, the objective function and the constraint function are the functional of the trajectory, and under complex obstacles, trajectory planning becomes extremely complex, and due to the constraint action of the obstacle, the optimal value has wide local multi-solution.
Disclosure of Invention
In order to solve the problems, the invention provides a method for planning the optimal trajectory of the dynamic performance of the industrial robot in the obstacle environment.
In order to achieve the purpose, the invention adopts the technical scheme that:
the optimal trajectory planning method for the dynamic performance of the industrial robot in the obstacle environment comprises the following steps:
s1, inputting an environment map and robot body information through an input layer, and outputting space-time information of a track through an output layer so as to drive the robot to complete a given task;
s2, obtaining a collision-free path through a C space efficient RRT-Connect algorithm, and then pruning and smoothing the path;
and S3, optimizing the path planned in the second stage into a dynamic executable track through a dynamic optimizer.
Further, the environment map is rapidly acquired through a laser radar scanning technology.
Further, the step S2 completes the trimming operation of the path by:
for a sequence of sampling nodes path Q ═ Q (Q)1，q2，…，qk) If q isi-1And q isi+1Can be directly communicated with each other by deleting the position and pose point coordinates qiCutting a short path;
for the poses between pose points, calculating intermediate pose points through linear interpolation, detecting each intermediate pose point by adopting a collision detection function, and finally ensuring that all the intermediate pose points belong to a barrier-free configuration space Cfree。
Further, the path smoothing operation in step S2 adopts a B-spline fitting pose point sequence, if it is detected that the fitted trajectory collides, the path sampling is returned and the sampling operation is continued, and if it is detected that the smoothed path does not collide, the smoothing operation is successful, and the dynamic planning can be directly performed.
Further, the step S3 includes the following steps:
s31, the trajectory Q of the robot is assumed to be (Q)1，q2，…，qkT), wherein qkDefining a path node and T as a track timeObjective function c (q):
in the formula, the first term is the square sum of joint moments and represents the track energy consumption; the second term is the sum of the squares of the joint jerks, representing the smoothness of the trajectory; the third term represents track mileage time, and the weighted sum of the three terms is used as a target function, wherein tau is a joint torque vector and can be obtained by calculation through a robot inverse dynamics formula;
is a joint jerk vector, T is a track time variable, and is directly obtained through parameterization track
And the value of T, Ke、Kj、KtA weight factor for each objective function;
s32, obtaining the following optimization problem according to the formula of the objective function (1):
min C(Q) (2)
the formula (2) is a target function, the formula (3) is a constraint function, and the constraint functions are joint speed, joint acceleration and joint torque in sequence;
and S33, solving the constraint function by an SQP algorithm to obtain the optimal track.
Compared with the prior art, the invention has the following beneficial effects:
establishing a path pruning algorithm and a path smoothing algorithm by adopting an RRT-Connect algorithm; path planning and dynamics planning are integrated together, and an optimal dynamic track of the industrial robot is obtained under the working condition of a complex obstacle; compared with the traditional parameter track optimization method, the method has obvious advantages in track planning efficiency and quality. The method has stronger guiding significance and reference value for the dynamics track planning under the complex environment of the industrial robot.
Drawings
Fig. 1 is a schematic diagram of a hierarchical plan.
Fig. 2 is a schematic diagram of path optimization.
Fig. 3 is a diagram illustrating SQP algorithm paths.
FIG. 4 is a diagram illustrating the RRT-Connect algorithm path.
Fig. 5 is a schematic diagram of an integrated trajectory planning path.
Fig. 6 is a plot of planning time versus time.
Fig. 7 is a trace time comparison graph.
FIG. 8 is a graph comparing joint velocity:
in the figure: (a) is the velocity profile of the joint 1; (b) is the velocity profile of the joint 2; (c) is the velocity profile of the joint 3; (d) the velocity profile of the joint 4.
