CN112147889A - Combined obstacle crossing track planning method for quadruped robot - Google Patents
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Abstract
The invention discloses a combined obstacle crossing track planning method for a quadruped robot, which comprises the steps of establishing a CPG model, and controlling the quadruped robot to walk on a flat road surface in a periodic gait through a standard oscillation signal output by the model; when an obstacle appears on a flat road surface, determining an optimal obstacle crossing starting point according to obstacle distance information returned by the sensor, and changing the CPG rhythm regulation step length to enable the robot to reach the optimal obstacle crossing starting point in the previous step of obstacle crossing; and drawing a track of the obstacle crossing foot end based on an improved composite cycloid rule, and controlling the robot to cross the obstacle. The invention combines the traditional CPG strategy and the foot end trajectory planning strategy, and realizes the stable obstacle crossing of the quadruped robot.
Description
Technical Field
The invention relates to the field of gait planning of quadruped robots, in particular to a combined obstacle crossing track planning method of the quadruped robot.
Background
With the development of industrial technology, the quadruped robot has good mobility and can traverse a complex environment with obstacles. Reasonable selection of landing points under terrain conditions of disturbed distribution is a key capability of quadruped robots, especially special-purpose robots. While numerous control methods have been used to control the motion of quadruped robots, their performance is still far behind that of animals in the biological world.
Compared with other control strategies, the biological control method based on the Central Pattern Generator (CPG) can effectively improve the motion stability and environmental adaptability of the robot by using the characteristics of the motion mode of animals in the nature, and the energy consumption is lower than that of a foot-end track method under the same route. Through the motion observation of the quadruped organisms, the gait of the organisms on the flat ground approaches to the periodic gait, but tends to the free gait on the undulating ground, and the phase relation and the step length period in the gait period can be planned in real time according to the external environment. The traditional CPG lacks the interaction with external environment information, so the CPG is more suitable for generating regular rhythm gait on a flat road surface. The appearance of the obstacle breaks the rhythm of the robot, and if the CPG method is continuously adopted for obstacle crossing, although the obstacle crossing can be realized by adjusting feedback parameters, the control process is complicated, the traditional CPG obstacle crossing method is complex in design, and the generated angle signal cannot intuitively represent the obstacle crossing track. At the moment, the method based on foot end trajectory planning is more direct, the contact between the foot end and the obstacle can be effectively avoided, the obstacle shape is attached, and the performance is better.
Disclosure of Invention
The invention aims to provide a combined obstacle crossing track planning method for a four-footed robot, which solves the problem that the four-footed robot suddenly encounters obstacles when walking normally under CPG rhythm gait.
The technical solution for realizing the purpose of the invention is as follows: a four-foot robot composite obstacle crossing trajectory planning method comprises the following steps:
step 2, when an obstacle appears on a flat road surface, determining an optimal obstacle crossing starting point, and changing the CPG rhythm regulation step length according to obstacle distance information returned by the sensor so that the robot reaches the optimal obstacle crossing starting point in the previous step of obstacle crossing;
and 3, drawing a track of the obstacle crossing foot end based on a composite cycloid rule, and controlling the robot to cross the obstacle.
Further, in step 1, a CPG model is established, and a quadruped robot is controlled to walk on a flat road surface with periodic gait by a standard oscillation signal output by the model, specifically:
the CPG model adopts a Hopf oscillator as a unit model of the CPG, the movement of hip joints and knee joints of four legs is respectively controlled through 4 Hopf harmonic oscillators, the coordination among the feet of the four feet is realized by constructing a specific phase relation among the 4 oscillators, and the formed mathematical model of the CPG model is as follows:
in the formula, xiAnd yiIs the output of each leg rhythm oscillator, x, of the four-legged robotiIs the hip joint trajectory of the ith leg, yiIs the knee joint trajectory of the jth leg; r isi 2＝xi 2+yi 2；ωiAdjusting the coefficient for the frequency of the oscillator; μ is the oscillator amplitude adjustment coefficient; alpha is a constant coefficient and is used for controlling the speed of the oscillator converging to a limit ring;
the transformation matrix from the oscillator j to the oscillator i is used for explaining the phase relationship between every two oscillators and is defined as the following formula:
wherein
Representing the phase difference of oscillator i and oscillator j;
and converting the signal output by the CPG into an angle control signal of the hip and knee joint, wherein the mapping relation is as follows:
wherein, thetahiAnd thetakiAngle control signals for hip joint and knee joint on ith leg, respectively, AkAnd AhThe amplitude of the knee and hip joint movements, respectively.
