Active force control method of rimless wheel based on double spring loaded inverted pendulum model

Abstract

The present invention relates to an active force control method for a rimless wheel based on a double-spring-loaded inverted pendulum model. The method takes each movement step of the rimless wheel as a cycle and runs in a cycle; and the supporting leg at the beginning of each movement step and the supporting leg at the end of the movement step are each equivalent to a spring, so that the two equivalent springs and the concentrated mass of the rimless wheel together constitute a double-spring-loaded inverted pendulum model. The active force control method based on the double-spring-loaded inverted pendulum model includes eight main steps, namely, applying compensation force, calculating the starting energy of the current step, calculating the ending energy of the current step, calculating the energy loss value of the current step, estimating the energy compensation value of the next step, calculating the leg stiffness adjustment value, calculating the next step compensation force, and assigning values ​​in the cycle. The present invention provides a leg compensation force calculation and application method for maintaining the energy stability of the rimless wheel system. The overall calculation is fast, and the continuous and stable movement of the rimless wheel in terrains such as horizontal ground and stairs can be achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of rimless wheel motion, and more specifically, provides a rimless wheel active force control method based on a double-spring loaded inverted pendulum model. Background Art

[0002] The boundless wheel is a classic motion mechanism used to simulate footed walking. The boundless wheel mechanism is used as a basic model to explore the intrinsic characteristics and innate factors behind the energy-efficient rhythmic motion of footed bionic gait, and further study the force generation mechanism of the motion on the basis of stable motion. This can provide a basis for the future realization of comprehensive bionics of the human neuromuscular-skeletal system for footed robots.

[0003] Invention patents ZL202110139486.7 and invention patents ZL202110138734.6, respectively, take a flat single-wheeled edgeless wheel model and an asymmetric double-wheeled edgeless wheel model as the objects, and provide their respective motion behavior analysis methods on spatial inclined planes; the invention patent with application number CN202010890342.0 provides a motion behavior regulation method for a symmetrical edgeless wheel model on inclined plane terrain; the invention patent with application number CN202010890340.1 provides a stability regulation method and system for passive rhythmic walking of an asymmetric edgeless wheel model. In these schemes, all of them use only the gravity of the edgeless wheel itself to produce a spontaneous stable motion behavior gait down the inclined plane without using a power source and active control, which belongs to the "passive dynamic walking" technology, and all of them adjust the edgeless wheel model's own structural parameters or initial motion state parameters to achieve the regulation of the edgeless wheel's motion behavior.

[0004] In summary, how to further realize the active force control of the rimless wheel on the basis of the existing technical solutions, so that the rimless wheel can simulate "active dynamic movement" behaviors such as foot running and jumping on non-slope terrain such as flat ground, is an important basic issue and technical development direction in this field. Summary of the invention

[0005] In response to the demand for active force control of edgeless wheels, the present invention proposes an active force control method for edgeless wheels based on a double-spring loaded inverted pendulum model. This scheme realizes active leg force by actively adjusting the stiffness of the supporting legs during the movement of the edgeless wheels, and effectively compensates for the system energy continuously lost due to periodic foot-end collisions, providing a practical technical solution for the edgeless wheels to continuously maintain the system energy state expected by the user.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] An active force control method for a rimless wheel based on a double-spring loaded inverted pendulum model, wherein the rimless wheel comprises inner spokes and an axle, the spokes rotate around the axle; the inner spokes comprise a group of legs; and the total mass of the rimless wheel is m.

[0008] The leg has the ability to exert force along its own axis, and the specific forms of exerting force include moving along its own axis, stretching and retracting along its own axis, and relying on elastic devices attached along its own axis.

[0009] The spring-loaded inverted pendulum model is used to establish the control model of a single leg, that is, all legs are represented by equivalent springs in the control, the length of all equivalent springs in the free state is R0, and their initial stiffness is k.

[0010] The rotation process of the rimless wheel on the ground includes a single-leg support rotation stage and a double-leg support rotation stage; if any leg is in a support state and the leg is parallel to the coronal plane, this moment is recorded as the beginning of a new movement step.

