CN110727271A - Robot motion primitive determining method and device - Google Patents
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Abstract
The invention provides a robot motion primitive determining method and device, which can avoid the problems that the robot is easy to fall into local minimum or difficult to track a path when carrying out path tracking control. The method comprises the following steps: determining an initial state vector of the robot; determining a translational motion speed interval and a yaw velocity interval which are reached by the robot in the time of generating the motion elements, and equally dividing the translational motion speed interval into m-1 parts and equally dividing the yaw velocity interval into N-1 parts according to the number N of the generated motion elements, wherein N is m x N; and (3) taking the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain a motion element generated under the control vector. The invention relates to the technical field of robot path planning.
Description
Technical Field
The invention relates to the technical field of robot path planning, in particular to a method and a device for determining a robot motion primitive.
Background
Path planning is a basic premise for realizing autonomous navigation of a robot. The robot acquires perception information of the environment by means of a sensor in the movement process, and meanwhile, an environment map is created. In the path planning process, the robot motion primitives determine the connection relationship between nodes, and one state node can be converted to another state node through the motion primitives. And (3) searching a series of motion primitives transformed from an initial state to a target state according to the barrier information marked on the environment map by the path planning, namely planning to generate a collision-free safe path.
The motion primitives are used as a representation mode of a node connection relationship in path planning, and usually a robot is regarded as a particle and generated by adopting straight line connection, such as a 4-connection grid and an 8-connection grid, and the motion primitives generated by adopting the method do not consider the kinematic constraint conditions of the robot, so that the robot is easy to fall into local minimum or difficult to track a path when performing path tracking control.
The Chinese patent with the application number of 201610348356.3 discloses a mobile robot path planning method based on a dynamic motion element learning model, the method adopts a handle to control the motion of a robot, records the motion track of the robot as a sample of the dynamic motion element model, and obtains the parameters of the dynamic motion element model by establishing the dynamic motion element model and training by utilizing the track sample, and the motion element generation process is complex and time-consuming and is greatly influenced by the manual operation level.
Disclosure of Invention
The invention aims to solve the technical problem of providing a robot motion primitive determining method and device to solve the problems that in the prior art, the motion primitive is generated without considering the kinematic constraint condition of a robot, so that the robot is easy to fall into local minimum or difficult to track a path when performing path tracking control, and the motion primitive generating process is complex and time-consuming.
In order to solve the above technical problem, an embodiment of the present invention provides a method for determining a robot motion primitive, including:
determining an initial state vector of the robot;
determining a translational motion speed interval and a yaw velocity interval which are reached by the robot in the time of generating the motion elements, and equally dividing the translational motion speed interval into m-1 parts and equally dividing the yaw velocity interval into N-1 parts according to the number N of the generated motion elements, wherein N is m x N;
and taking the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain a motion element generated under the control vector, wherein i is 1, 2.
Further, the starting state vector is zs＝[xs,ys,θs]TWherein z represents a state vector, x and y represent displacements of the robot along the x direction and the y direction respectively, theta represents a heading angle of the robot, subscript s represents a start, and superscript T represents a matrix transposition.
Further, the step of determining a translational motion speed interval and a yaw rate interval reached by the robot within the time of generating the motion primitives, and equally dividing the translational motion speed interval into m parts and equally dividing the yaw rate interval into N parts according to the number N of generated motion primitives comprises the following steps:
determining the translation motion speed interval [ v ] reached by the robot in the time t generated by the motion primitives-at,vs+at]And yaw angular velocity interval [ omega ]s-αt,ωs+αt]Wherein v represents the speed of the translational motion of the robot, ω represents the yaw rate of the robot, and a and α represent the acceleration at the translational motion of the robot and the yaw acceleration at the yaw motion, respectively;
according to the number N of the robot motion elements, equally dividing a translational motion speed interval into m-1 parts, equally dividing a yaw angle speed interval into N-1 parts, and satisfying the following conditions: n — m × N, then: translational motion speed corresponding to endpoint iYaw rate corresponding to endpoint j
Further, the step of taking the translational motion velocity corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain a motion primitive generated under the control vector includes:
within the time of motion primitive generation, with u ═ vi,ωj]TThe constant speed is used as a control vector, and the robot is determined at the sampling time t according to the determined initial state vector of the robot and the kinematic constraint of the robotfThe time-dependent state is:
wherein u represents a control vector, (x)f,yf,θf) Indicating that the robot is at the sampling time tfState vector of (x)f,yf,θf) Is a discrete point on the motion primitive, tfAny sampling moment in time t generated by a motion primitive is designated;
connecting state vectors at different sampling moments in the time of generating the motion primitive to obtain a control vector u ═ vi,ωj]TThe next generated motion primitive.