Fig. 9 is a diagram comparing joint jerk:
in the figure: (a) is a joint jerk map of the joint 1; (b) is a joint jump map of the joint 2, and (c) is a joint jump map of the joint 3; (d) is a map of the joint jerk of the joint 4.
Fig. 10 is a joint torque comparison chart.
In the figure: (a) is a joint torque diagram of the joint 1; (b) is a joint torque chart of the joint 2; (c) is a joint torque diagram of the joint 3; (d) a torque profile of 4.
Detailed Description
In order that the objects and advantages of the invention will be more clearly understood, the invention is further described in detail below with reference to examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The embodiment of the invention provides a general and practical extremely strong obstacle track planning frame which is divided into three layers, wherein the first layer is an information input and output layer, the input layer mainly provides a known environment map and robot body information, and the environment map is quickly obtained by a laser radar scanning technology. The output layer outputs the space-time information of the track so as to drive the robot to complete a given task; the second layer and the third layer are respectively the trajectory planning for the geometric space and the energy space, and the two stages are the basic parts of the whole trajectory planning. In the second stage, as shown in fig. 1, a path between fixed poses is searched in a configuration space, and path smoothness and efficiency are enhanced through path pruning and smoothing operations; and in the third stage, planning a dynamic optimal track according to the dynamic characteristic function. Due to dynamic planning, collision between the path and the obstacle may occur, and the path after dynamic planning needs to return to the first stage again to perform collision detection so as to ensure the safety of the path. These two processes are repeated until a kinetically optimal trajectory is obtained. The following mainly describes a specific scheme of path planning and dynamic trajectory planning.
In the embodiment, the RRT-Connect algorithm is adopted for path planning, and the algorithm is integrated into an industrial robot dynamics trajectory planning algorithm. Pseudo code of RRT-Connect algorithm is shown in Table 1, and is initialized first, from qint、qgoaConstruct two trees T respectivelyaAnd TbThen, entering an iterative process of double-tree alternate expansion, wherein each step of iteration needs to complete the following extended expansion step; calling a subprogram RandomConfig (), and uniformly and randomly selecting a configuration point q in a C spacerandInvoking Extend algorithm to make TaDirection q of the flowrandExtending a step length of lambda to generate a new node qnewThen call Connect algorithm to let TbDirection q of the flownewExtending a plurality of λ steps; if T isbNode(s) and qnewCan be completely connected, then return to the solution path (T)a，Tb) (ii) a Otherwise, calling the SWAP subroutine to SWAP two trees TaAnd TbAnd re-executing the process until the algorithm returns a communication path or reaches the upper limit k of the iteration times, and exiting.
TABLE 1 RRT-Connect Algorithm
In the embodiment, the path pruning and smoothing operations are completed through the following path pruning algorithm and path smoothing algorithm, so that a basis is provided for dynamic trajectory planning.
Path pruning
For a sequence of sampling nodes path Q ═ Q (Q)1，q2，…，qk) Applying the pruning algorithm prune (Q), if qi-1And q isi+1Can be directly communicated with each other, the position and pose point coordinate q is deletediThe path is pruned, which in turn prunes the path. For the spaced pose points, detecting each pose point by linearly interpolating the intermediate pose points and sequentially adopting a collision detection function, and finally ensuring that all the pose points belong to Cfree(unobstructed conformational space).
As shown in table 2, the pruning algorithm prune (Q) first inputs the trajectory Q, then detects whether there is a collision between any two pose points in a successive loop, and if no collision is detected, deletes the pose point sandwiched between any two pose points, and directly connects the two pose points, so as to achieve the purpose of deleting the path redundant pose points. The path pruning algorithm based on collision detection is summarized in table 2, and the result is shown in fig. 2(b) by a thick line, and compared with the break line before pruning, it can be found that the path efficiency after pruning is relatively high, and the path length is obviously reduced. After trimming, the path is shortened, but the efficiency is not high enough because the path is still broken, and therefore, the following path smoothing operation is required.