[0011] When the movement of the endless wheel is in the nth step, the equivalent spring corresponding to the leg that is in the supporting state at the beginning of the movement step is called the equivalent spring c. As the endless wheel continues to rotate, when the other leg adjacent to the leg is in the supporting state and the other leg is parallel to the coronal plane, it is recorded as the end of the nth step and the beginning of the n+1th step. The equivalent spring corresponding to the other leg is called the equivalent spring f. That is, if the endless wheel has moved to the nth step, it means that all the legs have been in the supporting state and parallel to the coronal plane a total of n times. The equivalent spring c, the equivalent spring f and the concentrated mass of the endless wheel together constitute a double-spring loaded inverted pendulum model.

[0012] When the movement of the endless wheel is in the nth step, the energy of the endless wheel at the start of the step is marked as the current step starting energy Ecn of the endless wheel, the energy of the endless wheel at the end of the step is marked as the current step ending energy Efn of the endless wheel, the energy lost during this step of movement is marked as the current step energy loss value ΔENn of the endless wheel, the energy actively compensated during this step of movement is marked as the current step energy compensation value ΔEPn of the endless wheel, and the compensation force continuously applied during this step of movement to obtain the current step energy compensation value ΔEPn is marked as the current step compensation force Fn of the endless wheel.

[0013] In a gravitational field with a gravitational acceleration of g, when the movement of the rimless wheel is at the nth step, the method steps for the rimless wheel to perform active force control are as follows:

[0014] Step 1, applying a compensation force in the nth step of the endless wheel according to the current step compensation force Fn calculated in the n-1th step;

[0015] Step 2, calculate the starting energy Ecn of the current step according to the real-time velocity Vcn of the center of mass of the endless wheel at the start of the nth step, the length Rcn of the equivalent spring c at the start of the nth step, and the angle θcn between the equivalent spring c and the vertical direction at the start of the nth step;

[0016] Step 3, calculate the current step termination energy Efn according to the real-time velocity Vfn of the center of mass of the rimless wheel at the end of the nth step, the length Rfn of the equivalent spring f at the end of the nth step, and the angle θfn between the equivalent spring f and the vertical direction at the end of the nth step;

[0017] Step 4, calculating the current step energy loss value ΔENn according to the current step starting energy Ecn, the current step ending energy Efn, and the current step energy compensation value ΔEPn;

[0018] Step 5, estimating the next step energy compensation value ΔEPn+1 according to the current step energy loss value ΔENn, the current step termination energy Efn, and the expected next step termination energy Efdes;

[0019] Step 6, calculating the leg stiffness adjustment value Δk according to the next energy compensation value ΔEPn+1;

[0020] Step 7, calculating the next compensation force Fn+1 according to the leg stiffness adjustment value Δk, the real-time length Rc of the equivalent spring c, and the real-time length Rf of the equivalent spring f;

[0021] Step 8, after the nth step of the boundless wheel is completed, the value of n+1 is assigned to n, that is, the value of Fn+1 is assigned to Fn and the value of ΔEPn+1 is assigned to ΔEPn at the same time, and the process returns to step 1 and loops until the motion task is completed.

[0022] Among them, the length Rfn of the equivalent spring f at the end of the nth step is equal to the length Rcn+1 of the equivalent spring c at the beginning of the n+1th step.

[0023] The specific method for calculating the starting energy Ecn of the current step in step 2 is:

[0024] Ecn=m×(Vcn) 2 / 2+m×g×Rcn×cos(θcn)+k×(R0-Rcn) 2 / 2;

[0025] If the value of the angle θcn is 0, the calculation method of the starting energy Ecn of the current step is simplified to:

[0026] Ecn=m×(Vcn) 2 / 2+m×g×Rcn+k×(R0-Rcn) 2 / 2.

[0027] If the rimless wheel is a simplified plane rimless wheel and it moves on a horizontal ground, the value of the angle θcn is 0.

