Leveling control method for multi-point support platform

Abstract

The present disclosure discloses a leveling control method for a multi-point support platform, which comprises the steps: respectively measuring and obtaining a load-bearing interaction matrix and a deformation interaction matrix of the platform to construct a load-bearing and deformation joint control matrix; calculating the optimal loads of the legs and measuring the current loads of the legs to obtain the load deviation rates of the legs, and determining if the platform warrants leveling in combination with the two-dimensional inclination angles of the platform; constructing a platform geometry and leg load joint control equation according to the two-dimensional inclination angles of the platform, the load deviations of the legs and the load-bearing and deformation joint control matrix, calculating the actuation quantities of the legs and performing synchronous leveling; and determining the load deviation rates of the legs and the two-dimensional inclination angles of the platform cyclically and performing the actuation control until the leveling goal is achieved. The method is capable of synchronously realizing the geometric leveling of the platform and the load control of the legs, and can significantly improve the speed, geometric accuracy, process stability, leg load-bearing stability and control robustness of the leveling control for the multi-point support platform.

Claims

1. A leveling control method for a multi-point support platform, with each leg of the platform having an equivalent length of maximum stroke, comprising the following steps: step 1, assigning serial numbers 1-n respectively to n legs; driving an i-th leg to generate a set displacement vertical thereto for each i, with the n legs other than the i-th leg remaining fixed, and i ranging from 1-n; measuring and calculating a load increment of each leg in ascending order from 1 to n, and sequentially inputting the load increments into an i-th row of an n×n dimensional matrix from column one to column n; and deleting three rows of data corresponding to any three legs not located on a straight line from the n×n dimensional matrix to construct a (n−3)×n dimensional load-bearing interaction matrix $\begin{array}{cc}{\left[K_f\right]}_{\left(n-3\right)\times n}={\left[\begin{array}{cccc}{f}_{11}& f_{12}& \mathrm{.Math.}& f_{1n}\\ f_{21}& f_{22}& \mathrm{.Math.}& f_{2n}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ f_{n1}& f_{n2}& \mathrm{.Math.}& f_{nn}\end{array}\right]}_{\left(n-3\right)\times n};& \left(1\right)\end{array}$ step 2, measuring inclination angle variations θ.sub.ix and θ.sub.iy of the platform around longitudinal and transverse directions in synchronization with the driving each i-th leg to generate the set displacement vertical thereto of step 1, and inputting θ.sub.ix and θ.sub.y into a first and a second row of an i-th column of a 2×n dimensional matrix respectively to construct a 2×n dimensional deformation interaction matrix $\begin{array}{cc}{\left[\theta \right]}_{2\times n}={\left[\begin{array}{cccc}{\theta }_{1x}& {\theta }_{2x}& \mathrm{.Math.}& {\theta }_{nx}\\ {\theta }_{1y}& {\theta }_{2y}& \mathrm{.Math.}& {\theta }_{ny}\end{array}\right]}_{2\times n};& \left(2\right)\end{array}$ step 3, sequentially inputting the load-bearing interaction matrix into first (n-3) rows of an (n−1)×n dimensional matrix, and sequentially inputting the deformation interaction matrix into last two rows of the (n−1)×n dimensional matrix to construct a load-bearing and deformation joint control matrix $\begin{array}{cc}{\left[\begin{array}{c}{K}_f\\ \theta \end{array}\right]}_{\left(n-1\right)\times n}={\left[\begin{array}{cccc}{f}_{11}& f_{12}& \mathrm{.Math.}& f_{1n}\\ f_{21}& f_{22}& \mathrm{.Math.}& f_{2n}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ f_{n1}& f_{n2}& \mathrm{.Math.}& f_{nn}\\ {\theta }_{1x}& {\theta }_{2x}& \mathrm{.Math.}& {\theta }_{nx}\\ {\theta }_{1y}& {\theta }_{2y}& \mathrm{.Math.}& {\theta }_{ny}\end{array}\right]}_{\left(n-1\right)\times n};& \left(3\right)\end{array}$ step 4, establishing a coordinate system by taking mass center of the platform as an origin of the coordinate system and longitudinal, transverse and vertical directions of the platform as an x, a y and a z axis respectively; denoting a coordinate of each connection point between the each leg and the platform as (x.sub.i, y.sub.i, z.sub.i), total weight of the platform as G, and ideal load quota of the each leg as F.sub.i.sup.s respectively for each i, and by taking minimum mean square error of loads of all legs F.sub.i with the ideal load quotas of all the legs as a goal and torque balance of the platform along the x axis, torque balance of the platform along the y axis and force balance along the z axis as constraints, obtaining optimal load model of the legs as expression (4) $\begin{array}{cc}\{\begin{array}{c}\min \frac{1}{2}\underset{i=1}{\overset{n}{.Math.