CN110653818A - Inverse kinematics solving method for planar gas-driven soft mechanical arm - Google Patents

Inverse kinematics solving method for planar gas-driven soft mechanical arm Download PDF

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CN110653818A
CN110653818A CN201910878124.2A CN201910878124A CN110653818A CN 110653818 A CN110653818 A CN 110653818A CN 201910878124 A CN201910878124 A CN 201910878124A CN 110653818 A CN110653818 A CN 110653818A
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arm
mechanical arm
planar gas
space parameters
actuator
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CN110653818B (en
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王学谦
张志远
梁斌
王松涛
孟得山
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Shenzhen International Graduate School of Tsinghua University
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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
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1615—Programme controls characterised by special kind of manipulator, e.g. planar, scara, gantry, cantilever, space, closed chain, passive/active joints and tendon driven manipulators
    • B25J9/1625—Truss-manipulator for snake-like motion
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • 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

Abstract

The invention provides a planar gas drive soft mechanical arm inverse kinematics solving method, which comprises the following steps: sequentially confirming configuration space parameters of an arm section of the planar gas drive soft mechanical arm according to the target position, wherein the configuration space parameters comprise a bending angle and an arc length of the arm section, and the planar gas drive soft mechanical arm comprises at least one arm section; calculating actuator space parameters of an arm segment of the planar gas-driven soft mechanical arm based on the configuration space parameters, wherein the actuator space parameters comprise the length of each actuator of the arm segment; calculating drive space parameters of the arm segment based on the actuator space parameters, the drive space parameters including input air pressures to drive the respective actuators; updating the arm shape and the end coordinates of the arm section through a positive kinematics algorithm of the planar gas-drive soft mechanical arm; designing constraint conditions to accurately find a target position within a plurality of steps of iteration; the inverse kinematics has high precision and short calculation time to solve the requirement; the trajectory planning of the planar gas drive soft mechanical arm is quickly realized, and a plurality of target points are sequentially solved.

Description

Inverse kinematics solving method for planar gas-driven soft mechanical arm
Technical Field
The invention relates to the technical field of soft robots, in particular to a planar gas-driven soft mechanical arm inverse kinematics solving method.
Background
Correctly positioning and orienting a robot in three-dimensional (3D) space requires at least 6 degrees of freedom (DOF): 3 for determining position and 3 for determining direction. An ultra-redundant manipulator or soft-bodied robot has multiple degrees of freedom that are higher than the minimum number of degrees of freedom required to perform a particular task.
In recent years, soft robots have become a research focus in the field of robots. Compared with the traditional rigid robot, the soft robot can better avoid obstacles, and has strong fault tolerance, good flexibility and high energy efficiency. The soft robot has various applicable scenes, and is very suitable for operation in unstructured and space-limited environments, such as pipeline flaw detection, ruin rescue, space exploration and the like.
However, the flexibility of a soft robot often depends on its inherent structure. Therefore, they are difficult to model and difficult to control. In the case of the modularized pneumatic soft mechanical arm, the soft robot belongs to an under-actuated system, the Jacobian matrix of the soft robot is difficult to obtain, and various redundant solutions exist in the inverse kinematics of the soft robot, so that the optimal solution is difficult to obtain.
In order to solve the inverse kinematics problem of soft robots, the existing documents propose machine learning algorithms, real-time finite element methods, visual servo control, new optimization methods or closed methods, etc., which have the main disadvantage that the quality of the solution cannot be guaranteed, and the posture of the whole body or the end effector is not considered in the solution.
The Cyclic Coordinate Descent (CCD) algorithm, a derivative-free optimization algorithm, finds the local minimum of the objective function cyclically by using a line search in one coordinate direction of the current point in each iteration. Some authors have shown that under the assumption that the coordinates are minimized one by one, the method converges to minimize the function. However, the traditional CCD algorithm is only used for joint-driven rigid mechanical arms, and cannot be directly used for air-driven flexible mechanical arms with variable lengths.