[0028] The specific method for calculating the current step termination energy Efn in step 3 is:

[0029] Efn=m×(Vfn) 2 / 2+m×g×Rfn×cos(θfn)+k×(R0-Rfn) 2 / 2;

[0030] If the value of the angle θfn is 0, the calculation method of the current step termination energy Efn is simplified to:

[0031] Efn=m×(Vfn) 2 / 2+m×g×Rfn+k×(R0-Rfn) 2 / 2.

[0032] If the rimless wheel is a simplified plane rimless wheel and it moves on a horizontal ground, the value of the angle θfn is 0.

[0033] The specific method for calculating the energy loss value ΔENn of the current step in step 4 is:

[0034] ΔENn=Ecn+ΔEPn-Efn.

[0035] The specific method for estimating the next energy compensation value ΔEPn+1 in step 5 is:

[0036] ΔEPn+1=Efdes+ΔENn-Efn.

[0037] When the motion of the endless wheel is in step 1, that is, the value of n is 1, the value of the current step energy compensation value ΔEPn in step 4 is:

[0038] ΔEPn=0.

[0039] The specific method for calculating the leg stiffness adjustment value Δk in step 6 is:

[0040] Δk=2×(ΔEPn+1) / (R0-Rfn) 2 .

[0041] A specific method for calculating the next compensation force Fn+1 in step 7 is:

[0042] If only the equivalent spring c is in the supporting state, then

[0043] Fn+1=Δk×(R0-Rc)=2×(ΔEPn+1)×(R0-Rc) / (R0-Rfn) 2 ;

[0044] If only the equivalent spring f is in the supporting state, then

[0045] Fn+1=Δk×(R0-Rf)=2×(ΔEPn+1)×(R0-Rf) / (R0-Rfn) 2 .

[0046] Another specific method for calculating the next compensation force Fn+1 in step 7 is:

[0047] If only the equivalent spring c is in the supporting state, then

[0048] Fn+1=Δk×(Rc-Rfn)=2×(ΔEPn+1)×(Rc-Rfn) / (R0-Rfn) 2 ;

[0049] If only the equivalent spring f is in the supporting state, then

[0050] Fn+1=Δk×(Rf-Rfn)=2×(ΔEPn+1)×(Rf-Rfn) / (R0-Rfn) 2 .

[0051] In step 1, a compensating force is applied during the nth step of the endless wheel, and its specific action period is from the beginning of the nth step, that is, from the time when the leg corresponding to the equivalent spring c is in a supporting state and parallel to the coronal plane, until the leg is no longer in a supporting state.

[0052] Compared with the prior art, the present invention has the following significant features:

[0053] (1) Based on the double-spring loaded inverted pendulum model, a method for calculating and applying the leg compensation force to maintain the energy stability of the system is given. This method not only enables the continuous and stable movement of the rimless wheel on horizontal ground, small steps, stairs and other terrains, but also gives the rimless wheel a certain active anti-disturbance capability.

[0054] (2) The method of applying force to the axial direction of the leg connecting rod by a boundless wheel is adopted. This axial force can be achieved through various methods such as rapid axial movement of the rigid leg, rapid axial extension and retraction of the retractable leg, and relying on the action of an elastic device attached to the axial direction of the rigid leg. It is easy to implement.

[0055] (3) The energy compensation value, leg stiffness adjustment value, and compensation force value are all estimated in advance, and the overall calculation is fast, which is suitable for application scenarios with fast movement of rimless wheels. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a schematic diagram of the rimless wheel and the double-spring loaded inverted pendulum model thereof according to the present invention.

[0057] Figure 2It is a schematic flow chart of the method for active force control of the endless wheel of the present invention.

[0058] Figure 3 This is an example of force control for a flat edgeless wheel with a spring; Figure 3 (a) shows the schematic diagram of the continuous change of the system compensation force Fn during the movement of the rimless wheel on the step terrain. Figure 3 (b) is a schematic diagram showing the change in speed of the rimless wheel along the sagittal plane horizontal direction during the movement; Figure 3 (c) is a schematic diagram showing the movement of the flat edgeless wheel in the stepped terrain;

[0059] Figure 3 (d) shows a detailed schematic diagram of the stepped terrain. DETAILED DESCRIPTION

[0060] The following is a further detailed description of an active force control method for a rimless wheel based on a double-spring loaded inverted pendulum model proposed by the present invention in combination with the embodiments and drawings. However, the following embodiments are only illustrative, and the protection scope of the present invention is not limited to these embodiments.