Further, in step 2, according to the obstacle distance information returned by the sensor, an optimal obstacle crossing starting point is determined, and the CPG rhythm adjustment step length is changed, so that the robot reaches the obstacle crossing starting point one step before obstacle crossing, specifically:
the control of the step length of a single leg is realized by adjusting the positive and negative values of the hip joint angle signal, so that the robot can fall to the optimal obstacle crossing starting point, and the correlation between the step length and the positive and negative values of the hip joint is as follows:
Si＝L sinθhi -+L sinθhi +
wherein S isiRepresents the step length of the ith leg of the four-legged robot, L represents the leg length, and thetahi -And thetahi +Respectively representing the positive and negative values of the hip joint angle signal.
Further, in step 3, a obstacle crossing foot end track is drawn based on a composite cycloid rule to control the robot to cross the obstacle, and the specific method is as follows:
the improved compound cycloid method is adopted to correct the step height function in the z-axis direction so as to solve the problem of leg lifting instant acceleration jump, and the compound cycloid equation is as follows:
wherein S and H respectively represent the step length and the step height of the foot end track of the quadruped robot; t is gait cycle; t is sampling time; x is a robot step function with respect to time t; z is a function of the robot step-up with respect to time t.
Further, in step 3, the optimal step length of the obstacle crossing trajectory is determined on the premise of the lowest energy consumption, and specifically:
a certain mathematical relationship exists between the leg lifting height and the optimal step length:
wherein S represents the step length of the obstacle-crossing leg, M is the mass of a single leg, M is the mass of the robot body, H is the leg lifting height, H is the height of the center of mass of the robot body in the upright state of the robot, and c is the equivalent distance (c belongs to [0, H/2]) for the leg swinging and landing process to work; and determining the leg lifting height H according to the known height information of the obstacle, solving the step length S which enables the robot to have the lowest energy consumption in the obstacle crossing process by using the mathematical model, and substituting the step length S into a foot end track formula to obtain the obstacle crossing foot end track.
A combined obstacle crossing track planning system of a four-foot robot uses the combined obstacle crossing track planning method of the four-foot robot to plan obstacle crossing tracks, and comprises the following steps:
the flat motion module is used for establishing a CPG model and controlling the quadruped robot to walk on a flat road surface in a periodic gait through a standard oscillation signal output by the model;
the obstacle crossing preparation module is used for determining an optimal obstacle crossing starting point when an obstacle appears on a flat road surface, and changing the CPG rhythm regulation step length according to obstacle distance information returned by the sensor so that the robot can reach the optimal obstacle crossing starting point in the previous step of obstacle crossing;
and the obstacle crossing module is used for drawing the track of the obstacle crossing foot end based on the composite cycloid rule and controlling the robot to cross the obstacle.
A computer device comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the processor realizes the combined obstacle crossing trajectory planning method of the quadruped robot when executing the computer program.
A computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the above-described quadruped robot compound obstacle crossing trajectory planning method.
Compared with the prior art, the invention has the following remarkable advantages: 1) changing the CPG rhythm in the step before obstacle crossing based on the obstacle environment model to enable the swing legs of the robot to fall to the optimal obstacle crossing starting point which is planned in advance; 2) aiming at the problem that the traditional compound cycloid equation has sudden change of the acceleration of the initial point and the drop foot point, the compound cycloid equation is corrected, the obstacle crossing foot end track which is in a shape of an obstacle is designed, the energy consumption is reduced, and accurate and stable obstacle crossing is realized.