The above background disclosure is only for the purpose of assisting understanding of the concept and technical solution of the present invention and does not necessarily belong to the prior art of the present patent application, and should not be used for evaluating the novelty and inventive step of the present application in the case that there is no clear evidence that the above content is disclosed at the filing date of the present patent application.
Disclosure of Invention
The invention provides a solving method for inverse kinematics of a planar gas-driven soft mechanical arm, aiming at solving the existing problems.
In order to solve the above problems, the technical solution adopted by the present invention is as follows:
a planar gas drive soft mechanical arm inverse kinematics solving method comprises the following steps: s1: sequentially confirming configuration space parameters of an arm section of the planar gas drive soft mechanical arm according to a target position, wherein the configuration space parameters comprise a bending angle and an arc length of the arm section, and the planar gas drive soft mechanical arm comprises at least one arm section; s2: calculating actuator space parameters for arm segments of the planar air-driven soft robotic arm based on the configuration space parameters, the actuator space parameters including a length of each actuator of the arm segments; s3: calculating drive space parameters for the arm segments based on the actuator space parameters, the drive space parameters including input air pressures to drive respective actuators; s4: updating the arm shape and the terminal coordinates of the arm section through a positive kinematic algorithm of the planar air-driven soft mechanical arm; s5: and designing a constraint condition.
Preferably, the step of obtaining configuration space parameters of the arm segment in the step S1 includes the following steps: s11: setting PcFor the position of the end of the forearm segment, PeFor the current end point position of the robot arm, PfCalculating to obtain a vector P for the position of the tail end point of the mechanical arm targetcPeAnd PcPfThe included angle alpha is the point PeIs bent to PcPfRequired bend angle on the link:
Figure BDA0002205009210000021
s12: the feasible distance d is selected within the range of the length variation of the actuator so that the point P after bending iseAnd point PfThe distance between them is minimal:
Figure BDA0002205009210000022
s13: calculating the bending angle of the arm section according to the included angle alpha:
Figure BDA0002205009210000023
wherein, theta1The bending angle corresponding to the previous arm shape; s14: sequentially calculating configuration space parameters of the arm section, a bending radius r and a central arc length s according to the distance d and the bending angle theta:
Figure BDA0002205009210000024
preferably, the formula of the actuator of the arm segment is:
Figure BDA0002205009210000025
wherein l1And l2The length of the actuators on both sides of the arm segment, respectively, and a is the mounting distance between the actuators.
Preferably, the drive space parameters of the arm segment are calculated by a least squares fitting experiment and from a functional relationship between the actuator length and the input air pressure level:
Figure BDA0002205009210000026
wherein, P1And P2Respectively, the magnitude of the input air pressure.
Preferably, the translation relationship between the base coordinate system { W } and the end coordinate system { O } of the planar gas drive robot is described by a homogeneous translation matrix,wherein R is a rotation matrix; pdIs a displacement vector, the final form of the homogeneous transformation matrix is:
Figure BDA0002205009210000032
wherein, θ is a bending angle of rotation around the Z axis, - Φ is a torsion angle of rotation around the Z axis, and Φ is a torsion angle of rotation around the Y axis, then the positive kinematic equation of the planar gas drive soft mechanical arm is expressed as:
Figure BDA0002205009210000033
and the positive kinematic equation is used for updating the arm shape of the plane air-driven soft mechanical arm.
Preferably, the constraint condition includes: limiting the selection range of the distance d according to the change range of the central arc length of the planar gas-driven soft mechanical arm, so that the length of the actuator obtained by each calculation always changes within an allowable range; assume that the length of the actuator ranges l1,l2∈[lmin,lmax]Then the following linear constraint can be designed:
Figure BDA0002205009210000035
if the distance D is within the limit range, the distance D is equal to the distance D; if the distance D is outside the limit range, the distance D is equal to the limit boundary value:
Figure BDA0002205009210000036
limiting the selection range of the bending angle theta according to the actual bending angle range of the planar gas-driven soft mechanical arm:
Figure BDA0002205009210000038
preferably, the constraint condition includes: introducing the parameter k reduces the magnitude of each calculation of the bending angle theta:wherein n is the total arm segment number of the planar gas drive soft mechanical arm, and i is the current calculated arm segment number.
