# US 2025/0144801 A1 · Manipulator execution path planning method for complex space guided measurement task

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- Number: US 2025/0144801 A1
- Document ID: US20250144801A1
- Status: Published application
- Kind: A1
- Application number: 19/018,106
- Filed: 2025-01-13
- Published: 2025-05-08
- Earliest claimed: 2024-08-23
- Assignees: China Jiliang University
- Applicants: China Jiliang University
- Inventors: Zai LUO; Wensong JIANG; Yan WANG; Li YANG; Minyue LI; Dian BIAN; Yaru LI
- Web page: https://patentgrep.com/patent/US20250144801A1

## CPC

- B25J 9/1666: {Avoiding collision or forbidden zones}
- B25J 9/1602: {characterised by the control system, structure, architecture}
- B25J 9/163: {learning, adaptive, model based, rule based expert control}
- B25J 9/1676: {Avoiding collision or forbidden zones}
- G05B 2219/40476: Collision, planning for collision free path
- G05B 2219/40499: Reinforcement learning algorithm
- B25J: MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES ({manipulators specially adapted for use in surgery A61B34/70; manipulators used in cleaning hollow articles B08B9/04}; manipulators associated with rolling mills B21B39/20; manipulators associated with forging machines B21J13/10; {manipulators associated with picking-up and placing mechanisms B23P19/007}; means for holding wheels or parts thereof B60B30/00; {vehicles with ground-engaging propulsion means, e.g. walking members B62D57/02, B62D57/032; devices for picking-up and depositing articles or materials between conveyors B65G47/90, B65G47/91; manipulators with gripping or holding means for transferring packages B65H67/065}; cranes B66C; {manipulators used in the protection or supervision of pipe-line installations F17D5/00; walking equipment adapted for nuclear steam-generators F22B37/006}; manipulators specially adapted for, or associated with, nuclear reactors G21C; {apparatus used for handling wafers during manufacture or treatment of semiconductor H10P72/50})
- G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G)

## Abstract

A manipulator execution path planning method for a complex space guided measurement task, includes: determining a measurement space of a manipulator and a starting point and a target point of a path; determining an obstructed space and a free space of the measurement space and a proportion of the obstructed space in the measurement space using a collision algorithm, and classifying and constructing a space compression model according to the proportion of the obstructed space in the measurement space to compress the measurement space and remove an invalid space; finding candidate paths for connecting the starting point and the target point by constructing an adjacent node tree connected topology network; finding a required path in the candidate paths, and performing high-order curve fitting to obtain a final path; discretizing the final path, and solving joint angles of the manipulator to obtain a joint track.

## Claims

### Claim 1

A manipulator execution path planning method for a complex space guided measurement task, comprising the following steps:
S1, determining a measurement space Ω of a manipulator;
S2, determining a starting point and a target point of a manipulator path;
S3, using a collision algorithm, determining an obstructed space Ω0 and a free space Ωf of the measurement space Ω; and determining a proportion of the obstructed space in the measurement space; wherein a calculation formula for the proportion is expressed as:
λ
=
Ω
0
/
Ω
,
λϵ
(
0
,
1
]
;
S4, constructing a space compression model to compress the measurement space and remove an invalid space in the measurement space; wherein S4 specifically comprises: when λ>0.5, constructing a first model to compress the measurement space; and when λ≤0.5, constructing a hyper-ellipsoidal model to compress the measurement space; wherein the first model is expressed as:
{
x
=
k
1
·
t
y
=
k
2
·
[
(
x
-
k
3
)
+
k
4
]
+
t
·
ε
or
{
x
=
k
1
·
t
y
=
k
2
·
[
(
x
-
k
3
)
+
k
4
]
+
2
·
t
·
ε
z
=
k
5
·
[
(
x
-
k
3
)
+
k
6
]
+
2
·
t
·
ε
;
wherein k1 is a boundary value of the measurement space, and k1=maxΩ−minΩ; k2, k3, k4, k5 and k6 are constants related to the starting point and the target point; t∈(0,1) is a random number conforming to uniform distribution; ε is a compression constant, and ε=γλ, wherein γ is a constant;
the hyper-ellipsoidal model is expressed as:
F
⁡
(
x
,
y
,
z
)
=
(
x
-
x
0
)
2
a
0
2
+
(
y
-
y
0
)
2
a
1
2
+
(
z
-
z
0
)
2
a
2
2
-
1
;
wherein a0 is a long axis, a0=∥xi−xg∥; xi is the starting point; xg is the target point; a1 is a medial axis,
a
1
=
c
⁡
(
t
)
2
-
a
0
2
2
2
;
a2 is a short axis,
a
2
=
c
⁡
(
t
)
2
-
a
0
2
2
4
;
c(t) is a path length obtained last time; and (x0, y0, z0) is coordinates of the starting point;
S5, in the compressed measurement space Ωn, finding candidate paths for connecting the starting point and the target point by constructing an adjacent node tree connected topology network according to a preset iterative step length, and constructing a candidate path dataset by using all the candidate paths;
S6, establishing a reinforcement learning drive model for the candidate path dataset, and finding a required path by utilizing a target equation with the shortest path and time;
S7, performing high-order curve fitting on the required path to achieve the smoothing of the required path and obtain a final path;
S8, discretizing the final path obtained in step S7, solving and calculating joint angles of the manipulator by using an inverse kinematics algorithm, and determining an angle of each joint of the manipulator to obtain a joint path of each joint moving in a space; and
S9, calculating whether interference exists between each joint path and the obstructed space; when the interference exists between a joint path and the obstructed space, adjusting parameters of the space compression model, and returning to S4 to be re-performed; and when no interference exists between any joint path and the obstructed space, completing path control from the starting point to the target point on the manipulator according to the joint path of each joint moving in the space in S8.