[0061] Figure 1 FIG. 1 is a schematic diagram of the edgeless wheel and its double spring loaded inverted pendulum model according to the present invention. Figure 1 As shown, the rimless wheel in the present invention includes inner spokes and an axle, and the spokes rotate around the axle; the inner spokes include a group of legs; the total mass of the rimless wheel is m.

[0062] The legs of the endless wheels have the ability to exert force along their own axis, and the specific forms of force generation include movement along their own axis, extension and retraction along their own axis, and relying on an elastic device attached along their own axis. Any of the above methods can achieve force generation along the axis of the leg, that is, the legs of the endless wheels can be of high rigidity structure, but have the ability to move quickly along the direction of the leg connecting rod, so as to achieve force generation by relying on the rapid pedaling of the foot end and the ground; the legs of the endless wheels can also be of elastic structure, which can be extended or shortened along the direction of the leg connecting rod like a spring, and thus adjust the active force generation of the legs; the legs of the endless wheels can also be of high rigidity structure, but another elastic device is connected in series along the direction of its leg connecting rod, and the active extension or shortening of the elastic device is relied on to provide the legs with driving force along the direction of the leg connecting rod.

[0063] The spring-loaded inverted pendulum model is used to establish the control model of a single leg, that is, all legs are represented by equivalent springs in the control, the length of all equivalent springs in the free state is R0, and their initial stiffness is k.

[0064] The plane formed by the forward direction of the rimless wheel and the direction of its perpendicular to the ground is defined as the sagittal plane of the rimless wheel, and the plane perpendicular to the sagittal plane and containing its perpendicular to the ground is defined as the coronal plane of the rimless wheel. The rotation process of the rimless wheel on the ground includes a single-leg support rotation stage and a double-leg support rotation stage; if any leg is in a supporting state and the leg is parallel to the coronal plane or the leg connecting rod is in the pre-defined coronal plane, then this moment is recorded as the beginning of a new movement step. The coronal plane here is relative to the forward direction of the rolling of the rimless wheel.

[0065] When the movement of the endless wheel is in the nth step, the equivalent spring corresponding to the leg that is in the supporting state at the beginning of the movement step is called the equivalent spring c. As the endless wheel continues to rotate, when the other leg adjacent to the leg is in the supporting state and the other leg is parallel to the coronal plane or located in the coronal plane, it is recorded as the end of the nth step and the beginning of the n+1th step. The equivalent spring corresponding to the other leg is called the equivalent spring f. That is, if the endless wheel has moved to the nth step, it means that all the legs have been in the supporting state and parallel to the coronal plane a total of n times. The equivalent spring c, the equivalent spring f and the concentrated mass of the endless wheel together constitute a double-spring loaded inverted pendulum model.

[0066] When the movement of the endless wheel is in the nth step, the energy of the endless wheel at the start of the step is marked as the current step starting energy Ecn of the endless wheel, the energy of the endless wheel at the end of the step is marked as the current step ending energy Efn of the endless wheel, the energy lost during this step of movement is marked as the current step energy loss value ΔENn of the endless wheel, the energy actively compensated during this step of movement is marked as the current step energy compensation value ΔEPn of the endless wheel, and the compensation force continuously applied during this step of movement to obtain the current step energy compensation value ΔEPn is marked as the current step compensation force Fn of the endless wheel.

[0067] Figure 2 FIG. 2 is a flow chart of the method for actively controlling the force of the edgeless wheel in the present invention. Figure 2 As shown, in a gravitational field with a gravitational acceleration of g, when the movement of the rimless wheel on the horizontal ground is at the nth step, the method steps for the rimless wheel to perform active force control are:

[0068] Step 1, based on the current step compensation force Fn calculated in the n-1 step, apply the compensation force in the n-step movement of the endless wheel.

