# US 11,992,946 B2 · Redundant robot joint acceleration planning method, redundant robot using the same, and computer readable storage medium

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- Number: US 11,992,946 B2
- Document ID: US11992946B2
- Status: Granted
- Kind: B2
- Application number: 17/553,758
- Filed: 2021-12-16
- Published: 2023-03-30
- Granted: 2024-05-28
- Earliest claimed: 2021-09-27
- Assignees: Ubkang (Qingdao) Technology Co., Ltd.
- Applicants: Ubtech Robotics Corp Ltd
- Inventors: Yizhang Liu; Youjun Xiong; Xuan Luo; Xianwen Zeng; Ligang Ge; Chunyu Chen
- Web page: https://patentgrep.com/patent/US11992946B2

## CPC

- B25J 9/1643: {redundant control}
- B25J 9/1651: {acceleration, rate control}
- B25J 9/1607: {Calculation of inertia, jacobian matrixes and inverses}
- G05B 2219/40367: Redundant manipulator
- G05B 2219/40519: Motion, trajectory planning
- 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 joint acceleration planning method, a redundant robot using the same, and a computer readable storage medium are provided. The method includes: obtaining an optimization objective function, a joint acceleration inequation constraint function and a joint acceleration equation constraint function corresponding to the optimization target from a quadratic programming function library, where the optimization objective function is an objective function obtained based on the upper and lower limits of the optimization target and a Euclidean distance algorithm; and obtaining a joint acceleration planning result by performing a quadratic optimization solving on a joint acceleration of each of the target joints of the robot at time k according to the end Cartesian space speed at time k+1, the joint parameter set of the target joints of the robot at time k, the sampling period, the optimization objective function, the joint acceleration inequation constraint function, and the joint acceleration equation constraint function.

## Claims

### Claim 1

A computer-implemented joint acceleration planning method for a redundant robot, comprising:
receiving a joint acceleration planning request, wherein the joint acceleration planning request carries an optimization target, a sampling period, an end Cartesian space speed at time k+1, and a joint parameter set of a plurality of target joints of the robot at time k;
obtaining a quadratic programming function library, and obtaining an optimization objective function, a joint acceleration inequation constraint function and a joint acceleration equation constraint function corresponding to the optimization target from the quadratic programming function library, wherein the optimization objective function is an objective function obtained based on the upper and lower limits of the optimization target and a Euclidean distance algorithm; and
obtaining a joint acceleration planning result by performing a quadratic optimization solving on a joint acceleration of each of the target joints of the robot at time k according to the end Cartesian space speed at time k+1, the joint parameter set of the target joints of the robot at time k, the sampling period, the optimization objective function, the joint acceleration inequation constraint function, and the joint acceleration equation constraint function;
wherein when the optimization target is a joint speed, the optimization objective function is determined by:
determining the joint speed of the i-th target joint at time k+1 according to the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a speed Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on the joint speed of the i-th target joint at time k+1 and an average value of upper and lower limits of the joint speed of the i-th target joint;
obtaining a square value of a difference value of the upper and lower limits of the joint speed of the i-th target joint by performing a square calculation on the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a speed Euclidean distance ratio of the i-th target joint at time k+1 by dividing the speed Euclidean distance of the i-th target joint at time k+1 by the square value of the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a first objective function by summing the speed Euclidean distance ratios of all the target joints at time k+1; and
obtaining the optimized objective function when the optimization target is the joint speed by performing a minimum value solving on the first objective function.

### Claim 2 (depends on 1)

The method of claim 1, wherein when the optimization target is the joint speed, the joint acceleration of the i-th target joint at time k is constrained by the upper limit of the joint speed of the i-th target joint, the lower limit of the joint speed of the i-th target joint, the upper limit of the joint acceleration of the i-th target joint, and the lower limit of the joint acceleration of the i-th target joint;
the joint acceleration inequation constraint function when the optimization target is the joint speed is:
max
⁡
(
(
v
i
min
-
v
i
(
k
)
)
T
,
a
i
min
)
≤
a
i
(
k
)
≤
min
⁡
(
(
v
i
min
-
v
i
(
k
)
)
T
,
a
i
max
)
;
where, Vimax is the upper limit of the joint speed of the i-th target joint, Vimin is the lower limit of the joint speed of the i-th target joint, aimax is the upper limit of the joint acceleration of the i-th target joint, aimin is the lower limit of the joint acceleration if the i-th target joint, Vi(k) is the joint speed of the i-th target joint at time k, ai(k) is the joint acceleration of the i-th target joint at time k, and T is the sampling period.