Preferably by determining the target position PfAnd a straight line PcPeDetermines the sign of the angle θ increment:
preferably, the vector PcPeAnd PcPfWhen parallel, the configuration space parameter of the current arm segment is not changed, and the next arm segment is directly calculated; and if all the arm sections are singular, randomly selecting a bending angle theta to avoid initial singularity.
The invention also provides a computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of the above.
The invention has the beneficial effects that: the method is directly used for the gas-driven flexible mechanical arm with variable length, and configuration space parameters including the bending angle, the torsion angle and the arc length of an arm section can be calculated by designing constraint conditions; further calculating actuator space parameters and driving space parameters, and updating the arm shape and the terminal coordinates of the arm section through a positive kinematics algorithm of the planar gas-driven soft mechanical arm; by finding the target position accurately within several iterations; the algorithm meets the inverse kinematics solving requirements of higher precision and shorter calculation time; based on the algorithm, the trajectory planning of the planar gas drive soft mechanical arm can be rapidly realized, and a plurality of target points are sequentially solved.
Drawings
Fig. 1 is a schematic diagram of a method for solving inverse kinematics of a planar gas-driven soft mechanical arm according to an embodiment of the present invention.
Figure 2(a) is a schematic view of an initial configuration of a planar gas-driven soft robot according to an embodiment of the present invention.
FIG. 2(b) is a schematic view of a retracting planar gas-driven soft robot according to an embodiment of the present invention.
Figure 2(c) is a schematic view of a pure curved planar gas-driven soft robot according to an embodiment of the present invention.
Figure 2(d) is a schematic view of an elongated planar gas-driven soft robot according to an embodiment of the present invention.
Figure 3 is a schematic view of a planar gas-driven soft robot according to an embodiment of the present invention.
FIG. 4 is a mathematical model of a planar gas-driven soft robot according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of a method for obtaining configuration space parameters of the arm segment according to an embodiment of the present invention.
FIG. 6(a) is a schematic view of a planar air-driven soft robot arm before changing the shape of the end arm according to an embodiment of the present invention.
FIG. 6(b) is a schematic view of the contracted planar air-driven soft robot with its end arm shape changed according to the embodiment of the present invention.
Fig. 7 is a schematic diagram illustrating a calculation of a bending angle according to an embodiment of the present invention.
FIG. 8 is a flow chart illustrating a method for solving inverse kinematics of a planar gas-driven soft robotic arm according to an embodiment of the present invention.
FIG. 9 is a flow chart illustrating a method for solving inverse kinematics of a planar gas-driven soft robotic arm according to an embodiment of the present invention.
FIG. 10 is a schematic view of a single, inflatable elongate actuator in accordance with an embodiment of the present invention.
Figure 11 is a schematic view of a planar gas-driven soft robot according to an embodiment of the present invention.
Figure 12 is a schematic view of the working space of a five-segment planar gas-driven soft robot according to an embodiment of the present invention.
FIGS. 13(a) -13(d) are schematic diagrams illustrating the results of a five-segment planar gas-driven soft robot solution according to an embodiment of the present invention.
FIGS. 14(a) -14(d) are schematic diagrams illustrating the results of the solution for the five-segment planar gas-driven soft robot with constraints added in accordance with an embodiment of the present invention.
FIG. 15(a) is a diagram showing the result of the solution of the present invention applied to the central arc length contraction type soft mechanical arm.
FIG. 15(b) is a schematic diagram of the solution of the present invention applied to a central arc length invariant soft robotic arm.
Fig. 16(a) -16(b) are schematic diagrams of CCD algorithm solution results after adding an angle θ increment sign selection function in the embodiment of the present invention.
Fig. 17(a) is a schematic diagram of a solution result of the CCD algorithm in which the solution target position of the ten segments of soft mechanical arms is the origin of coordinates of the whole arm in the embodiment of the present invention.