Drawings
FIG. 1 is a block flow diagram of the present invention.
FIG. 2 is an illustration of the advancing direction of a single leg of a quadruped robot
Fig. 3 is a schematic diagram of an obstacle crossing track of the quadruped robot.
FIG. 4 is a diagram of simulation obstacle surmounting of the webots platform.
Fig. 5 is a trajectory planning curve for the foot end of the obstacle crossing leg.
Fig. 6 shows the hip joint and knee joint angle changes of the quadruped robot.
Fig. 7 is a graph of foot end trajectory at various stages of an obstacle crossing leg.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
As shown in fig. 1, a method for planning a composite obstacle crossing trajectory of a quadruped robot includes the following steps:
further, the specific method of CPG modeling is:
the Hopf oscillators are used as a unit model of the CPG, the 4 Hopf harmonic oscillators respectively control the movement of hip joints and knee joints of four legs, and the inter-foot coordination of four feet is realized by constructing a specific phase relation among the 4 oscillators. The mathematical model of the formed CPG network is as follows:
in the formula, xiAnd yiIs the output of each leg rhythm oscillator, x, of the four-legged robotiIs the hip joint trajectory of the ith leg, yiIs the knee joint trajectory of the jth leg; r isi 2＝xi 2+yi 2；ωiAdjusting the coefficient for the frequency of the oscillator; μ is the oscillator amplitude adjustment coefficient; alpha is a constant coefficient and is used for controlling the speed of the oscillator converging to a limit ring; r (theta)i j) The transformation matrix from the oscillator j to the oscillator i is used for explaining the phase relationship between every two oscillators and is defined as the following formula:
wherein theta isi jRepresenting the phase difference of oscillator i and oscillator j.
And converting the signal output by the CPG into an angle control signal of the hip and knee joint, wherein the mapping relation is as follows:
wherein, thetahiAnd thetakiAngle control signals for hip joint and knee joint on ith leg, respectively, AkAnd AhThe amplitude of the knee and hip joint movements, respectively. By varying thetahiAnd thetakiGenerate different gait signals, thereby realizing the rhythm gait of the quadruped robot on the flat ground.
Step 2, when an obstacle appears on a flat road surface, determining an optimal obstacle crossing starting point, and changing the CPG rhythm regulation step length according to obstacle distance information returned by the sensor so that the robot reaches the optimal obstacle crossing starting point in the previous step of obstacle crossing;
further, the specific method for the robot to change the CPG rhythm regulation step length is as follows:
in order to simplify the calculation and facilitate the control, the output signal of only the hip joint angle is changed in the CPG model mapping described in step 1, fig. 2 is an example of the advancing direction of one leg of the quadruped robot, and the correlation between the step size and the positive and negative angle values of the hip joint can be obtained as follows:
Si＝L sinθhi -+L sinθhi +
wherein S isiRepresents the step length of the ith leg of the four-legged robot, L represents the leg length, and thetahi -And thetahi +And respectively representing the positive and negative values of the hip joint angle signal, taking the vertical line as a boundary, taking the left side as the boundary, taking the right side as the boundary, and dividing the positive and negative values so as to conveniently and freely adjust the step length in the second step. And step one, the step is moved on the flat ground, and the step length of each period is not changed, namely the positive and negative are equal, so that the positive and negative are not required to be divided.