### Claim 3 (depends on 1)

The method of claim 1, wherein when the optimization target is a joint position, the optimization objective function is determined by:
determining the joint position of the i-th target joint at time k+1 according to the joint position of the i-th target joint at time k, the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a position Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on a difference value between the joint position of the i-th target joint at time k+1 and upper and lower limits of the joint position of the i-th target joint;
obtaining a square value of an average value of the upper and lower limits of the joint position of the i-th target joint by performing a squaring calculation on an average value of the upper and lower limits of the joint position of the i-th target join;
obtaining a position Euclidean distance ratio of the i-th target joint at time k+1 by dividing the position Euclidean distance of the i-th target joint at time k+1 by the square value of the average value of the upper and lower limits of the joint position of the i-th target joint;
obtaining a second objective function by summing the position Euclidean distance ratios of all the target joints at time k+1; and
obtaining the optimized objective function when the optimization target is the joint position by performing a minimum value solving on the second objective function.

### Claim 4 (depends on 1)

The method of claim 1, wherein when the optimization target is a joint position and a joint speed, the optimization objective function is determined by:
determining the joint position of the i-th target joint at time k+1 according to the joint position of the i-th target joint at time k, the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a position Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on a difference value between the joint position of the i-th target joint at time k+1 and upper and lower limits of the joint position of the i-th target joint;
obtaining a square value of an average value of the upper and lower limits of the joint position of the i-th target joint by performing a squaring calculation on an average value of the upper and lower limits of the joint position of the i-th target join;
obtaining a position Euclidean distance ratio of the i-th target joint at time k+1 by dividing the position Euclidean distance of the i-th target joint at time k+1 by the square value of the average value of the upper and lower limits of the joint position of the i-th target joint;
obtaining a third objective function by summing the position Euclidean distance ratios of all the target joints at time k+1;
determining the joint speed of the i-th target joint at time k+1 according to the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a speed Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on the joint speed of the i-th target joint at time k+1 and an average value of upper and lower limits of the joint speed of the i-th target joint;
obtaining a square value of a difference value of the upper and lower limits of the joint speed of the i-th target joint by performing a square calculation on the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a speed Euclidean distance ratio of the i-th target joint at time k+1 by dividing the speed Euclidean distance of the i-th target joint at time k+1 by the square value of the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a fourth objective function by summing the speed Euclidean distance ratios of all the target joints at time k+1;
obtaining a fifth objective function by calculating a weighted sum of the third objective function and the fourth objective function; and
obtaining the optimized objective function when the optimization target is the joint position and joint speed by performing a minimum value solving on the fifth objective function.

### Claim 5 (depends on 1)

The method of claim 1, wherein when the optimization target is a joint angle, the optimization objective function is determined by:
obtaining a joint angle change speed of the i-th target joint at time k by performing a joint angle change speed calculation according to the joint speed of the i-th target joint at time k;
obtaining a joint angle change acceleration of the i-th target joint at time k by performing a joint angle change acceleration calculation according to the joint acceleration of the i-th target joint at time k;
determining the joint angle of the i-th target joint at time k+1 according to the joint angle of the i-th target joint at time k, the joint angle change speed of the i-th target joint at time k, and the joint angle change acceleration of the i-th target joint at time k, and the sampling period;
obtaining an angular Euclidean distance of the i-th target joint is at time k+1 by performing a Euclidean distance calculation on the joint angle of the i-th target joint at time k+1 and an average value of upper and lower limits of the joint angle of the i-th target joint;
obtaining a square value of a difference value between the upper and lower limits of the joint angle of the i-th target joint by performing a square calculation on the difference value of the upper and lower limits of the joint angle of the i-th target joint;
obtaining an angular Euclidean distance ratio of the i-th target joint at time k+1 by dividing the angular Euclidean distance of the i-th target joint at time k+1 by the square value of the difference value between the upper and lower limits of the joint angle of the i-th target joint;
obtaining a fifth objective function by summing the angular Euclidean distance ratios of all the target joints at time k+1; and
obtaining the optimized objective function when the optimization target is the joint angle by performing a minimum value solving on the fifth objective function.