Further, the state vectors at different sampling time are connected in the time of generating the motion primitive, and a control vector u ═ v is obtainedi,ωj]TThe following generated motion primitives include:
in the time of generating the motion primitive, if the termination state vector is not at the grid center of the environment map, translating the termination state vector to the grid center by adopting a rounding method;
connecting the state vectors at different sampling times to obtain a control vector u ═ vi,ωj]TThe next generated motion primitive.
An embodiment of the present invention further provides a device for determining a robot motion primitive, including:
the determining module is used for determining an initial state vector of the robot;
the robot comprises an equally dividing module, a judging module and a judging module, wherein the equally dividing module is used for determining a translational motion speed interval and a yaw angular velocity interval which are reached by the robot in the time of generating motion primitives, and equally dividing the translational motion speed interval into m-1 parts and equally dividing the yaw angular velocity interval into N-1 parts according to the generated number N of the motion primitives, wherein N is m x N;
and the generating module is used for taking the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain a motion element generated under the control vector, wherein i is 1,2, and.
Further, the starting state vector is zs＝[xs,ys,θs]TWherein z represents a state vector, x and y represent displacements of the robot along the x direction and the y direction respectively, theta represents a heading angle of the robot, subscript s represents a start, and superscript T represents a matrix transposition.
Further, the halving module comprises:
a first determining unit for determining the translational motion speed interval [ v ] reached by the robot in the time t of the generation of the motion primitives-at,vs+at]And yaw angular velocity interval [ omega ]s-αt,ωs+αt]Wherein v represents the speed of the translational motion of the robot, ω represents the yaw rate of the robot, and a and α represent the acceleration at the translational motion of the robot and the yaw acceleration at the yaw motion, respectively;
and the equally dividing unit is used for equally dividing the translational motion speed interval into m-1 parts and the yaw velocity interval into N-1 parts according to the generated number N of the robot motion elements, and meets the following requirements: n — m × N, then: translational motion speed corresponding to endpoint iThe transverse line corresponding to the end point jAngular velocity of oscillation
Further, the generating module includes:
a second determination unit for generating a motion primitive with u ═ v in timei,ωj]TThe constant speed is used as a control vector, and the robot is determined at the sampling time t according to the determined initial state vector of the robot and the kinematic constraint of the robotfThe time-dependent state is:
wherein u represents a control vector, (x)f,yf,θf) Indicating that the robot is at the sampling time tfState vector of (x)f,yf,θf) Is a discrete point on the motion primitive, tfAny sampling moment in time t generated by a motion primitive is designated;
a generating unit for connecting the state vectors at different sampling time points within the time of generating the motion primitive to obtain a control vector u ═ vi,ωj]TThe next generated motion primitive.
Further, the generating unit is configured to, during the time of generating the motion primitive, if the termination state vector is not at the grid center of the environment map, translate the termination state vector to the grid center by using a rounding method; also for concatenating the state vectors at different sampling instants, resulting in a control vector u ═ vi,ωj]TThe next generated motion primitive.
The technical scheme of the invention has the following beneficial effects:
in the scheme, the initial state vector of the robot is determined; determining a translational motion speed interval and a yaw velocity interval which are reached by the robot in the time of generating the motion elements, and equally dividing the translational motion speed interval into m-1 parts and equally dividing the yaw velocity interval into N-1 parts according to the number N of the generated motion elements, wherein N is m x N; and (3) taking the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain a motion element generated under the control vector. In this way, the reachable state of the robot in the time of generating the motion primitives is determined according to the kinematic constraints of the robot, so that the motion primitives under various different control vectors are generated, the problems that the robot is easy to fall into local minimum or difficult to track paths when the robot carries out path tracking control can be avoided, and the generation process of the motion primitives is simple.