}}{\left(F_i-F_i^s\right)}^2\\ s.t.\\ \underset{i=1}{\overset{n}{.Math.}}{F}_i-G=0\\ \underset{i=1}{\overset{n}{.Math.}}{F}_i{x}_i=0\\ \underset{i=1}{\overset{n}{.Math.}}{F}_i{y}_i=0\end{array};& \left(4\right)\end{array}$ solving expression (4) by means of the Lagrange Multiplier Method to obtain optimal loads of all the legs F.sub.i* satisfying expression (5) $\begin{array}{cc}{\left\{\begin{array}{c}{F}_1^{*}\\ F_2^{*}\\ \mathrm{.Math.}\\ F_n^{*}\\ a\\ b\\ c\end{array}\right\}}_{\left(n+3\right)\times 1}={\left[\begin{array}{ccccccc}1& 0& \mathrm{.Math.}& 0& 1& x_1& y_1\\ 0& 1& \mathrm{.Math.}& 0& 1& x_2& y_2\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ 0& 0& \mathrm{.Math.}& 1& 1& x_n& y_n\\ 1& 1& \mathrm{.Math.}& 1& 0& 0& 0\\ x_1& x_2& \mathrm{.Math.}& x_n& 0& 0& 0\\ y_1& y_2& \mathrm{.Math.}& y_n& 0& 0& 0\end{array}\right]}_{\left(n+3\right)\times \left(n+3\right)}^{-1}{\left\{\begin{array}{c}{F}_1^s\\ F_2^s\\ \mathrm{.Math.}\\ F_n^s\\ G\\ 0\\ 0\end{array}\right\}}_{\left(n+3\right)\times 1};& \left(5\right)\end{array}$ step 5, measuring a current load of the each leg, and calculating a load deviation rate between the each current load with the each optimal load of the each leg; and measuring each two-dimensional inclination angle of the platform around the x and y axes; step 6, comparing the load deviation rates of the legs and the two-dimensional inclination angles of the platform with the set load deviation rate threshold and inclination angle threshold respectively to determine if the leg locking conditions is satisfied: on condition the load deviation rates of all the legs and all the two-dimensional inclination angles of the platform are smaller than or equal to the load deviation rate threshold and inclination angle threshold respectively, proceeding to concluding the leveling control method, otherwise proceeding to step 7; step 7, substituting the optimal loads of the legs described in step 4, the current loads of the legs described in step 5, the two-dimensional inclination angles of the platform described in step Sand the load-bearing and deformation joint control matrix described in step 3 into expression (6) to construct a platform geometry and leg load joint control equation $\begin{array}{cc}{\left[\begin{array}{c}{K}_f\\ \theta \end{array}\right]}_{\left(n-1\right)\times n}{\left\{\Delta x_i\right\}}_{n\times 1}={\left\{\begin{array}{c}{F}_i^t-F_i^{*}\\ {\theta }_m^t\end{array}\right\}}_{\left(n-1\right)\times 1};& \left(6\right)\end{array}$ wherein F.sub.i.sup.t being the current load, F.sub.1* being the optimal load, {F.sub.i.sup.t-F.sub.i*} being a (n-3)×1 dimensional column vector obtained corresponding to deletion of data of the three legs described in step 1, ${\theta }_m^t=\left\{\begin{array}{c}\Delta {\theta }_x\\ \Delta {\theta }_y\end{array}\right\}$ being the inclination angles of the platform around the x and y axes; by solving expression (6) with the Generalized Inverse Method, obtaining actuation quantities Δx.sub.i of the legs for the geometric leveling and load control of the platform; step 8, controlling the legs to synchronously actuate for leveling in proportion to the actuation quantities of the legs obtained in step 7, until achieving the actuation quantities of the legs; step 9, measuring a current load of the each leg, and calculating a load deviation rate between the each current load with the each optimal load of the each leg; and measuring each two-dimensional inclination angle of the platform around the x and y axes; step 10, comparing the load deviation rates of the legs and the two-dimensional inclination angles of the platform with the set load deviation rate threshold and inclination angle threshold respectively to determine if the leg locking condition is satisfied: on condition the load deviation rates of all the legs and all the two-dimensional inclination angles of the platform are smaller than or equal to the load deviation rate threshold and inclination angle threshold respectively, concluding the leveling control method; otherwise proceeding to step 11; step 11, re-substituting the current loads of the legs and the two-dimensional inclination angles of the platform described in step 9 into the platform geometry and leg load joint control equation described in step 7, calculating the actuation quantities of the legs and executing steps 8 and 9 until the leg locking condition is satisfied, and concluding the leveling control method.