### Claim 6 (depends on 1)

The method of claim 1, wherein when the optimization target is one of a joint position, the joint position and a joint speed, and a joint angle, the joint acceleration of the i-th target joint at time k is constrained by the upper limit of the joint position of the i-th target joint, the lower limit of the joint position of the i-th target joint, the upper limit of the joint speed of the i-th target joint, and the lower limit of the joint speed of the i-th target joint, the upper limit of the joint acceleration of the i-th target joint, and the lower limit of the joint acceleration of the i-th target joint;
the joint acceleration inequation constraint function when the optimization target is one of the joint position, the joint position and joint speed, and the joint angle is:
max
⁡
(
2
⁢
(
d
i
min
-
(
d
i
(
k
)
+
v
i
(
k
)
·
T
)
)
T
2
,
(
v
i
min
-
v
i
(
k
)
)
T
,
a
i
min
)
≤
a
i
(
k
)
≤
min
⁡
(
2
⁢
(
d
i
max
-
(
d
i
(
k
)
+
v
i
(
k
)
·
T
)
)
T
2
,
(
v
i
max
-
v
i
(
k
)
)
T
,
a
i
max
)
;
where, dimax is the upper limit of the joint position of the i-th target joint, dimin is the lower limit of the joint position of the i-th target joint, vimax is the upper limit of the joint speed of the i-th target joint, vimin is the lower limit of the joint speed of the i-th target joint, aimax is the upper limit of the joint acceleration of the i-th target joint, aimin is the lower limit of the joint acceleration of the i-th target joint, di(k) is the joint position of the i-th target joint at time k, vi(k) is the joint speed of the i-th target joint at time k, ai(k) is the joint acceleration of the i-th target joint at time k, and T is the sampling period.

### Claim 7

A redundant robot, comprising:
a processor;
a memory coupled to the processor; and
one or more computer programs stored in the memory and executable on the processor;
wherein, the one or more computer programs comprise:
instructions for receiving a joint acceleration planning request, wherein the joint acceleration planning request carries an optimization target, a sampling period, an end Cartesian space speed at time k+1, and a joint parameter set of a plurality of target joints of the robot at time k;
instructions for obtaining a quadratic programming function library, and obtaining an optimization objective function, a joint acceleration inequation constraint function and a joint acceleration equation constraint function corresponding to the optimization target from the quadratic programming function library, wherein the optimization objective function is an objective function obtained based on the upper and lower limits of the optimization target and a Euclidean distance algorithm; and
instructions for obtaining a joint acceleration planning result by performing a quadratic optimization solving on a joint acceleration of each of the target joints of the robot at time k according to the end Cartesian space speed at time k+1, the joint parameter set of the target joints of the robot at time k, the sampling period, the optimization objective function, the joint acceleration inequation constraint function, and the joint acceleration equation constraint function;
wherein when the optimization target is a joint position. the optimization objective function is determined by:
determining the joint position of the i-th target joint at time k+1 according to the joint position of the i-th target joint at time k, the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a position Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on a difference value between the joint position of the i-th target joint at time k+1 and upper and lower limits of the joint position of the i-th target joint:
obtaining a square value of an average value of the upper and lower limits of the joint position of the i-th target joint by performing a squaring calculation on an average value of the upper and lower limits of the joint position of the i-th target join;
obtaining a position Euclidean distance ratio of the i-th target joint at time k+1 by dividing the position Euclidean distance of the i-th target joint at time k+1 by the square value of the average value of the upper and lower limits of the joint position of the i-th target joint;
obtaining a second objective function by summing the position Euclidean distance ratios of all the target joints at time k+1; and
obtaining the optimized objective function when the optimization target is the joint position by performing a minimum value solving on the second objective function.