Drawings
Fig. 1 is a schematic flow chart of a robot motion primitive determination method according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a coordinate system of a robot according to an embodiment of the present invention;
FIG. 3 is a diagram of a control vector u according to an embodiment of the present invention9＝[1,0.5]TA schematic diagram of motion elements generated under action;
FIG. 4 shows a starting state vector z of the robot according to the embodiment of the present inventions＝[0,0,0]TA schematic diagram of a lower motion primitive;
fig. 5 is a schematic structural diagram of a robot motion primitive determination apparatus according to an embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
The invention provides a method and a device for determining a motion element of a robot, aiming at the problems that the motion element is generated without considering the kinematic constraint condition of the robot, so that the robot is easy to fall into local minimum or difficult in path tracking when performing path tracking control, and the generation process of the motion element is complex and time-consuming.
Example one
As shown in fig. 1, a method for determining a robot motion primitive provided by an embodiment of the present invention includes:
s101, determining an initial state vector of the robot;
s102, determining a translational motion speed interval and a yaw velocity interval which are reached by the robot within the time of generating motion elements, and equally dividing the translational motion speed interval into m-1 parts and equally dividing the yaw velocity interval into N-1 parts according to the generated number N of the motion elements, wherein N is m × N;
and S103, taking the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain a motion element generated under the control vector, wherein i is 1,2, and m, j is 1, 2.
The robot motion primitive determining method of the embodiment of the invention determines the initial state vector of the robot; determining a translational motion speed interval and a yaw velocity interval which are reached by the robot in the time of generating the motion elements, and equally dividing the translational motion speed interval into m-1 parts and equally dividing the yaw velocity interval into N-1 parts according to the number N of the generated motion elements, wherein N is m x N; and (3) taking the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain a motion element generated under the control vector. In this way, the reachable state of the robot in the time of generating the motion primitives is determined according to the kinematic constraints of the robot, so that the motion primitives under various different control vectors are generated, the problems that the robot is easy to fall into local minimum or difficult to track paths when the robot carries out path tracking control can be avoided, and the generation process of the motion primitives is simple.
The robot motion primitive determining method provided by the embodiment of the invention can be used for generating motion primitives for various differentially driven robots, so that the robot path planning is realized.
In this embodiment, it is assumed that the robot works on a flat ground, and therefore, the robot can be operated on a machineThe motion of the person is simplified by considering only the translation of the robot in the x, y (also can be written: X, Y) direction and the yaw motion around the z-axis, ignoring the displacement in the vertical direction, the pitch angle and the roll angle, as shown in fig. 2, where v denotes the velocity of the translation motion of the robot and v denotes the velocity of the translation motion of the robotx、vyThe translational motion speeds of the robot along the x direction and the y direction are respectively, omega represents the yaw velocity of the robot, and then x and y should satisfy the kinematic constraint condition of the formula (1):
wherein x and y respectively represent the displacement of the robot along the x direction and the y direction,
respectively representing first derivatives of x and y to time, v representing the translational motion speed of the robot, theta representing the heading angle of the robot, and theta being equal to 0 and 2 pi;
if z is [ x, y, theta ]]TRepresents a state vector, u ═ v, ω]TThe control vector is expressed, omega represents the yaw velocity of the robot, and the state transition equation expression of the robot can be obtained according to the formula (1):
in this embodiment, assume that the initial state vector of the robot is zs＝[xs,ys,θs]TThe starting control vector is us＝[vs,ωs]TWherein z represents a state vector, subscript s represents a start, and superscript T represents a matrix transpose; the acceleration of the robot during the translational motion and the yaw angular acceleration of the robot during the yaw motion are respectively represented by a and alpha, and the translational motion speed section which can be reached by the robot within the time (also called simulation time) t generated by the motion elements is [ v [ v ] ]s-at,vs+at](wherein v ∈ [ v [ ]s-at,vs+at]) And a yaw angular velocity interval of [ omega ]s-αt,ωs+αt](wherein ω ∈ [ ω ])s-αt,ωs+αt])。
In the embodiment, according to the number N of generated robot motion elements, a translational motion speed interval is equally divided into m-1 parts, a yaw angular velocity interval is equally divided into N-1 parts, and the following conditions are met: n — m × N, then: translational motion speed corresponding to endpoint i
Yaw rate corresponding to endpoint j
In the present embodiment, during the time of motion primitive generation, u ═ vi,ωj]TThe constant speed is used as a control vector, and the robot is determined at the sampling time t according to the determined initial state vector of the robot and the kinematic constraint of the robotfThe time-dependent state is:
wherein u represents a control vector, (x)f,yf,θf) Indicating that the robot is at the sampling time tfState vector of time, tfRefers to any sampling moment in the simulation time t generated by the motion primitive;
in this embodiment, the sampling time t of the robot within the simulation time t of the motion primitive generation can be obtained according to equation (3)fSampling state of time (x)f,yf,θf) These sampling states are discrete points on the motion primitive, which are connected to form different motion primitives, resulting in a control vector u ═ vi,ωj]TThe next generated motion primitive.