2. The leveling control method for a multi-point support platform of claim 1, wherein the set displacement described in step 1 is in a range of 1% to 5% of the maximum stroke.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0024] FIG. 1 is a flow chart of the leveling control method for the multi-point support platform of the present disclosure;

[0025] FIG. 2 is a simplified schematic diagram of the structure of the multi-point support platform of the present disclosure.

EMBODIMENTS

[0026] For clearer understanding of the object, the technical solution and the advantages of the present disclosure, the present disclosure is further described in detail in combination with the attached drawings and embodiments hereunder. It is understood that the specific embodiments described herein are meant only to explain, not to limit, the present disclosure.

[0027] FIG. 1 is a flow chart of the leveling control method for the multi-point support platform provided by an embodiment of the present disclosure.

[0028] FIG. 2 is a simplified schematic diagram of the structure of the multi-point support platform provided by an embodiment of the present disclosure. The model comprises n legs K.sub.1, K.sub.2, . . . K.sub.n-1, K.sub.n, n leg drivers A, n force sensors B and one two-dimensional inclination angle sensor C.

[0029] The leveling control method for the multi-point support platform of the present disclosure corrects the defects of prior art leveling process in low precision, low speed, the poor robustness, incomplete control of the load of legs, even weak leg and overloading. In the multi-point support platform, each leg of the platform has an equivalent length of maximum stroke. The leveling control method for the multi-point support platform comprises the following steps:

[0030] Step 1, assigning serial numbers 1-n respectively to n legs; a leg driver A driving the first leg K.sub.1 to produce a set displacement vertical thereto, i.e. in the z-axis direction while keeping the lower ends of the other n-1 legs fixed, denoting load increments of the first to n-th legs measured by the force sensors B as load-bearing interaction coefficients f.sub.11, f.sub.12, . . . f.sub.1n, and then inputting f.sub.11, f.sub.12, . . . f.sub.1n into the first row of a n×n dimensional matrix sequentially; sequentially operating the second to n-th legs in the same way to construct the n×n dimensional matrix; and because the platform has three rigid degrees of freedom, that is translation along z-axis, rotations around x-axis and y-axis, the n×n dimensional matrix is a singular matrix of rank three, thus need deleting three rows of data corresponding to any three legs that are not located on a straight line from the n×n dimensional matrix to construct a (n−3)×n dimensional load-bearing interaction matrix

[00010]${\left[K_f\right]}_{\left(n-3\right)\times n}={\left[\begin{array}{cccc}{f}_{11}& f_{12}& \mathrm{.Math.}& f_{1n}\\ f_{21}& f_{22}& \mathrm{.Math.}& f_{2n}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ f_{n1}& f_{n2}& \mathrm{.Math.}& f_{nn}\end{array}\right]}_{\left(n-3\right)\times n}.$

[0031] Step 2, the two-dimensional inclination angle sensor C measuring and obtaining inclination angle variations θ.sub.1x and θ.sub.1y of the platform around the x and y axes in synchronization with the driving the first leg K.sub.1 to produce a set displacement vertical thereto of step 1, and inputting θ.sub.1x and θ.sub.1y into the first and second rows of the first column of a 2×n dimensional matrix respectively; measuring and obtaining two-dimensional inclination angle variations of the platform in the same way with the second to n-th legs to produce a set displacement vertical thereto of step 1 to construct a 2×n dimensional deformation interaction matrix