### Claim 8 (depends on 7)

The redundant robot of claim 7, wherein when the optimization target is a joint speed, the optimization objective function is determined by:
determining the joint speed of the i-th target joint at time k+1 according to the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a speed Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on the joint speed of the i-th target joint at time k+1 and an average value of upper and lower limits of the joint speed of the i-th target joint;
obtaining a square value of a difference value of the upper and lower limits of the joint speed of the i-th target joint by performing a square calculation on the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a speed Euclidean distance ratio of the i-th target joint at time k+1 by dividing the speed Euclidean distance of the i-th target joint at time k+1 by the square value of the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a first objective function by summing the speed Euclidean distance ratios of all the target joints at time k+1; and
obtaining the optimized objective function when the optimization target is the joint speed by performing a minimum value solving on the first objective function.

### Claim 9 (depends on 8)

The redundant robot of claim 8, wherein when the optimization target is the joint speed, the joint acceleration of the i-th target joint at time k is constrained by the upper limit of the joint speed of the i-th target joint, the lower limit of the joint speed of the i-th target joint, the upper limit of the joint acceleration of the i-th target joint, and the lower limit of the joint acceleration of the i-th target joint;
the joint acceleration inequation constraint function when the optimization target is the joint speed is:
max
⁡
(
(
v
i
min
-
v
i
(
k
)
)
T
,
a
i
min
)
≤
a
i
(
k
)
≤
min
⁡
(
(
v
i
min
-
v
i
(
k
)
)
T
,
a
i
max
)
;
where, vimax is the upper limit of the joint speed of the i-th target joint, vimin is the lower limit of the joint speed of the i-th target joint, aimax is the upper limit of the joint acceleration of the i-th target joint, aimin is the lower limit of the joint acceleration of the i-th target joint, vi(k) is the joint speed of the i-th target joint at time k, ai(k) is the joint acceleration of the i-th target joint at time k, and T is the sampling period.

### Claim 10 (depends on 7)

The redundant robot of claim 7, wherein when the optimization target is a joint position and a joint speed, the optimization objective function is determined by:
determining the joint position of the i-th target joint at time k+1 according to the joint position of the i-th target joint at time k, the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a position Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on a difference value between the joint position of the i-th target joint at time k+1 and upper and lower limits of the joint position of the i-th target joint;
obtaining a square value of an average value of the upper and lower limits of the joint position of the i-th target joint by performing a squaring calculation on an average value of the upper and lower limits of the joint position of the i-th target join;
obtaining a position Euclidean distance ratio of the i-th target joint at time k+1 by dividing the position Euclidean distance of the i-th target joint at time k+1 by the square value of the average value of the upper and lower limits of the joint position of the i-th target joint;
obtaining a third objective function by summing the position Euclidean distance ratios of all the target joints at time k+1;
determining the joint speed of the i-th target joint at time k+1 according to the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a speed Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on the joint speed of the i-th target joint at time k+1 and an average value of upper and lower limits of the joint speed of the i-th target joint;
obtaining a square value of a difference value of the upper and lower limits of the joint speed of the i-th target joint by performing a square calculation on the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a speed Euclidean distance ratio of the i-th target joint at time k+1 by dividing the speed Euclidean distance of the i-th target joint at time k+1 by the square value of the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a fourth objective function by summing the speed Euclidean distance ratios of all the target joints at time k+1;
obtaining a fifth objective function by calculating a weighted sum of the third objective function and the fourth objective function; and
obtaining the optimized objective function when the optimization target is the joint position and joint speed by performing a minimum value solving on the fifth objective function.