[0069] Step 2, calculate the starting energy Ecn of the current step according to the real-time velocity Vcn of the center of mass of the endless wheel at the beginning of the nth step, the length Rcn of the equivalent spring c at the beginning of the nth step, and the angle θcn between the equivalent spring c and the vertical direction at the beginning of the nth step. The real-time velocity Vcn of the center of mass here is a velocity vector in space, which can be decomposed into multiple component velocities.

[0070] Step 3, calculate the current step termination energy Efn based on the real-time velocity Vfn of the center of mass of the rimless wheel at the end of step n, the length Rfn of the equivalent spring f at the end of step n, and the angle θfn between the equivalent spring f and the vertical direction at the end of step n. The real-time velocity Vfn of the center of mass is a velocity vector in space, which can be decomposed into multiple component velocities.

[0071] Step 4, calculate the current step energy loss value ΔENn according to the current step starting energy Ecn, the current step ending energy Efn, and the current step energy compensation value ΔEPn.

[0072] Step 5, based on the current step energy loss value ΔENn, the current step termination energy Efn, and the expected next step termination energy Efdes, estimate the next step energy compensation value ΔEPn+1. The expected next step termination energy Efdes can be given by the user in real time, or calculated in real time according to a pre-set rule; for example, the value of the current step termination energy Efn can be assigned to Efdes, so that the energy of the system in the next step remains constant relative to the current step energy.

[0073] Step 6: Calculate the leg stiffness adjustment value Δk based on the next energy compensation value ΔEPn+1.

[0074] Step 7, calculate the next compensation force Fn+1 based on the leg stiffness adjustment value Δk, the real-time length Rc of the equivalent spring c, and the real-time length Rf of the equivalent spring f.

[0075] Step 8, after the nth step of the boundless wheel is completed, the value of n+1 is assigned to n, that is, the value of Fn+1 is assigned to Fn and the value of ΔEPn+1 is assigned to ΔEPn at the same time, and the process returns to step 1 and loops until the motion task is completed.

[0076] Among them, the length Rfn of the equivalent spring f at the end of the nth step is equal to the length Rcn+1 of the equivalent spring c at the beginning of the n+1th step.

[0077] The specific method for calculating the starting energy Ecn of the current step in step 2 is:

[0078] Ecn=m×(Vcn) 2 / 2+m×g×Rcn×cos(θcn)+k×(R0-Rcn) 2 / 2;

[0079] If the value of the angle θcn is 0, the calculation method of the starting energy Ecn of the current step is simplified to:

[0080] Ecn=m×(Vcn) 2 / 2+m×g×Rcn+k×(R0-Rcn) 2 / 2.

[0081] The calculation of the starting energy Ecn of the current step is divided into three parts, namely the kinetic energy, gravitational potential energy and elastic potential energy of the system, among which the gravitational potential energy at the default horizontal plane height is zero.

[0082] Considering that the real-time velocity Vcn of the center of mass can be obtained by the sensor, and the sensor usually specifically detects the components in each direction along the sensor's own coordinate system, here (Vcn) 2 It can be calculated by the sum of the squares of the velocity components.

[0083] The specific method for calculating the current step termination energy Efn in step 3 is:

[0084] Efn=m×(Vfn) 2 / 2+m×g×Rfn×cos(θfn)+k×(R0-Rfn) 2 / 2;

[0085] If the value of the angle θfn is 0, the calculation method of the current step termination energy Efn is simplified to:

[0086] Efn=m×(Vfn) 2 / 2+m×g×Rfn+k×(R0-Rfn) 2 / 2.

[0087] The calculation of the current step end energy Efn is similar to the calculation of the current step start energy Ecn, which is also divided into three parts, namely the system's kinetic energy, gravitational potential energy and elastic potential energy, where the gravitational potential energy at the default horizontal plane height is zero.

[0088] Here (Vfn) 2 The calculation is the same as above (Vcn) 2 The calculation is similar to that of , and in practice it can be calculated as the sum of the squares of the velocity components measured by the sensor.

[0089] The specific method for calculating the energy loss value ΔENn of the current step in step 4 is:

[0090] ΔENn=Ecn+ΔEPn-Efn.