Fig. 17(b) is a schematic diagram of a solution result of a CCD algorithm in which the solution target position of the thirty-segment soft mechanical arms is the origin of coordinates of the whole arm in the embodiment of the present invention.
Fig. 17(c) is a schematic diagram of the solution result of the CCD algorithm with the target position of the fifty segments of the soft mechanical arms as the origin of coordinates of the whole arm according to the embodiment of the present invention.
FIGS. 18(a) -18(d) are schematic diagrams illustrating the results of the trajectory planning for a five-segment soft robotic arm in accordance with embodiments of the present invention.
Wherein 1-first actuator, 2-second actuator, 3-center line, 4-installation distance between two actuators, 5-center arc length, 6-first arm section, 7-second arm section, 8-third arm section, 9-first arm shape, 10-second arm shape, 11-air pipe, 12-sealing joint, 13-air cavity, 14-elastic matrix, 15-fiber winding line, 16-first arm section, 17-second arm section, 18-first iteration, 19-second iteration.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects to be solved by the embodiments of the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and the embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
It will be understood that when an element is referred to as being "secured to" or "disposed on" another element, it can be directly on the other element or be indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or be indirectly connected to the other element. In addition, the connection may be for either a fixing function or a circuit connection function.
It is to be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in an orientation or positional relationship indicated in the drawings for convenience in describing the embodiments of the present invention and to simplify the description, and are not intended to indicate or imply that the referenced device or element must have a particular orientation, be constructed in a particular orientation, and be in any way limiting of the present invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the embodiments of the present invention, "a plurality" means two or more unless specifically limited otherwise.
Example 1
The traditional CCD algorithm is only used for a rigid mechanical arm driven by a joint and cannot be directly used for a soft mechanical arm driven by air and with a variable length. The main reason is that the configuration space parameters of the rigid mechanical arm are the rotation angle or the sliding length of each joint, and the configuration space parameters of the air-driven soft mechanical arm are the bending angle, the torsion angle and the arc length of each arm section.
As shown in fig. 1, the present invention provides a method for solving inverse kinematics of a planar gas-driven soft mechanical arm, which is characterized by comprising the following steps:
s1: sequentially confirming configuration space parameters of an arm section of the planar gas drive soft mechanical arm according to a target position, wherein the configuration space parameters comprise a bending angle and an arc length of the arm section, and the planar gas drive soft mechanical arm comprises at least one arm section;
s2: calculating actuator space parameters for arm segments of the planar air-driven soft robotic arm based on the configuration space parameters, the actuator space parameters including a length of each actuator of the arm segments;
s3: calculating drive space parameters for the arm segments based on the actuator space parameters, the drive space parameters including input air pressures to drive respective actuators;
s4: updating the arm shape and the terminal coordinates of the arm section through a positive kinematic algorithm of the planar air-driven soft mechanical arm;
s5: and designing a constraint condition.
As shown in fig. 2(a), the planar air-driven soft mechanical arm is generally composed of several inflatable arm segments connected in series, a single arm segment is composed of a first actuator 1 and a second actuator 2 connected in parallel, the installation distance 4 between the two actuators, and theoretically, the arm segments composing the soft mechanical arm can be any number. The configuration space parameters of the individual arm segments are the bending angle and the arc length. Depending on whether the central arc length of the arm segments changes during actuation, the individual arm segments can be divided into three types:
as shown in fig. 2(b), the inflatable contractible arm segments have a central arc length of 5 < the central line of 3;
as shown in fig. 2(c), the arm segments are inflated with pure bending, and the central arc length 5 is the central line 3, i.e. the arc length remains unchanged during actuation;
as shown in fig. 2(d), the elongated arm section is inflated with a central arc length 5 > the centre line 3.
As shown in fig. 3, a planar gas-driven soft robot typically uses only one type of arm segment. The planar air-driven soft mechanical arm in the figure comprises three arm segments of the same type, namely a first arm segment 6, a second arm segment 7 and a third arm segment 8.