### Claim 11 (depends on 7)

The redundant robot of claim 7, wherein when the optimization target is a joint angle, the optimization objective function is determined by:
obtaining a joint angle change speed of the i-th target joint at time k by performing a joint angle change speed calculation according to the joint speed of the i-th target joint at time k;
obtaining a joint angle change acceleration of the i-th target joint at time k by performing a joint angle change acceleration calculation according to the joint acceleration of the i-th target joint at time k;
determining the joint angle of the i-th target joint at time k+1 according to the joint angle of the i-th target joint at time k, the joint angle change speed of the i-th target joint at time k, and the joint angle change acceleration of the i-th target joint at time k, and the sampling period;
obtaining an angular Euclidean distance of the i-th target joint is at time k+1 by performing a Euclidean distance calculation on the joint angle of the i-th target joint at time k+1 and an average value of upper and lower limits of the joint angle of the i-th target joint;
obtaining a square value of a difference value between the upper and lower limits of the joint angle of the i-th target joint by performing a square calculation on the difference value of the upper and lower limits of the joint angle of the i-th target joint;
obtaining an angular Euclidean distance ratio of the i-th target joint at time k+1 by dividing the angular Euclidean distance of the i-th target joint at time k+1 by the square value of the difference value between the upper and lower limits of the joint angle of the i-th target joint;
obtaining a fifth objective function by summing the angular Euclidean distance ratios of all the target joints at time k+1; and
obtaining the optimized objective function when the optimization target is the joint angle by performing a minimum value solving on the fifth objective function.

### Claim 12 (depends on 7)

The redundant robot of claim 7, wherein when the optimization target is one of a joint position, the joint position and a joint speed, and a joint angle, the joint acceleration of the i-th target joint at time k is constrained by the upper limit of the joint position of the i-th target joint, the lower limit of the joint position of the i-th target joint, the upper limit of the joint speed of the i-th target joint, and the lower limit of the joint speed of the i-th target joint, the upper limit of the joint acceleration of the i-th target joint, and the lower limit of the joint acceleration of the i-th target joint;
the joint acceleration inequation constraint function when the optimization target is one of the joint position, the joint position and joint speed, and the joint angle is:
max
⁡
(
2
⁢
(
d
i
min
-
(
d
i
(
k
)
+
v
i
(
k
)
·
T
)
)
T
2
,
(
v
i
min
-
v
i
(
k
)
)
T
,
a
i
min
)
≤
a
i
(
k
)
≤
min
⁡
(
2
⁢
(
d
i
max
-
(
d
i
(
k
)
+
v
i
(
k
)
·
T
)
)
T
2
,
(
v
i
max
-
v
i
(
k
)
)
T
,
a
i
max
)
;
where, dimax is the upper limit of the joint position of the i-th target joint, dimin is the lower limit of the joint position of the i-th target joint, Vimax is the upper limit of the joint speed of the i-th target joint, vimin is the lower limit of the joint speed of the i-th target joint, aimax is the upper limit of the joint acceleration of the i-th target joint, aimin is the lower limit of the joint acceleration of the i-th target joint, di(k) is the joint position of the i-th target joint at time k, vi(k) is the joint speed of the i-th target joint at time k, ai(k) is the joint acceleration of the i-th target joint at time k, and T is the sampling period.