Step 3, drawing an obstacle crossing track based on a composite cycloid rule, setting a step length based on the lowest energy consumption principle, further obtaining a low-impact obstacle crossing track fitting the shape of an obstacle, and enabling the swing legs to cross the obstacle;
further, the specific method for planning the foot end track by improving the compound cycloidal method comprises the following steps:
in order to achieve ideal obstacle-crossing gait, make the movement safer, the gait smooth and good, the planned foot end trajectory needs to meet the following constraint conditions:
(1) the foot end track of the quadruped robot starts to fall to the obstacle crossing starting point planned in advance and ends at the target point;
(2) in the whole swing period, all parts of the foot end and the leg part do not collide and contact with the barrier;
(3) the foot end track in the swing period of the quadruped robot is smooth, and the joint angle, the angular velocity and the angular acceleration are continuous, smooth and have no sudden change;
(4) the joint angle, the angular speed and the joint moment of each leg of the robot do not exceed the allowable range;
(5) the leg lifting and landing are carried out by swinging the legs and landing at the same moment, so that the leg lifting and landing are carried out at the foot end with zero impact;
the traditional method adopts a compound cycloid formal equation as the foot end locus of the swing leg of the quadruped robot, and the form is as follows:
wherein S and H respectively represent the step length and the step height of the foot end track of the quadruped robot; t is gait cycle; t is sampling time; x (t) is a robot step function with respect to time t; z (T) is the robot step height function with respect to time T, the acceleration equation of which is a multiple of the cosine function, where T is 0 and T is TmAcceleration jump can occur at any moment, and the instant of lifting the leg requires to generate larger contact force. Aiming at the problem of acceleration abrupt change, the invention corrects the step height function in the z-axis direction.
Designing trajectory equations with T-0 and T-TmAt the moment, because the swing legs move on the z axis and need to lift and then fall, the z-axis displacement curve is solved by using a method of sine mode motion of the x axis of the cycloid equation
Where n is a natural number, and n is 0,1,2,3, …. The velocity function can be determined by integration
Wherein C is a constant generated by integration, and according to the speed requirement of the foot end of the robot: to obtain
And
further obtaining:
when k is 1, the track of the foot end of the quadruped robot is displayed as an oblique line in an Oxz plane, and the performance of the quadruped robot for crossing the obstacle is influenced; if the k value is larger, the addition and subtraction of the foot end speed of the quadruped robot are frequently changed, and the leg performance consumption is increased, so that the k is reasonably considered to be 2.
Integral determination of displacement
Wherein, C2Is a constant generated by integration, z is required by the trackt＝0＝0、
And
the motion curve equation in the z-axis direction is obtained by a piecewise function method as follows:
and (3) obtaining an improved composite cycloid equation after arrangement, namely an obstacle crossing trajectory function:
the robot may modify parameters S, H and T according to different motion environments and speed requirements. The invention is based on the scene that the robot meets the obstacle under the CPG rhythm gait, the obstacle information can be obtained by a sensor, and if the obstacle can be crossed, the obstacle crossing strategy provided by the invention is implemented. The following mathematical model provides a theoretical basis for the existence of the optimal step size on the premise of the lowest energy consumption: a certain mathematical relationship exists between the leg lifting height and the optimal step length:
wherein M is the mass of a single leg, M is the mass of a robot body, H is the leg lifting height, H is the height of the mass center of the robot body in the upright state of the robot, and c is the equivalent distance (c is equal to 0, H/2) for doing work in the process of falling to the ground by swinging the phase leg. And determining the leg lifting height H according to the known height information of the obstacle, solving the step length S which enables the robot to have the lowest energy consumption in the obstacle crossing process by using the mathematical model, substituting the step length S into a foot end track formula to obtain an obstacle crossing foot end track, wherein the obstacle crossing schematic diagram is shown in figure 3.
Examples
In order to verify the validity of the scheme of the invention, simulation experiments are carried out.
A quadruped robot is built on a Webots simulation platform, and is shown in figure 4. The basic parameters of the robot are as follows: and (3) constructing a circular obstacle with the radius of 5 cm, wherein M is 10kg, M is 100kg, h is 0.6M, and setting the obstacle crossing step height of the robot according to the obstacle height information: h is 0.1m and c is 0. Then based on the above parameters, the optimal step length can be calculated by the optimal step length formula:
the swing period T is set to 0.5s, and a foot end trajectory curve obtained by simulation in MATLAB is shown in fig. 5. As can be seen from fig. 5, the simulated trajectory substantially meets the expected requirements. The obstacle crossing motion trajectory curve is smooth and continuous, the obstacle crossing position requirement is met, sudden change does not exist at the starting moment and the ending moment, and the acceleration and the speed are zero, so that the impact on the ground is small. During crossing of the upper plane of the obstacle, the curve is almost horizontalThis means that both the velocity and the acceleration are approximately equal to 0, which effectively reduces the impact of a possible obstacle crossing during the actual obstacle crossing.