[0091] The specific method for estimating the next energy compensation value ΔEPn+1 in step 5 is:

[0092] ΔEPn+1=Efdes+ΔENn-Efn.

[0093] When the motion of the endless wheel is in step 1, that is, when the value of n is 1, the value of the current step energy compensation value ΔEPn in step 4 is: ΔEPn = 0. That is, when designing a program according to this method, ΔEP1 can be assigned a value of 0 in advance at the initial stage of program operation.

[0094] The specific method for calculating the leg stiffness adjustment value Δk in step 6 is:

[0095] Δk=2×(ΔEPn+1) / (R0-Rfn) 2 .

[0096] A specific method for calculating the next compensation force Fn+1 in step 7 is:

[0097] If only the equivalent spring c is in the supporting state, then

[0098] Fn+1=Δk×(R0-Rc)=2×(ΔEPn+1)×(R0-Rc) / (R0-Rfn) 2 ;

[0099] If only the equivalent spring f is in the supporting state, then

[0100] Fn+1=Δk×(R0-Rf)=2×(ΔEPn+1)×(R0-Rf) / (R0-Rfn) 2 .

[0101] Another specific method for calculating the next compensation force Fn+1 in step 7 is:

[0102] If only the equivalent spring c is in the supporting state, then

[0103] Fn+1=Δk×(Rc-Rfn)=2×(ΔEPn+1)×(Rc-Rfn) / (R0-Rfn) 2 ;

[0104] If only the equivalent spring f is in the supporting state, then

[0105] Fn+1=Δk×(Rf-Rfn)=2×(ΔEPn+1)×(Rf-Rfn) / (R0-Rfn) 2 .

[0106] Two specific methods for calculating the next compensation force Fn+1 in step 7 are given above, wherein the latter method makes the compensation force close to 0 at the beginning of each step, and as the endless wheel continues to roll, the compensation force value gradually increases as the compression of the equivalent spring c is continuously released, that is, the compensation force value is gradually applied from small to large in each step; in contrast, if the former method is used, the compensation force value is gradually applied from large to small in each step.

[0107] In step 1, the compensation force is applied in the nth step of the endless wheel, and the specific action period is from the beginning of the nth step, that is, from the time when the leg corresponding to the equivalent spring c is in the supporting state and parallel to the coronal plane, until the leg is no longer in the supporting state, or until the leg corresponding to the equivalent spring f is also in the supporting state. After adopting this time period scheme for applying the compensation force, the specific method of calculating the next compensation force Fn+1 in the above step 7 only includes the case where only the equivalent spring c is in the supporting state.

[0108] Figure 3 The figure shows an example of a spring-loaded flat wheel moving on a step, wherein the wheel adopts the active force control scheme provided by the present invention. Figure 3 As shown in (d), the parameter h represents the height of the step, the parameter x represents the length of the step, the step length is 5m, and the number of steps crossed in the following simulation process is 3; Figure 3 (a) shows the continuous change of the system compensation force Fn during the motion process; Figure 3 (b) shows the change in velocity of the rimless wheel along the sagittal plane during the movement; Figure 3 (c) shows the movement of the plane endless wheel in the stepped terrain. The plane endless wheel model consists of 8 telescopic legs and a central mass point. Each telescopic leg is equipped with a spring to achieve force control and simulate the effect of the legs stepping on the ground when a person walks. The leg length of the plane endless wheel is 0.6m, the free length R0 of the equivalent spring of the leg is 0.15m, the stiffness k of the equivalent spring is 400N / m, and the total mass m of the endless wheel is 5kg; the initial rotation angle of the plane endless wheel is 0rad, the initial rotation angular velocity is 4.36rad / s, the initial horizontal velocity and vertical velocity are 0.7m / s and 0m / s respectively, and the expected horizontal velocity and vertical velocity are 1.2m / s and 0m / s respectively. In this example, when the boundless wheel just steps onto the steps, the gravitational potential energy increases and the kinetic energy decreases relatively, so the horizontal speed decreases, the energy ΔEPn+1 required to compensate for the next gait cycle increases, and the compensation force Fn+1 applied to the supporting leg increases; after 5 gait cycles, the movement tends to be stable, and the horizontal movement speed returns to about 1.2m / s. During the movement, three steps are crossed at about 7.5s, 12s, and 16.5s respectively. The average time to cross a step is 4.5s. The average speed of movement on a step is about 1.1m / s, and the movement distance is equal to the length of the step. If the steps in this terrain scene are regarded as disturbances existing in flat terrain, this example also shows that the active force control scheme provided by the present invention can not only realize the continuous and stable movement of the boundless wheel in horizontal ground, stairs and other terrains, but also give the boundless wheel a certain active anti-disturbance ability.