### Claim 2 (depends on 1)

The manipulator execution path planning method according to claim 1, wherein S5 specifically comprises:
S51, presetting an iterative step length δ, that is, expanding nodes for a distance δ every time during search;
S52, starting from the starting point, initializing a first node;
S53, searching a new node around the current node according to the preset iterative step length δ; and
S54, connecting the new node to the current node to construct the adjacent node tree connected topology network.

### Claim 3 (depends on 2)

The manipulator execution path planning method according to claim 2, wherein S51 further comprises:
presetting a threshold φ, wherein when a distance from the new node to the target point is smaller than or equal to the threshold φ, the target point is considered to be reached, and a cycle step is no longer performed; and a search range is the compressed measurement space Ωn.

### Claim 4 (depends on 2)

The manipulator execution path planning method according to claim 2, wherein S53 specifically comprises:
S531, supposing that the current node is xn(t);
S532, respectively calculating Euclidean distances from all the nodes in the adjacent node tree connected topology network to the current node xn(t), selecting the closest node as the closest point xf(t), and backwards extending a new node from xf(t);
S533, determining a new node xn(t+1) by calculation, wherein a formula is expressed as:
x
n
(
t
+
1
)
=
x
n
(
t
)
+
δ
·
x
r
(
t
)
-
x
f
(
t
)
❘
"\[LeftBracketingBar]"
x
r
(
t
)
-
x
f
(
t
)
❘
"\[RightBracketingBar]"
+
x
g
(
t
)
-
x
r
(
t
)
❘
"\[LeftBracketingBar]"
x
g
(
t
)
-
x
r
(
t
)
❘
"\[RightBracketingBar]"
;
wherein xr(t) is a preselected point possible to become the next node; and
S534, repeating above steps to determine whether a distance from the new node xn(t+1) to the target point is smaller than the threshold φ, if so, stopping the repetition; and if not, further performing steps S431 to S434.

### Claim 5 (depends on 1)

The manipulator execution path planning method according to claim 1, wherein S7 comprises:
S71, selecting a type and an order of a high-order curve according to complexity, curvature change and smoothness requirements of the required path;
S72, taking a key point or node of the required path as a control point for the high-order curve fitting; and
S73, performing the high-order curve fitting by using the selected type and order of the high-order curve and the control point to generate a curve representing a smoothed path of the required path, i.e., the final path.

### Claim 6 (depends on 1)

The manipulator execution path planning method according to claim 1, wherein S8 comprises:
S81, initializing structural parameters of the manipulator, wherein the structural parameters comprise a linkage length, linkage torsion, linkage offset, and the joint angles;
S82, discretizing the final path to form discrete point sequences, wherein the discrete point sequences are taken as path points of motion of the manipulator;
S83, calculating, by using the inverse kinematics algorithm according to the structural parameters and the path points of the manipulator, an angle value required to be reached by each joint, corresponding to each path point, of the manipulator; and
S84, generating a track of change of the angle of each joint of the manipulator with time, i.e., a motion process of the manipulator from the starting point to a target position, according to a result solved by using the inverse kinematics algorithm.