As shown in fig. 4, the mathematical model of the planar gas-driven soft mechanical arm includes four spatial parameters: the task space parameter, the configuration space parameter, the actuator space parameter and the driving space parameter are shown in fig. 3. For a planar air-driven soft mechanical arm, the task space coordinate y is constantly equal to 0, and the configuration space torsion angle
Figure BDA0002205009210000073
Is also always equal to 0.
As shown in fig. 5, obtaining configuration space parameters of the arm segment includes the following steps:
s11: as shown in FIGS. 6(a) and 6(b), P is setcFor the position of the end of the forearm segment, PeFor the current end point position of the robot arm, PfCalculating to obtain a vector P for the position of the tail end point of the mechanical arm targetcPeAnd PcPfThe included angle alpha is the point PeIs bent to PcPfRequired bend angle on the link:
Figure BDA0002205009210000071
s12: the feasible distance d is selected within the range of the length variation of the actuator so that the point P after bending iseAnd point PfThe distance between them is minimal:
wherein the distance D is the point PcAnd point PfThe distance between them.
S13: calculating the bending angle of the arm section according to the included angle alpha:
as shown in fig. 7, according to the assumption of constant curvature, the circular arcs corresponding to the front and back of the arm shape change of the end segment can be drawn in the sub-coordinate system of the end segment. The figures include a first arm 9 and a second arm 10. Further, a bending angle theta of
Figure BDA0002205009210000081
Wherein, theta1The bending angle corresponding to the previous arm shape;
s14: sequentially calculating configuration space parameters of the arm section, a bending radius r and a central arc length s according to the distance d and the bending angle theta:
Figure BDA0002205009210000082
Figure BDA0002205009210000083
wherein the central arc length s of the pure bending type arm section is constantly equal to the initial central line length l of the arm section.
Preferably, step S4 specifically includes:
the relationship between the base coordinate system { W } and the end coordinate system { O } of the soft robot may be described by a homogeneous transformation matrix:
wherein R is a rotation matrix; pdIs a displacement vector.
As can be seen from fig. 3, the complete process of coordinate system transformation of a single-arm segment includes four steps: 1) rotating the torsion angle phi around the Y-axis (phi is 0 for a planar soft-body manipulator); 2) rotating the bend angle θ about the z-axis; 3) origin of coordinates translation vector Pd(ii) a 4) Rotating the torsion angle negative phi around the Z axis; the final form of the transformation matrix is therefore as follows:
Figure BDA0002205009210000085
the positive kinematic equation for the soft mechanical arm is expressed as:
Figure BDA0002205009210000086
according to the bending angle and the central arc length of each arm section calculated in the steps, the integral arm shape of the soft mechanical arm can be updated by the formula (10).
As shown in fig. 8, updating the arm shape of each arm segment in turn starting from the arm segment near the base to the end arm segment can complete one iteration of the calculation. Among them, there are the following disadvantages:
(1) the length of the actuator can be changed at will, and in practical conditions, the length of the mechanical arm can be changed only within a certain range;
(2) the motion constraint for avoiding collision does not exist, and the size of the theta angle can be changed at will;
(3) the bending angle is suddenly changed, so that the service life of the mechanical arm is influenced;
(4) the variation range of the actuator is limited, a large error may be generated for some target positions or the target positions cannot be found at all, once the end point of the soft mechanical arm exceeds the target position, the target position cannot be found reversely;
(5) the inverse kinematics solution problem at the singular point cannot be solved.
Aiming at the problems, the improvement method of the algorithm is as follows:
(1) the selection range of the distance d is limited according to the designed change range of the central arc length of the soft mechanical arm, so that the length of the actuator obtained by each calculation always changes within an allowable range. Assume that the length of the actuator ranges from
l1,l2∈[lmin,lmax] (11)
Then the following linear constraints can be designed
Figure BDA0002205009210000091
Figure BDA0002205009210000092
If the distance D is within the limit range, the distance D is equal to the distance D; if the distance D is outside the limit range, the distance D is equal to the limit boundary value.