Claims

1. A method for active force control of a rimless wheel based on a double-spring loaded inverted pendulum model, characterized in that: The rimless wheel comprises inner spokes and an axle, the spokes rotate around the axle; the inner spokes comprise a set of legs; the total mass of the rimless wheel is m; The leg has the ability to exert force along its own axis, and the specific forms of exerting force include moving along its own axis, stretching along its own axis, and relying on an elastic device attached along its own axis; A spring-loaded inverted pendulum model is used to establish a control model for a single leg, that is, in the control, all the legs are represented by equivalent springs, the length of all the equivalent springs in the free state is R0, and their initial stiffness is k; The rotational movement process of the rimless wheel on the ground includes a single-leg support rotation stage and a double-leg support rotation stage; if any of the legs is in a support state and the leg is parallel to the frontal plane, this moment is recorded as the beginning of a new movement step; When the movement of the endless wheel is in the nth step, the equivalent spring corresponding to the leg in the supporting state at the beginning of the movement step is called an equivalent spring c. As the endless wheel continues to rotate, when another leg adjacent to the leg is in the supporting state and the other leg is parallel to the coronal plane, it is recorded as the end of the nth step and the beginning of the n+1th step. The equivalent spring corresponding to the other leg is called an equivalent spring f. That is, if the endless wheel has moved to the nth step, it means that all the legs have been in the supporting state and parallel to the coronal plane for a total of n times. The equivalent spring c, the equivalent spring f and the concentrated mass of the endless wheel together constitute the double-spring loaded inverted pendulum model. When the movement of the endless wheel is in the nth step, the energy of the endless wheel at the start of the step is marked as the current step start energy Ecn of the endless wheel, the energy of the endless wheel at the end of the step is marked as the current step end energy Efn of the endless wheel, the energy lost during the movement of this step is marked as the current step energy loss value ΔENn of the endless wheel, the energy actively compensated during the movement of this step is marked as the current step energy compensation value ΔEPn of the endless wheel, and the compensation force continuously applied during the movement of this step to obtain the current step energy compensation value ΔEPn is marked as the current step compensation force Fn of the endless wheel; In a gravitational field with a gravitational acceleration of g, when the movement of the rimless wheel is in the nth step, the method steps for the rimless wheel to perform active force control are as follows: Step 1, applying a compensation force in the nth step of the endless wheel according to the current step compensation force Fn calculated in the n-1th step; Step 2, calculating the starting energy Ecn of the current step according to the real-time velocity Vcn of the center of mass of the endless wheel at the start of the nth step, the length Rcn of the equivalent spring c at the start of the nth step, and the angle θcn between the equivalent spring c and the vertical direction at the start of the nth step; Step 3, calculating the current step termination energy Efn according to the real-time velocity Vfn of the center of mass of the endless wheel at the end of the nth step, the length Rfn of the equivalent spring f at the end of the nth step, and the angle θfn between the equivalent spring f and the vertical direction at the end of the nth step; Step 4, calculating the current step energy loss value ΔENn according to the current step starting energy Ecn, the current step ending energy Efn, and the current step energy compensation value ΔEPn; Step 5, estimating the next step energy compensation value ΔEPn+1 according to the current step energy loss value ΔENn, the current step termination energy Efn, and the expected next step termination energy Efdes; Step 6, calculating the leg stiffness adjustment value Δk according to the next energy compensation value ΔEPn+1; Step 7, calculating the next compensation force Fn+1 according to the leg stiffness adjustment value Δk, the real-time length Rc of the equivalent spring c, and the real-time length Rf of the equivalent spring f; Step 8, after the nth step of the endless wheel is completed, the value of n+1 is assigned to n, that is, the value of Fn+1 is assigned to Fn, and the value of ΔEPn+1 is assigned to ΔEPn, and the process returns to step 1 and runs in a loop until the movement task is completed; The length Rfn of the equivalent spring f at the end of the nth step is equal to the length Rcn+1 of the equivalent spring c at the beginning of the n+1th step.