TABLE 2 Path pruning Algorithm
Smooth path
A spline curve is generally adopted for fitting the trimmed pose points in the smooth path, a B-spline is adopted for fitting a pose point sequence, however, if collision of the fitted track is detected, path sampling is required to be returned, sampling operation is continued, and if no collision of the smooth path is detected, the smooth operation is successful, and dynamic planning can be directly carried out. The smoothing function smooth (q) is shown in table 3, and the result of the smoothing operation is shown by the solid line in fig. 2(c), and it can be seen that the trajectory efficiency is greatly improved after the path optimization.
TABLE 3 Path smoothing Algorithm
Fig. 2 illustrates an example of path optimization, where a rectangle represents a high-dimensional C space, and a solid line in fig. 2(a) is a path after RRT-Connect sampling planning, it can be seen that the efficiency of this path is not high, and the path meanders in an obstacle space, and a pre-trimming algorithm is adopted, and the path after trimming, as shown in fig. 2(b) by a thick line, is compared with a broken line before trimming, it can be found that the efficiency of the path after trimming is relatively high, and the path length is significantly reduced. Fig. 2(c) shows the path after smoothing, which has a smaller curvature and higher efficiency than the break line before smoothing, and is suitable for robot control. And then, on the basis of the second section, planning a dynamic track to enable the track to better accord with the driving characteristics of the physical equipment of the industrial robot.
Dynamics planning system
Suppose that the trajectory Q of the robot is (Q)1，q2，…，qk，T)(qkIs a path node, T is a trajectory time), an objective function c (q) is defined:
the first term in the formula (1) is the square sum of joint moments and represents the track energy consumption; the second term is the sum of the squares of the joint jerks, representing the smoothness of the trajectory; and the third term represents track mileage time, and the weighted sum of the three terms is used as an objective function, wherein tau is a joint torque vector and can be calculated through a robot inverse dynamics formula.
For jumping of jointsVector, T is track time variable, and is directly obtained by parameterizing track
And the value of T, Ke、Kj、KtFor the weight factors of each objective function, the following optimization problem can be written according to the objective function (1) formula:
min C(Q) (2)
the above equation (2) is an objective function, and the equation (3) is a constraint function, which is sequentially a joint velocity, a joint acceleration and a joint torque constraint. The above optimization problem is typically a non-linear optimization problem. In consideration of the large scale and complexity of the problems in practical application, the method adopts the SQP algorithm with higher calculation efficiency to solve the constraint optimization problem, and solves the dynamic performance track optimization problem in an off-line calculation mode. The optimal trajectory is obtained through the path and dynamics integrated planning system of the industrial robot, and the method provided by the invention is verified through the following experiments.
Experimental study
The experiment is established by taking industrial feeding and discharging and forging industry as backgrounds and specially aiming at grabbing operation. Grab object recognition and target recognition selectable specialized vision development companies (Scape Technologies A/S)3) The eye system provided is characterized in that a three-dimensional grid scanner fixed on a tool coordinate system is developed, the scanner provides dense point clouds, obstacle point clouds can be found, and a document [14 ] is adopted]The method for constructing the polyhedron through the point cloud comprises the steps of constructing a simplified geometric body of the obstacle, and enveloping the simplified aggregate with a high-order surface or matching a geometric model so as to achieve the purpose of reducing obstacle avoidance calculation amount. And path planning, collision detection and trajectory planning are carried out, and the integrated planning system provided by the invention is adopted to carry out off-line planning to generate the robot trajectory.
The experimental robot adopts a domestic China digital robot, and the model of a controller of the experimental robot is as follows: MC800(HNC), which communicates with external computers using industrial ethernet. The robot is equipped with a suction cup and a pneumatic gripper to grasp the object. Target recognition and planning software, on an external computer, configured to: a Pentium (R) G620 processor, a main frequency of 2.66Hz, a memory of 3.41GB, a Windows XP operating system and a single-thread programming realization adopted by trajectory planning.