Figure BDA0002205009210000093
(2) Limiting the selection range of the angle theta according to the actual bending angle range of the designed soft mechanical arm;
Figure BDA0002205009210000101
(3) the parameter k is introduced to reduce the size of the angle theta calculated each time, and the final arm shape of the mechanical arm can be obtained by including the parameter, and a group of effective middle arm shapes can be obtained, so that a proper solution is obtained;
Figure BDA0002205009210000102
wherein n is the total arm segment number, and i is the current calculation arm segment number.
(4) By judging the target position PfAnd a straight line PcPeDetermining the sign of the angle theta increment;
Figure BDA0002205009210000103
(5) when vector PcPeAnd PcPfWhen in parallel, the configuration space parameter of the current arm section is not changed, and the next arm section is directly calculated; if all the arm sections are singular, randomly selecting an angle theta to avoid initial singularity;
with the above constraints added, the improved algorithm flow chart is shown in fig. 9.
Example 2
As shown in fig. 10, the planar gas-driven soft mechanical arm used in the experiment is composed of a single gas-filled extension-type actuator, although the single gas-filled extension-type actuator only has axial extension freedom, two actuators are connected in parallel to form a soft mechanical arm module with two degrees of freedom of plane bending and axial extension, and a plurality of modules are connected in series to form the complete planar soft mechanical arm, as shown in fig. 11.
As shown in FIG. 10, the single inflation extension type actuator includes an air tube 11, a sealing joint 12, an air chamber 13, an elastic body 14, and a filament winding wire 15.
As shown in fig. 11, the first arm segment 16 and the second arm segment 17 together comprise a planar soft mechanical arm.
The length of the single actuator can be set to be 100mm-150mm, and the installation distance a is 28 mm. Under this condition, the bending range of the single arm segment is-1.786 rad to 1.786 rad.
As shown in fig. 12, according to the positive kinematics model, the working space of the 5-segment soft robot is a huge solution space, and it is a great challenge to select the optimal solution, i.e. other spatial parameters corresponding to each target point cannot be directly obtained.
13(a) -13(d), to test the feasibility of the algorithm, target points were randomly selected in four quadrants within the base { W } of the soft robot arm, and the inverse kinematics solution was shown when using the initial algorithm without any constraints.
The experimental result shows that by using the algorithm, the target position can be accurately found by the five-segment type soft mechanical arm through one iteration, and the positioning error is 0, namely delta is 0 mm. However, the lengths of some actuators are beyond the physical range, and taking the target point in the first quadrant as an example, the lengths of the actuators corresponding to the final arm shape of the soft mechanical arm are shown in table 1.
TABLE 1 Final arm shape for each actuator length
Figure BDA0002205009210000111
As shown in fig. 14(a) -14(d), with the addition of constraints, the same target point is solved by using the improved algorithm, and the result of solving the inverse kinematics of the five-segment manipulator is shown in the figure.
The experimental result shows that the target position can still be accurately found by the five-segment type soft mechanical arm by using the algorithm, and the positioning error is very small, wherein delta is 1 mm. Similarly, taking the target point in the first quadrant as an example, the lengths of the actuators corresponding to the final arm shape of the soft mechanical arm are shown in table 2, and the lengths of the actuators are all within the physical range.
TABLE 2 Final arm shape for each actuator length
Figure BDA0002205009210000112
Comparing fig. 13 and 14, it can be seen that for most target positions in the four quadrants, the algorithm can always find the target position accurately after one iteration. The improved CCD algorithm can effectively control the length of the central arc length of each arm section. Although the precision of a single iteration of partial target positions is reduced, target position points can still be accurately found through multiple iterations.
Further, the results for the central arc length contracted and unaltered planar soft mechanical arms for the target position in the first quadrant are shown in fig. 15(a) and 15 (b). The initial actuator lengths for the two types of soft robotic arms were 150mm and 100mm, respectively. The positioning error of the contracting type soft mechanical arm is 0. Since the compliance of the central length invariant robot is inferior to the other two types, the positioning error is 1.624mm, which is only 0.325% of the entire length of the robot.