The angular changes of the hip joint and the knee joint can be obtained by solving the cycloid equation based on the foot end trajectory planning through the four-foot robot kinematics inverse solution as shown in fig. 6. The response of the joint angle is consistent with the obstacle crossing trajectory shown in fig. 5, and it can be seen that the simulation result conforms to the planned obstacle crossing trajectory.
Fig. 7 shows the overall process of the composite obstacle crossing trajectory planning strategy presented herein. The first stage corresponds to the foot end track of the robot walking on a flat road with the periodic gait of the CPG; the second stage changes the CPG rhythm, adjusts the stride, and changes the rhythm corresponding to the obstacle crossing previous step to reach the track of the optimal obstacle crossing starting point; and the third stage corresponds to a composite cycloid foot end obstacle crossing track which crosses the optimal step length based on the lowest energy consumption, and the track has the characteristic of fitting the shape of an obstacle.
The invention mainly solves the problem of stable walking control of the quadruped robot when encountering obstacles suddenly under the CPG rhythm gait. Aiming at the background that a quadruped robot suddenly meets an obstacle on a flat road surface, a CPG and foot end track combined composite obstacle crossing strategy is provided, and the original CPG rhythm gait is switched to the obstacle crossing gait to realize stable obstacle crossing. Firstly, CPG rhythm is changed in one step before obstacle crossing based on an obstacle environment model, so that a swing leg of a robot falls to a pre-planned optimal obstacle crossing initial point, and then a composite cycloid equation is corrected aiming at the problem that the acceleration of the initial point and the falling point suddenly changes in the traditional composite cycloid equation. A planned obstacle crossing curve is obtained through simulation in MATLAB, a four-legged robot is built on a Webots platform, the obstacle crossing process under the strategy is shown, the effectiveness of the strategy is verified through the simulation result, the designed obstacle crossing foot end track is attached to the shape of the obstacle, the energy consumption is lower, and accurate and stable obstacle crossing is realized.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (8)
1. A four-foot robot composite obstacle crossing track planning method is characterized by comprising the following steps:
step 1, establishing a CPG model, and controlling a quadruped robot to walk on a flat road surface in a periodic gait through a standard oscillation signal output by the model;
step 2, when an obstacle appears on a flat road surface, determining an optimal obstacle crossing starting point according to obstacle distance information returned by the sensor, and changing the CPG rhythm regulation step length to enable the robot to reach the optimal obstacle crossing starting point in the previous step of obstacle crossing;
and 3, drawing a track of the obstacle crossing foot end based on a composite cycloid rule, and controlling the robot to cross the obstacle.
2. The method for planning the composite obstacle crossing trajectory of the quadruped robot according to claim 1, wherein in step 1, a CPG model is established, and the quadruped robot is controlled to walk on a flat road surface with periodic gait by a standard oscillation signal output by the model, specifically:
the CPG model adopts a Hopf oscillator as a unit model of the CPG, the movement of hip joints and knee joints of four legs is respectively controlled through 4 Hopf harmonic oscillators, the coordination among the feet of the four feet is realized by constructing a specific phase relation among the 4 oscillators, and the formed mathematical model of the CPG model is as follows:
in the formula, xiAnd yiIs the output of each leg rhythm oscillator, x, of the four-legged robotiIs the hip joint trajectory of the ith leg, yiIs the knee joint trajectory of the jth leg; r isi 2＝xi 2+yi 2；ωiAdjusting the coefficient for the frequency of the oscillator; μ is the oscillator amplitude adjustment coefficient; alpha is a constant coefficient and is used for controlling the speed of the oscillator converging to a limit ring;
the transformation matrix from the oscillator j to the oscillator i is used for explaining the phase relationship between every two oscillators and is defined as the following formula:
wherein theta isi jRepresenting the phase difference of oscillator i and oscillator j;
and converting the signal output by the CPG into an angle control signal of the hip and knee joint, wherein the mapping relation is as follows:
wherein, thetahiAnd thetakiAngle control signals for hip joint and knee joint on ith leg, respectively, AkAnd AhThe amplitude of the knee and hip joint movements, respectively.