### Claim 13

A non-transitory computer readable storage medium for storing one or more computer programs, wherein the one or more computer programs comprise:
instructions for receiving a joint acceleration planning request, wherein the joint acceleration planning request carries an optimization target, a sampling period, an end Cartesian space speed at time k+1, and a joint parameter set of a plurality of target joints of the robot at time k;
instructions for obtaining a quadratic programming function library, and obtaining an optimization objective function, a joint acceleration inequation constraint function and a joint acceleration equation constraint function corresponding to the optimization target from the quadratic programming function library, wherein the optimization objective function is an objective function obtained based on the upper and lower limits of the optimization target and a Euclidean distance algorithm; and
instructions for obtaining a joint acceleration planning result by performing a quadratic optimization solving on a joint acceleration of each of the target joints of the robot at time k according to the end Cartesian space speed at time k+1, the joint parameter set of the target joints of the robot at time k, the sampling period, the optimization objective function, the joint acceleration inequation constraint function, and the joint acceleration equation constraint function;
wherein when the optimization target is a joint angle, the optimization objective function is determined by:
obtaining a joint angle change speed of the i-th target joint at time k by performing a joint angle change speed calculation according to the joint speed of the i-th target joint at time k;
obtaining a joint angle change acceleration of the i-th target joint at time k by performing a joint angle change acceleration calculation according to the joint acceleration of the i-th target joint at time k:
determining the joint angle of the i-th target joint at time k+1 according to the joint angle of the i-th target joint at time k, the joint angle change speed of the i-th target joint at time k, and the joint angle change acceleration of the i-th target joint at time k, and the sampling period;
obtaining an angular Euclidean distance of the i-th target joint is at time k+1 by performing a Euclidean distance calculation on the joint angle of the i-th target joint at time k+1 and an average value of upper and lower limits of the joint angle of the i-th target joint;
obtaining a square value of a difference value between the upper and lower limits of the joint angle of the i-th target joint by performing a square calculation on the difference value of the upper and lower limits of the joint angle of the i-th target joint;
obtaining an angular Euclidean distance ratio of the i-th target joint at time k+1 by dividing the angular Euclidean distance of the i-th target joint at time k+1 by the square value of the difference value between the upper and lower limits of the joint angle of the i-th target joint;
obtaining a fifth objective function by summing the angular Euclidean distance ratios of all the target joints at time k+1; and
obtaining the optimized objective function when the optimization target is the joint angle by performing a minimum value solving on the fifth objective function.

### Claim 14 (depends on 13)

The storage medium of claim 13, wherein when the optimization target is a joint speed, the optimization objective function is determined by:
determining the joint speed of the i-th target joint at time k+1 according to the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a speed Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on the joint speed of the i-th target joint at time k+1 and an average value of upper and lower limits of the joint speed of the i-th target joint;
obtaining a square value of a difference value of the upper and lower limits of the joint speed of the i-th target joint by performing a square calculation on the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a speed Euclidean distance ratio of the i-th target joint at time k+1 by dividing the speed Euclidean distance of the i-th target joint at time k+1 by the square value of the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a first objective function by summing the speed Euclidean distance ratios of all the target joints at time k+1; and
obtaining the optimized objective function when the optimization target is the joint speed by performing a minimum value solving on the first objective function.

### Claim 15 (depends on 14)

The storage medium of claim 14, wherein when the optimization target is the joint speed, the joint acceleration of the i-th target joint at time k is constrained by the upper limit of the joint speed of the i-th target joint, the lower limit of the joint speed of the i-th target joint, the upper limit of the joint acceleration of the i-th target joint, and the lower limit of the joint acceleration of the i-th target joint;
the joint acceleration inequation constraint function when the optimization target is the joint speed is:
max
⁡
(
(
v
i
min
-
v
i
(
k
)
)
T
,
a
i
min
)
≤
a
i
(
k
)
≤
min
⁡
(
(
v
i
min
-
v
i
(
k
)
)
T
,
a
i
max
)
;
where, V1max is the upper limit of the joint speed of the i-th target joint, vimin is the lower limit of the joint speed of the i-th target joint, aimax is the upper limit of the joint acceleration of the i-th target joint, aimin is the lower limit of the joint acceleration of the i-th target joint, vi(k) is the joint speed of the i-th target joint at time k, ai(k) is the joint acceleration of the i-th target joint at time k, and T is the sampling period.

### Claim 16 (depends on 13)

The storage medium of claim 13, wherein when the optimization target is a joint position, the optimization objective function is determined by:
determining the joint position of the i-th target joint at time k+1 according to the joint position of the i-th target joint at time k, the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a position Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on a difference value between the joint position of the i-th target joint at time k+1 and upper and lower limits of the joint position of the i-th target joint;
obtaining a square value of an average value of the upper and lower limits of the joint position of the i-th target joint by performing a squaring calculation on an average value of the upper and lower limits of the joint position of the i-th target join;
obtaining a position Euclidean distance ratio of the i-th target joint at time k+1 by dividing the position Euclidean distance of the i-th target joint at time k+1 by the square value of the average value of the upper and lower limits of the joint position of the i-th target joint;
obtaining a second objective function by summing the position Euclidean distance ratios of all the target joints at time k+1; and
obtaining the optimized objective function when the optimization target is the joint position by performing a minimum value solving on the second objective function.