In order to increase the efficiency of the collision detection algorithm, the barriers such as a desk, a box and the like adopt a hypersurface enveloping method, and a hypersurface equation is as follows:
Γ(x，y，z)：(x/ξ1)4+(y/ξ2)8+(z/ξ3)4-1 (4)
wherein ξ1、ξ2、ξ3Selecting proper coefficients for the coefficients of the hypersurface according to the size of the convex body, and meeting the condition of not colliding with the hypersurface as follows:
Γ(x，y，z)＞0 (5)
the six-degree-of-freedom industrial robot is used for taking out a workpiece from a box, bypassing obstacles such as a table and the like in the middle and finally putting the workpiece on a workbench to serve as a working target, and the algorithm designed by the invention is adopted for test verification. The path of the trajectory and the planning time are analyzed in comparison.
Track path versus time
Compared with the trajectory planning method, in the traditional teaching mode, the motion of the robot is essentially decided by the human brain, such as a collision detection and trajectory mode, although the reliability is high, the efficiency is low. The general grabbing operation process is as follows: after the target object is grabbed, the robot grabs the safe pose in the Cartesian space and moves linearly to the upper surface of the box, then a plurality of point-to-point linear motions are adopted to avoid collision, and finally the target pose moved by the robot is reached. Obviously, the efficiency is low because each line segment needs acceleration and deceleration. By adopting a nonlinear optimization penalty function, only the starting point pose, the end point pose and the barrier space position of the robot need to be given, and then optimization is carried out to obtain an optimal solution, so that the efficiency is higher than that of teaching, but the reliability is lower. By adopting the integrated planning method provided by the invention, tracks with higher efficiency and success rate can be obtained. Table 4 below shows the following three non-linear optimization algorithms: the traces planned by the SQP, PSO and GA algorithms are compared with the trace generated by the integrated planning method of the invention, the traces between 20 posture coordinates are respectively tested, and the test results are shown in Table 4.
TABLE 4 comparison of three traces
Tab.4 The comparison of three trajectory
As can be seen from Table 4, the method provided by the invention is superior to the other three algorithms in terms of average planning time, track mileage time, success rate and average path length. It is easy to find that the gradient optimization based SQP algorithm is superior to two evolution algorithms (PSO and GA) in planning speed and trajectory time, and the gradient optimization algorithm is faster than the population evolution algorithm in terms of algorithm itself, but the SQP algorithm needs a better initial value, and if the initial value is improper, the algorithm may fail.
Observing fig. 3, 4 and 5, it can be seen that in fig. 3, although a feasible solution is obtained by using the SQP algorithm of the nonlinear optimization technology, the efficiency of the path is not high, and the path is relatively tortuous, so that more time and control energy are consumed, in fig. 4 and 5, the path is obtained by using the method of the present invention, in fig. 4, although a communicated feasible path is obtained by sampling, the efficiency of the path is low, and after pruning, smoothing and dynamic optimization, the path is relatively smooth, and the pose distribution is relatively uniform.
The trajectory planning time is shown in fig. 6, 5 pose points are selected for comparison, and it can be seen that the method provided by the invention has the least time required for trajectory planning, the second time of the SQP algorithm and the most time consumed by PSO and GA. Therefore, the method provided by the invention has obvious advantages in planning time.
The track running time is as shown in fig. 7, 5 pose points are selected for comparison, and it can be seen that the track running time of the method provided by the invention is the minimum, and except the first pose point, the track time calculated by the SQP algorithm is similar to that of the method provided by the invention. At other pose points, the integrated planning scheme provided by the invention has the advantages that the track time is smaller than that of other three algorithms, the track time is shorter, and the efficiency of the robot for completing tasks is higher, so that the provided track planning algorithm has high efficiency, and the dynamics performance of the track is analyzed.
Through the above trajectory planning based on dynamics, a state curve of the industrial robot is obtained, and then the state characteristics of the robot in the operation process are analyzed.