In an embodiment of the foregoing method for determining a robot motion primitive, further, the connecting the state vectors at different sampling time instants within the time of generating the motion primitive to obtain the motion primitive generated under the control vector includes:
in the time of generating the motion primitive, if the termination state vector is not at the grid center of the environment map, translating the termination state vector to the grid center by adopting a rounding method;
connecting the state vectors at different sampling times to obtain a control vector u ═ vi,ωj]TThe next generated motion primitive.
In order to better understand the robot motion primitive determination method provided by the embodiment of the invention, the robot starting state vector z is useds＝[0,0,0]TAnd control vector u ═ vi,ωj]TGenerating robot motion primitives for example:
first, the acceleration a of the robot during translational motion is set to 0.5m/s2And the yaw angular acceleration of the robot during the yaw movement is alpha which is 0.25rad/s2. Within the time (simulation time) 2s of the generation of the motion primitive, the translational motion speed interval of the robot is [ -1m/s, 1m/s]The yaw angular velocity interval is [ -0.5rad/s, 0.5rad/s]。
Then, the translational velocity interval of the robot is equally divided into two parts to obtain 3 end points, namely-1 m/s, 0m/s and 1m/s respectively, and the yaw velocity interval is equally divided into two parts to obtain 3 end points, namely-0.5 rad/s, 0rad/s and 0.5rad/s respectively, so that the number of robot motion elements which can be generated is 9. Combining the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to obtain control vectors u1＝[-1,-0.5]T，u2＝[-1,0]T，u3＝[-1,0.5]T，u4＝[0,-0.5]T，u5＝[0,0]T，u6＝[0,0.5]T，u7＝[1,-0.5]T，u8＝[1,0]TAnd u9＝[1,0.5]T. In the simulation time 2s, the control vector is substituted into the formula (3), and the state vector of the robot can be calculated; specifically, the method comprises the following steps: sampling is carried out by taking 0.05s as a sampling period, and the motion primitives generated under the corresponding control vectors can be obtained by connecting the state vectors of the robot.
As shown in FIG. 3, FIG. 3 is an on-controlSystem vector u9＝[1,0.5]TAnd (3) generating a motion primitive under action, wherein arrows in the figure 3 represent the heading angles of the robot state sampling points. For the starting state of the robot, the robot motion primitive is calculated by all the control vectors, and the motion primitive of the robot in the starting state can be obtained, as shown in fig. 4, and fig. 4 shows the vector z of the robot in the starting states＝[0,0,0]TAnd the lower motion element comprises two pivot-turning motion elements and a static motion element.
Example two
The present invention also provides a specific embodiment of a robot motion primitive determining apparatus, which corresponds to the specific embodiment of the robot motion primitive determining method, and the robot motion primitive determining apparatus can achieve the object of the present invention by executing the flow steps in the specific embodiment of the method, so the explanation in the specific embodiment of the robot motion primitive determining method is also applicable to the specific embodiment of the robot motion primitive determining apparatus provided by the present invention, and will not be described again in the following specific embodiment of the present invention.
As shown in fig. 5, an embodiment of the present invention further provides a robot motion primitive determining apparatus, including:
the determining module 11 is used for determining an initial state vector of the robot;
an equally dividing module 12, configured to determine a translational motion speed interval and a yaw rate interval reached by the robot within the time of generating the motion primitives, and equally divide the translational motion speed interval into m-1 parts and the yaw rate interval into N-1 parts according to the generated number N of the motion primitives, where N is m × N;
and the generating module 13 is configured to obtain a control vector formed by the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j, determine the state of the robot according to the determined starting state vector of the robot and the kinematic constraint of the robot, and connect the states of the robot to obtain a motion primitive generated under the control vector, where i is 1, 2.