### Claim 17 (depends on 13)

The storage medium of claim 13, wherein when the optimization target is a joint position and a joint speed, the optimization objective function is determined by:
determining the joint position of the i-th target joint at time k+1 according to the joint position of the i-th target joint at time k, the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a position Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on a difference value between the joint position of the i-th target joint at time k+1 and upper and lower limits of the joint position of the i-th target joint;
obtaining a square value of an average value of the upper and lower limits of the joint position of the i-th target joint by performing a squaring calculation on an average value of the upper and lower limits of the joint position of the i-th target join;
obtaining a position Euclidean distance ratio of the i-th target joint at time k+1 by dividing the position Euclidean distance of the i-th target joint at time k+1 by the square value of the average value of the upper and lower limits of the joint position of the i-th target joint;
obtaining a third objective function by summing the position Euclidean distance ratios of all the target joints at time k+1;
determining the joint speed of the i-th target joint at time k+1 according to the joint speed of the i-th target joint at time k, the joint acceleration of the i-th target joint at time k, and the sampling period;
obtaining a speed Euclidean distance of the i-th target joint at time k+1 by performing a Euclidean distance calculation on the joint speed of the i-th target joint at time k+1 and an average value of upper and lower limits of the joint speed of the i-th target joint;
obtaining a square value of a difference value of the upper and lower limits of the joint speed of the i-th target joint by performing a square calculation on the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a speed Euclidean distance ratio of the i-th target joint at time k+1 by dividing the speed Euclidean distance of the i-th target joint at time k+1 by the square value of the difference value of the upper and lower limits of the joint speed of the i-th target joint;
obtaining a fourth objective function by summing the speed Euclidean distance ratios of all the target joints at time k+1;
obtaining a fifth objective function by calculating a weighted sum of the third objective function and the fourth objective function; and
obtaining the optimized objective function when the optimization target is the joint position and joint speed by performing a minimum value solving on the fifth obiective function.

### Claim 18 (depends on 13)

The storage medium of claim 13, wherein wherein when the optimization target is one of a joint position, the joint position and a joint speed, and a joint angle, the joint acceleration of the i-th target joint at time k is constrained by the upper limit of the joint position of the i-th target joint, the lower limit of the joint position of the i-th target joint, the upper limit of the joint speed of the i-th target joint, and the lower limit of the joint speed of the i-th target joint, the upper limit of the joint acceleration of the i-th target joint, and the lower limit of the joint acceleration of the i-th target joint;
the joint acceleration inequation constraint function when the optimization target is one of the joint position, the joint position and joint speed, and the joint angle is:
max
⁡
(
2
⁢
(
d
i
min
-
(
d
i
(
k
)
+
v
i
(
k
)
·
T
)
)
T
2
,
(
v
i
min
-
v
i
(
k
)
)
T
,
a
i
min
)
≤
a
i
(
k
)
≤
min
⁡
(
2
⁢
(
d
i
max
-
(
d
i
(
k
)
+
v
i
(
k
)
·
T
)
)
T
2
,
(
v
i
max
-
v
i
(
k
)
)
T
,
a
i
max
)
;
where, dimax is the upper limit of the joint position of the i-th target joint, dimin is the lower limit of the joint position of the i-th target joint, vimax is the upper limit of the joint speed of the i-th target joint, vimin is the lower limit of the joint speed of the i-th target joint, aimax is the upper limit of the joint acceleration of the i-th target joint, aimin is the lower limit of the joint acceleration of the i-th target joint, di(k) is the joint position of the i-th target joint at time k, vi(k) is the joint speed of the i-th target joint at time k, ai(k) is the joint acceleration of the i-th target joint at time k, and T is the sampling period.

### Claim 19 (depends on 13)

The storage medium of claim 13, wherein the joint acceleration planning request is inputted by the user; or
the joint acceleration planning request is sent by a third-party application system, or by a program at the sampling period.

### Claim 20 (depends on 13)

The storage medium of claim 13, wherein the optimization target is a joint speed and a joint angle.