[00011]${\left[\theta \right]}_{2\times n}={\left[\begin{array}{cccc}{\theta }_{1x}& {\theta }_{2x}& \mathrm{.Math.}& {\theta }_{\mathrm{nx}}\\ {\theta }_{1y}& {\theta }_{2y}& \mathrm{.Math.}& {\theta }_{ny}\end{array}\right]}_{2\times n}.$

[0032] Step 3, sequentially inputting the load-bearing interaction matrix into first (n-3) rows of an (n−1)×n dimensional matrix, and sequentially inputting the deformation interaction matrix into last two rows of the (n−1)×n dimensional matrix to construct a load-bearing and deformation joint control matrix

[00012]${\left[\begin{array}{c}{K}_f\\ \theta \end{array}\right]}_{\left(n-1\right)\times n}={\left[\begin{array}{cccc}{f}_{11}& f_{12}& \mathrm{.Math.}& f_{1n}\\ f_{21}& f_{22}& \mathrm{.Math.}& f_{2n}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ f_{n1}& f_{n2}& \mathrm{.Math.}& f_{nn}\\ {\theta }_{1x}& {\theta }_{2x}& \mathrm{.Math.}& {\theta }_{\mathrm{nx}}\\ {\theta }_{1y}& {\theta }_{2y}& \mathrm{.Math.}& {\theta }_{ny}\end{array}\right]}_{\left(n-1\right)\times n}.$

[0033] Step 4, establishing a coordinate system by taking the mass center of the platform as the origin of the coordinate system and the longitudinal, transverse and vertical directions of the platform as x, y and z axes respectively, wherein coordinates of the connection points between the legs and the platform are denoted as (x.sub.i, y.sub.i, z.sub.i), the total weight of the platform is denoted as G, the ideal load quotas of the legs are set as F.sub.i.sup.s respectively, and by taking the minimum mean square error of the loads of the legs F.sub.i and the ideal load quotas of the legs as the goal and torque balance of the platform along the x axis, torque balance of the platform along the y axis and force balance along the z axis as constraints, the optimal load calculation model of the legs satisfies

[00013]$\{\begin{array}{c}\min \frac{1}{2}\underset{i=1}{\overset{n}{.Math.}}{\left(F_i-F_i^s\right)}^2\\ s.t.\\ \underset{i=1}{\overset{n}{.Math.}}{F}_i-G=0\\ \underset{i=1}{\overset{n}{.Math.}}{F}_i{x}_i=0\\ \underset{i=1}{\overset{n}{.Math.}}{F}_i{y}_i=0\end{array}.$

[0034] The optimal load calculation model is solved by the Lagrange Multiplier Method, and the optimal loads of all the legs F.sub.i* satisfy

[00014]${\left\{\begin{array}{c}{F}_1^{*}\\ F_2^{*}\\ \mathrm{.Math.}\\ F_n^{*}\\ a\\ b\\ c\end{array}\right\}}_{\left(n+3\right)\times 1}={\left[\begin{array}{ccccccc}1& 0& \mathrm{.Math.}& 0& 1& x_1& y_1\\ 0& 1& \mathrm{.Math.}& 0& 1& x_2& y_2\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ 0& 0& \mathrm{.Math.}& 1& 1& x_n& y_n\\ 1& 1& \mathrm{.Math.}& 1& 0& 0& 0\\ x_1& x_2& \mathrm{.Math.}& x_n& 0& 0& 0\\ y_1& y_2& \mathrm{.Math.}& y_n& 0& 0& 0\end{array}\right]}_{\left(n+3\right)\times \left(n+3\right)}^{-1}{\left\{\begin{array}{c}{F}_1^s\\ F_2^s\\ \mathrm{.Math.}\\ F_n^s\\ G\\ 0\\ 0\end{array}\right\}}_{\left(n+3\right)\times 1}$

wherein a, b and c are intermediate calculation quantities.