The robot motion primitive determining device determines an initial state vector of a robot; determining a translational motion speed interval and a yaw velocity interval which are reached by the robot in the time of generating the motion elements, and equally dividing the translational motion speed interval into m-1 parts and equally dividing the yaw velocity interval into N-1 parts according to the number N of the generated motion elements, wherein N is m x N; and (3) taking the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain a motion element generated under the control vector. In this way, the reachable state of the robot in the time of generating the motion primitives is determined according to the kinematic constraints of the robot, so that the motion primitives under various different control vectors are generated, the problems that the robot is easy to fall into local minimum or difficult to track paths when the robot carries out path tracking control can be avoided, and the generation process of the motion primitives is simple.
In an embodiment of the foregoing robot motion primitive determining apparatus, further, the initial state vector is zs＝[xs,ys,θs]TWherein z represents a state vector, x and y represent displacements of the robot along the x direction and the y direction respectively, theta represents a heading angle of the robot, subscript s represents a start, and superscript T represents a matrix transposition.
In an embodiment of the foregoing robot motion primitive determining apparatus, further, the equally dividing module includes:
a first determining unit for determining the translational motion speed interval [ v ] reached by the robot in the time t of the generation of the motion primitives-at,vs+at]And yaw angular velocity interval [ omega ]s-αt,ωs+αt]Wherein v represents the speed of the translational motion of the robot, ω represents the yaw rate of the robot, and a and α represent the acceleration at the translational motion of the robot and the yaw acceleration at the yaw motion, respectively;
an equally dividing unit for generating the number according to the robot motion primitiveN, equally dividing the translational motion speed interval into m-1 parts, equally dividing the yaw angle speed interval into N-1 parts, and satisfying the following conditions: n — m × N, then: translational motion speed corresponding to endpoint i
Yaw rate corresponding to endpoint j
In an embodiment of the foregoing robot motion primitive determining apparatus, further the generating module includes:
a second determination unit for generating a motion primitive with u ═ v in timei,ωj]TThe constant speed is used as a control vector, and the robot is determined at the sampling time t according to the determined initial state vector of the robot and the kinematic constraint of the robotfThe time-dependent state is:
wherein u represents a control vector, (x)f,yf,θf) Indicating that the robot is at the sampling time tfState vector of (x)f,yf,θf) Is a discrete point on the motion primitive, tfAny sampling moment in time t generated by a motion primitive is designated;
a generating unit for connecting the state vectors at different sampling time points within the time of generating the motion primitive to obtain a control vector u ═ vi,ωj]TThe next generated motion primitive.
In an embodiment of the foregoing robot motion primitive determining apparatus, further, the generating unit is configured to, during the time of generating the motion primitive, if the termination state vector is not at the grid center of the environment map, translate the termination state vector to the grid center by a rounding method; also for concatenating the state vectors at different sampling instants, resulting in a control vector u ═ vi,ωj]TThe next generated motion primitive.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (10)
1. A robot motion primitive determination method, comprising:
determining an initial state vector of the robot;
determining a translational motion speed interval and a yaw velocity interval which are reached by the robot in the time of generating the motion elements, and equally dividing the translational motion speed interval into m-1 parts and equally dividing the yaw velocity interval into N-1 parts according to the number N of the generated motion elements, wherein N is m x N;
and taking the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain a motion element generated under the control vector, wherein i is 1, 2.
2. A robot motion primitive determination method according to claim 1, characterized in that the starting state vector is zs＝[xs,ys,θs]TWherein z represents a state vector, x and y represent displacements of the robot along the x direction and the y direction respectively, theta represents a heading angle of the robot, subscript s represents a start, and superscript T represents a matrix transposition.