Due to the limitation of the central arc length of a single arm segment of the mechanical arm, some target positions may have large errors or cannot be converged. As shown in FIGS. 16(a) and 16(b), the target position is on line P after the first iteration 18cPeAnd below, the sign of the theta increment is negative when the next first iteration is performed. After the first iteration 18 and the second iteration 19, the distance error between the end point of the mechanical arm and the target position is reduced to 0.
Some of the trajectories generated by the CCD algorithm are bionic, and the end curves of the intermediate iteration process are similar to some spiral curves observed in nature, such as the arm shape change process of ten-segment arm, thirty-segment arm and fifty-segment arm when the solving target position is the origin of the coordinates of the whole arm as shown in fig. 17(a) -17 (c). The fibonacci spiral is called a golden spiral, and its mathematical expression is:
Figure BDA0002205009210000121
Figure BDA0002205009210000123
as shown in fig. 17(a), the parameters a and b can be calculated by least square fitting using the relationship between the cartesian expression and the polar expression of the spiral. Through calculation, the mathematical expression of the arm shape change path of the ten segments of the soft mechanical arms is as follows:
Figure BDA0002205009210000124
|bf|＝0.2615rad (22)
Figure BDA0002205009210000125
as shown in fig. 17(b), the mathematical expression of the arm shape change path of the thirty-segment soft mechanical arm is:
Figure BDA0002205009210000126
|bf|＝0.3053rad (15)
Figure BDA0002205009210000127
as shown in fig. 17(c), the mathematical expression of the arm shape change path of the fifty segments of the soft mechanical arm is:
Figure BDA0002205009210000128
|bf|＝0.3052rad (28)
Figure BDA0002205009210000129
the mathematical expressions of the three arm-shaped change paths are close to a Fibonacci spiral, and the bionic three-arm-shaped change path has good bionic characteristics.
According to the experimental results, the designed CCD algorithm can accurately find the target position within a plurality of steps of iteration. The algorithm meets the requirement of inverse kinematics solution with higher precision and less calculation time. Based on the algorithm, the trajectory planning of the planar gas drive soft mechanical arm can be rapidly realized, and a plurality of target points are sequentially solved. The final arm shape of the soft robotic arm for each target point.
As shown in fig. 18(a) -18(d), the positioning error δ is set to 5mm, which is 1% of the initial length of the five-segment type soft robot arm.
All or part of the flow of the method of the embodiments may be implemented by a computer program, which may be stored in a computer readable storage medium and executed by a processor, to instruct related hardware to implement the steps of the embodiments of the methods. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, Read-only Memory (ROM), Random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution medium, etc. It should be noted that the computer readable medium may contain content that is subject to appropriate increase or decrease as required by legislation and patent practice in jurisdictions, for example, in some jurisdictions, computer readable media does not include electrical carrier signals and telecommunications signals as is required by legislation and patent practice.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several equivalent substitutions or obvious modifications can be made without departing from the spirit of the invention, and all the properties or uses are considered to be within the scope of the invention.

Claims (10)

1. A planar gas drive soft mechanical arm inverse kinematics solving method is characterized by comprising the following steps:
s1: sequentially confirming configuration space parameters of an arm section of the planar gas drive soft mechanical arm according to a target position, wherein the configuration space parameters comprise a bending angle and an arc length of the arm section, and the planar gas drive soft mechanical arm comprises at least one arm section;
s2: calculating actuator space parameters for arm segments of the planar air-driven soft robotic arm based on the configuration space parameters, the actuator space parameters including a length of each actuator of the arm segments;
s3: calculating drive space parameters for the arm segments based on the actuator space parameters, the drive space parameters including input air pressures to drive respective actuators;
s4: updating the arm shape and the terminal coordinates of the arm section through a positive kinematic algorithm of the planar air-driven soft mechanical arm;
s5: and designing a constraint condition.