3. The method for planning the composite obstacle crossing trajectory of the quadruped robot according to claim 1, wherein in step 2, the optimal obstacle crossing starting point is determined according to the obstacle distance information returned by the sensor, and the CPG rhythm adjustment step length is changed to enable the robot to reach the obstacle crossing starting point in the previous step of obstacle crossing, specifically:
the control of the step length of a single leg is realized by adjusting the positive and negative values of the hip joint angle signal, so that the robot can fall to the optimal obstacle crossing starting point, and the correlation between the step length and the positive and negative hip joint angle values is as follows:
Si＝Lsinθhi -+Lsinθhi +
wherein S isiRepresents the step length of the ith leg of the four-legged robot, L represents the leg length, and thetahi -And thetahi +Respectively representing the positive and negative values of the hip joint angle signal, with the vertical line as the boundary, the left side as the negative, and the right side as the positive.
4. The four-legged robot combined obstacle crossing trajectory planning method according to claim 1, wherein in step 3, a trajectory of an obstacle crossing foot end is planned based on a combined cycloid rule, and a robot is controlled to cross an obstacle, and the specific method is as follows:
the improved compound cycloid method is adopted to correct the step height function in the z-axis direction so as to solve the problem of leg lifting instant acceleration jump, and the compound cycloid equation is as follows:
wherein S and H respectively represent the step length and the step height of the foot end track of the quadruped robot; t is gait cycle; t is sampling time; x is a robot step function with respect to time t; z is a function of the robot step-up with respect to time t.
5. The four-legged robot composite obstacle crossing trajectory planning method according to claim 1, wherein in step 3, the optimal step length of the obstacle crossing trajectory is determined on the premise of lowest energy consumption, specifically:
a certain mathematical relationship exists between the leg lifting height and the optimal step length:
wherein S represents the step length of the leg crossing the obstacle, M is the mass of a single leg, M is the mass of the robot body, H is the leg lifting height, H is the height of the mass center of the robot body in the upright state of the robot, and c (c belongs to [0, H/2]) is the equivalent distance for the working process of the swing phase leg falling to the ground; and determining the leg lifting height H according to the known height information of the obstacle, solving the step length S which enables the robot to have the lowest energy consumption in the obstacle crossing process by using the mathematical model, and substituting the step length S into a foot end track formula to obtain the obstacle crossing foot end track.
6. A four-legged robot composite obstacle crossing trajectory planning system, which is characterized in that the obstacle crossing trajectory planning method of any one of claims 1 to 5 is used for planning the obstacle crossing trajectory, and comprises the following steps:
the flat motion module is used for establishing a CPG model and controlling the quadruped robot to walk on a flat road surface in a periodic gait through a standard oscillation signal output by the model;
the obstacle crossing preparation module is used for determining an optimal obstacle crossing starting point according to obstacle distance information returned by the sensor when an obstacle appears on a flat road surface, and changing the CPG rhythm regulation step length to enable the robot to reach the optimal obstacle crossing starting point in the previous step of obstacle crossing;
and the obstacle crossing module is used for drawing the track of the obstacle crossing foot end based on the improved composite cycloid rule and controlling the robot to cross the obstacle.
7. A computer apparatus comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the quadruped robotic compound obstacle crossing trajectory planning method of any one of claims 1-5 when executing the computer program.
8. A computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the quadruped robot compound obstacle crossing trajectory planning method of any one of claims 1-5.
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| CN113771046A (en) * | 2021-10-25 | 2021-12-10 | 中国北方车辆研究所 | Method for planning swing track of minimum Jerk index |
| CN113867350A (en) * | 2021-09-28 | 2021-12-31 | 北京炎凌嘉业机电设备有限公司 | Intelligent bionic foot type robot stepping behavior autonomous adaptation method |
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