3. The robot motion primitive determining method according to claim 2, wherein the determining the translational motion velocity section and the yaw velocity section reached by the robot within the time of the motion primitive generation, and the equally dividing the translational motion velocity section into m parts and the equally dividing the yaw velocity section into N parts according to the number N of the motion primitive generation comprises:
determining the translation motion speed interval [ v ] reached by the robot in the time t generated by the motion primitives-at,vs+at]And yaw angular velocity interval [ omega ]s-αt,ωs+αt]Wherein v represents the speed of the translational motion of the robot, ω represents the yaw rate of the robot, and a and α represent the acceleration at the translational motion of the robot and the yaw acceleration at the yaw motion, respectively;
according to the number N of the robot motion elements, equally dividing a translational motion speed interval into m-1 parts, equally dividing a yaw angle speed interval into N-1 parts, and satisfying the following conditions: n — m × N, then: translational motion speed corresponding to endpoint i
Yaw rate corresponding to endpoint j
4. The method for determining robot motion primitives according to claim 3, wherein the step of taking the translational motion velocity corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain the motion primitives generated under the control vector comprises the steps of:
within the time of motion primitive generation, with u ═ vi,ωj]TThe constant speed is used as a control vector, and the robot is determined at the sampling time t according to the determined initial state vector of the robot and the kinematic constraint of the robotfThe time-dependent state is:
wherein u represents a control vector, (x)f,yf,θf) Indicating that the robot is at the sampling time tfState vector of (x)f,yf,θf) Is a discrete point on the motion primitive, tfAny sampling moment in time t generated by a motion primitive is designated;
connecting state vectors at different sampling moments in the time of generating the motion primitive to obtain a control vector u ═ vi,ωj]TThe next generated motion primitive.
5. The robot motion primitive determining method according to claim 4, wherein the state vectors at different sampling time are connected in the time of motion primitive generation to obtain a control vector u ═ vi,ωj]TThe following generated motion primitives include:
in the time of generating the motion primitive, if the termination state vector is not at the grid center of the environment map, translating the termination state vector to the grid center by adopting a rounding method;
connecting the state vectors at different sampling times to obtain a control vector u ═ vi,ωj]TThe next generated motion primitive.
6. A robot motion primitive determination apparatus, comprising:
the determining module is used for determining an initial state vector of the robot;
the robot comprises an equally dividing module, a judging module and a judging module, wherein the equally dividing module is used for determining a translational motion speed interval and a yaw angular velocity interval which are reached by the robot in the time of generating motion primitives, and equally dividing the translational motion speed interval into m-1 parts and equally dividing the yaw angular velocity interval into N-1 parts according to the generated number N of the motion primitives, wherein N is m x N;
and the generating module is used for taking the translational motion speed corresponding to the endpoint i and the yaw velocity corresponding to the endpoint j to form a control vector, determining the state of the robot according to the determined initial state vector of the robot and the kinematic constraint of the robot, and connecting the states of the robot to obtain a motion element generated under the control vector, wherein i is 1,2, and.
7. Robot motion primitive determination device according to claim 6, characterized in that the starting state vector is zs＝[xs,ys,θs]TWherein z represents a state vector, x and y represent displacements of the robot along the x direction and the y direction respectively, theta represents a heading angle of the robot, subscript s represents a start, and superscript T represents a matrix transposition.
8. The robot motion primitive determination device of claim 7, wherein the aliquoting module comprises:
a first determining unit for determining the translational motion speed interval [ v ] reached by the robot in the time t of the generation of the motion primitives-at,vs+at]And yaw angular velocity interval [ omega ]s-αt,ωs+αt]Wherein v represents the speed of the translational motion of the robot, ω represents the yaw rate of the robot, and a and α represent the acceleration at the translational motion of the robot and the yaw acceleration at the yaw motion, respectively;
and the equally dividing unit is used for equally dividing the translational motion speed interval into m-1 parts and the yaw velocity interval into N-1 parts according to the generated number N of the robot motion elements, and meets the following requirements: n — m × N, then: translational motion speed corresponding to endpoint i
Yaw rate corresponding to endpoint j
9. The robot motion primitive determination device of claim 8, wherein the generation module comprises:
a second determination unit for generating a motion primitive with u ═ v in timei,ωj]TThe constant speed is used as a control vector, and the robot is determined at the sampling time t according to the determined initial state vector of the robot and the kinematic constraint of the robotfThe time-dependent state is:
wherein u represents a control vector, (x)f,yf,θf) Indicating that the robot is at the sampling time tfState vector of (x)f,yf,θf) Is a discrete point on the motion primitive, tfAny sampling moment in time t generated by a motion primitive is designated;
a generating unit for connecting the state vectors at different sampling time points within the time of generating the motion primitive to obtain a control vector u ═ vi,ωj]TThe next generated motion primitive.
10. The robot motion primitive determination device according to claim 9, wherein the generation unit is configured to translate the termination state vector to the grid center by a rounding method if the termination state vector is not at the grid center of the environment map during the time of motion primitive generation; also for concatenating the state vectors at different sampling instants, resulting in a control vector u ═ vi,ωj]TThe next generated motion primitive.
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