[0035] Step 5, the force sensors B measuring the current loads F.sub.i.sup.t actually borne by the legs, and calculating the load deviation rates of the legs according to the current loads F.sub.i.sup.t of the legs and corresponding optimal loads F.sub.i*:

[00015]$F_i^d=.Math.\frac{F_i^t-F_i^{*}}{F_i^{*}}.Math.;$

and the two-dimensional inclination angle sensor C measuring the inclination angles of the platform around the x and y axes: Δθ.sub.x, Δθ.sub.y.

[0036] Step 6, comparing the load deviation rates of the legs and the two-dimensional inclination angles of the platform with the set load deviation rate threshold and inclination angle threshold respectively to determine if the leg locking condition is satisfied: on condition the load deviation rates of all the legs are smaller than or equal to the load deviation rate threshold F.sub.i.sup.d≤ε.sub.F, and all the two-dimensional inclination angles of the platform are smaller than or equal to inclination angle threshold Δθ.sub.x≤ε.sub.θand Δθ.sub.y≤ε.sub.θ, concluding the leveling control method, otherwise proceeding to step 7.

[0037] Step 7, substituting the current loads of the legs, the optimal loads of the legs, the two-dimensional inclination angles of the platform and the load-bearing and deformation joint control matrix into the following expression to construct a platform geometry and leg load joint control equation

[00016]${\left[\begin{array}{c}{K}_f\\ \theta \end{array}\right]}_{\left(n-1\right)\times n}{\left\{\Delta x_i\right\}}_{n\times 1}={\left\{\begin{array}{c}{F}_i^t-F_i^{*}\\ {\theta }_m^t\end{array}\right\}}_{\left(n-1\right)\times 1}$

in the above expression, F.sub.i.sup.t is the current load, F.sub.i* is the optimal load, {F.sub.i.sup.t-F.sub.i*} is a (n−3)×1 dimensional column vector obtained after the data of

[00017]${\theta }_m^t=\left\{\begin{array}{c}\Delta {\theta }_x\\ \Delta {\theta }_y\end{array}\right\}$

[0038] the three legs described in step 1 are deleted, and are the inclination angles of the platform around the x and y axes, and by solving this expression with the Generalized Inverse Method, the actuation quantities Δx.sub.i of the legs that are needed for the realization of the geometric leveling of the platform and load control of the legs are obtained.

[0039] Step 8, dividing the calculated actuation quantities Δx.sub.i, of the legs by the maximum value of the actuation quantities respectively to obtain the proportional relationship between the actuation quantities of the legs, and controlling the leg drivers A to drive the legs to actuate according to the proportional relationship, until achieving the actuation quantities of the legs.

[0040] Step 9, the force sensors B measuring the current loads actually borne by the legs, and the two-dimensional inclination angle sensor C measuring the inclination angles of the platform around the x and y axes Δθ.sub.x, Δθ.sub.y.

[0041] Step 10, comparing the load deviation rates of the legs and the two-dimensional inclination angles of the platform with the set load deviation rate threshold and inclination angle threshold respectively to determine if the leg locking condition is satisfied: on condition the load deviation rates of all the legs are smaller than or equal to the load deviation rate threshold F.sub.i.sup.d≤ε.sub.F, and all the two-dimensional inclination angles of the platform are smaller than or equal to inclination angle threshold Δθ.sub.x≤ε.sub.θand Δθ.sub.y≤ε.sub.θ, concluding the leveling control method, otherwise proceeding to step 11;

[0042] Step 11, re-substituting the current loads of the legs and the two-dimensional inclination angles of the platform described in step 9 into the platform geometry and leg load joint control equation described in step 7 and calculating the actuation quantities of the legs and executing steps 8 and 9 until the locking condition is satisfied, then concluding the leveling control method.

[0043] Preferably, the set displacement described in step 1 is in the range of 1% to 5% of the maximum stroke.

[0044] Finally, it should be noted that the above descriptions are only preferred embodiments of the present disclosure with explanation of the relevant technical principles. Persons skilled in the art understand that the present disclosure is not limited to the particular embodiments described herein and that it is possible for persons skilled in the art to undertake any appreciable variation, readjustment or replacement without departing from the scope of protection of the present disclosure. Therefore, although the present disclosure is described in more detail through the above embodiments, the present disclosure is not limited to the above embodiments, but may include many other equivalent embodiments without departing from the conception of the present disclosure, which shall fall within the scope of the present disclosure as is described in the appended claims.