2. The method for solving inverse kinematics of a planar gas-driven soft mechanical arm according to claim 1, wherein the step of obtaining configuration space parameters of the arm segment in step S1 comprises the steps of:
s11: setting PcFor the position of the end of the forearm segment, PeFor the current end point position of the robot arm, PfCalculating to obtain a vector P for the position of the tail end point of the mechanical arm targetcPeAnd PcPfThe included angle alpha is the point PeIs bent to PcPfRequired bend angle on the link:
Figure FDA0002205009200000011
s12: the feasible distance d is selected within the range of the length variation of the actuator so that the point P after bending iseAnd point PfThe distance between them is minimal:
Figure FDA0002205009200000012
s13: calculating the bending angle of the arm section according to the included angle alpha:
Figure FDA0002205009200000013
wherein, theta1Corresponding to the last armBending angles;
s14: sequentially calculating configuration space parameters of the arm section, a bending radius r and a central arc length s according to the distance d and the bending angle theta:
Figure FDA0002205009200000014
Figure FDA0002205009200000021
3. the method for solving inverse kinematics of a planar gas-driven soft robotic arm according to claim 2, wherein the actuator of said arm segment is calculated by the formula:
Figure FDA0002205009200000022
wherein l1And l2The length of the actuators on both sides of the arm segment, respectively, and a is the mounting distance between the actuators.
4. The inverse kinematics solution method according to claim 3, wherein the driving space parameters of the arm segments are calculated by least squares fitting experiments and as a function of the actuator length and input air pressure level:
Figure FDA0002205009200000023
wherein, P1And P2Respectively, the magnitude of the input air pressure.
5. The method of solving inverse kinematics in a planar gas-driven soft robot as recited in claim 4, wherein the transformation relationship between the base coordinate system { W } and the end coordinate system { O } of said planar gas-driven soft robot is described by a homogeneous transformation matrix,
Figure FDA0002205009200000024
wherein R is a rotation matrix; pdIs a vector of the displacement of the object,
the final form of the homogeneous conversion matrix is:
Figure FDA0002205009200000025
theta is a bending angle of rotation around the Z axis, -phi is a torsion angle of rotation around the Z axis, and phi is a torsion angle of rotation around the Y axis; the positive kinematic equation of the planar gas-driven soft mechanical arm is expressed as:
Figure FDA0002205009200000026
and the positive kinematic equation is used for updating the arm shape of the plane air-driven soft mechanical arm.
6. The method for solving inverse kinematics of a planar gas-driven soft robotic arm according to claim 5, wherein said constraints comprise:
limiting the selection range of the distance d according to the change range of the central arc length of the planar gas-driven soft mechanical arm, so that the length of the actuator obtained by each calculation always changes within an allowable range; assume that the length range of the actuator is:
l1,l2∈[lmin,lmax]
then the following linear constraint can be designed:
Figure FDA0002205009200000031
s.t.lmin≤s+aθ≤lmax
lmin≤s-aθ≤lmax
Figure FDA0002205009200000032
s.t.lmin≤s+aθ≤lmax
lmin≤s-aθ≤lmax
if the distance D is within the limit range, the distance D is equal to the distance D; if the distance D is outside the limit range, the distance D is equal to the limit boundary value, and then the central arc length s is calculated according to the distance D.
Figure FDA0002205009200000033
Limiting the selection range of the bending angle theta according to the actual bending angle range of the planar gas-driven soft mechanical arm:
7. the method for solving inverse kinematics of a planar gas-driven soft robotic arm according to claim 6, wherein said constraints comprise: introducing the parameter k reduces the magnitude of each calculation of the bending angle theta:
Figure FDA0002205009200000035
wherein n is the total arm segment number of the planar gas drive soft mechanical arm, and i is the current calculated arm segment number.
8. The method of claim 5 wherein the inverse kinematics solution is determined by determining the target position PfAnd a straight line PcPeDetermines the sign of the angle θ increment:
Figure FDA0002205009200000041
9. the method of solving inverse kinematics in a planar gas-driven soft robotic arm according to claim 2, wherein the vector P iscPeAnd PcPfWhen parallel, the configuration space parameter of the current arm segment is not changed, and the next arm segment is directly calculated; and if all the arm sections are singular, randomly selecting a bending angle theta to avoid initial singularity.
10. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 9.
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