Compared with the joint speed shown in fig. 8, in the same time, the speed curve extreme values adopting the planning algorithm of the invention are all smaller than the result obtained by the SQP algorithm optimization, and under the condition of obstacles, the speed change is more stable, which shows that the speed generated by the planning algorithm of the invention is more stable.
Compared with the joint jump degree shown in fig. 9, it can be easily found that, except for 3 joints, the jump degree values of other joints are reduced by a large margin by adopting a comprehensive planning method, and compared with an SQP algorithm, the jump degree is reduced by a large margin, the joint 2 is more obvious, and has a smaller jump degree value, which indicates that the acceleration change is smaller, thereby being beneficial to reducing the vibration of the robot and enabling the dynamic characteristic of the robot to be more stable.
Analyzing fig. 10, it can be seen that, compared to the SQP planning algorithm, with the integrated optimization algorithm of the present invention, the integrated planned torque is slightly greater than the SQP algorithm planned torque in the joint 1. The maximum amplitude of the torque obtained by the algorithm of the invention is far smaller than the torque planned by the SQP algorithm, which shows that the torque change is stable, the dynamic characteristic of the track is better, and the accurate control of the servo position is facilitated.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be construed as the protection scope of the present invention.
Claims (4)
1. The method for planning the optimal trajectory of the dynamic performance of the industrial robot in the obstacle environment is characterized by comprising the following steps of:
s1, inputting an environment map and robot body information through an input layer, and outputting space-time information of a track through an output layer so as to drive the robot to complete a given task;
s2, obtaining a collision-free path through a C space efficient RRT-Connect algorithm, and then pruning and smoothing the path;
s3, optimizing the path planned in the second stage into a dynamic executable track through a dynamic optimizer;
s31, the trajectory Q of the robot is assumed to be (Q)1，q2，…，qkT), wherein qkDefining an objective function C (Q) as a path node and T as a track time:
in the formula, the first term is the square sum of joint moments and represents the track energy consumption; the second term is the sum of the squares of the joint jerks, representing the smoothness of the trajectory; the third term represents track mileage time, and the weighted sum of the three terms is used as a target function, wherein tau is a joint torque vector and can be obtained by calculation through a robot inverse dynamics formula;
is a joint jerk vector, T is a track time variable, and is directly obtained through parameterization track
And the value of T, Ke、Kj、KtA weight factor for each objective function;
s32, obtaining the following optimization problem according to the formula of the objective function (1):
min C(Q) (2)
the formula (2) is a target function, the formula (3) is a constraint function, and the constraint functions are joint speed, joint acceleration and joint torque in sequence;
and S33, solving the constraint function by an SQP algorithm to obtain the optimal track.
2. The method for planning a trajectory for optimizing the dynamic performance of an industrial robot in a barrier environment according to claim 1, characterized in that the environment map is rapidly acquired by a laser radar scanning technique.
3. The method for planning a trajectory for optimizing the dynamic performance of an industrial robot in an obstacle environment according to claim 1, wherein said step S2 is performed by performing the following steps:
for a sequence of sampling nodes path Q ═ Q (Q)1，q2，…，qk) If q isi-1And q isi+1Can be directly communicated with each other by deleting the position and pose point coordinates qiCutting a short path;
for the poses between pose points, calculating intermediate pose points through linear interpolation, detecting each intermediate pose point by adopting a collision detection function, and finally ensuring that all the intermediate pose points belong to a barrier-free configuration space Cfree。
4. The method for planning a trajectory for optimizing the dynamic performance of an industrial robot in an obstacle environment according to claim 1, wherein the path smoothing operation in step S2 adopts a B-spline fitting pose point sequence, if it is detected that the fitted trajectory collides, the path sampling is returned, the sampling operation is continued, and if it is detected that the smoothed path does not collide, the smoothing operation is successful, and the dynamic planning can be directly performed.
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