2. The method for active force control of a rimless wheel based on a double-spring loaded inverted pendulum model according to claim 1, characterized in that: The specific method for calculating the current step starting energy Ecn in step 2 is: Ecn=m×(Vcn) 2 / 2+m×g×Rcn×cos(θcn)+k×(R0-Rcn) 2 / 2; If the value of the angle θcn is 0, the calculation method of the current step starting energy Ecn is simplified to: Ecn=m×(Vcn) 2 / 2+m×g×Rcn+k×(R0-Rcn) 2 / 2。 3. The method for active force control of a rimless wheel based on a double-spring loaded inverted pendulum model according to claim 1, characterized in that: The specific method for calculating the current step termination energy Efn in step 3 is: Efn=m×(Vfn) 2 / 2+m×g×Rfn×cos(θfn)+k×(R0-Rfn) 2 / 2; If the value of the angle θfn is 0, the calculation method of the current step termination energy Efn is simplified to: Material=m×(Vfn) 2 / 2+m×g×Rfn+k×(R0-Rfn) 2 / 2.

4. The method for active force control of a rimless wheel based on a double-spring loaded inverted pendulum model according to claim 1, characterized in that: The specific method for calculating the energy loss value ΔENn of the current step in step 4 is: ΔENn=Ecn+ΔEPn-Efn.

5. The method for active force control of a rimless wheel based on a double-spring loaded inverted pendulum model according to claim 1, characterized in that: The specific method for estimating the next energy compensation value ΔEPn+1 in step 5 is: ΔEPn+1=Efdes+ΔENn-Efn.

6. The method for active force control of a rimless wheel based on a double-spring loaded inverted pendulum model according to claim 5, characterized in that: When the movement of the endless wheel is in step 1, that is, the value of n is 1, the value of the current step energy compensation value ΔEPn in step 4 is: ΔEPn=0.

7. The method for active force control of a rimless wheel based on a double-spring loaded inverted pendulum model according to claim 1, characterized in that: The specific method for calculating the leg stiffness adjustment value Δk in step 6 is: Δk=2×(ΔEPn+1) / (R0-Rfn) 2 。 8. The method for active force control of a rimless wheel based on a double-spring loaded inverted pendulum model according to claim 7, characterized in that: A specific method for calculating the next compensation force Fn+1 in step 7 is: If only the equivalent spring c is in the supporting state, then Fn+1=Δk×(R0-Rc)=2×(ΔEPn+1)×(R0-Rc) / (R0-Rfn) 2 ; If only the equivalent spring f is in the supporting state, then Fn+1=Δk×(R0-Rf)=2×(ΔEPn+1)×(R0-Rf) / (R0-Rfn) 2 。 9. The method for active force control of a rimless wheel based on a double-spring loaded inverted pendulum model according to claim 7, characterized in that: A specific method for calculating the next compensation force Fn+1 in step 7 is: If only the equivalent spring c is in the supporting state, then Fn+1=Δk×(Rc-Rfn)=2×(ΔEPn+1)×(Rc-Rfn) / (R0-Rfn) 2 ; If only the equivalent spring f is in the supporting state, then Fn+1=Δk×(Rf-Rfn)=2×(ΔEPn+1)×(Rf-Rfn) / (R0-Rfn) 2 。 10. The method for active force control of a rimless wheel based on a double-spring loaded inverted pendulum model according to claim 1, characterized in that: In step 1, a compensating force is applied during the nth step of movement of the endless wheel, and the specific action period is from the starting moment of the nth step, that is, from the time when the leg corresponding to the equivalent spring c is in a supporting state and parallel to the coronal plane, until the leg is no longer in a supporting state.

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