Wheel-legged balancing robot MPC control system

Abstract

The application discloses a wheel-leg balance robot MPC control system and relates to the technical field of robot control, comprising: a boundary correction module, which is used for acquiring system state parameters of a current period and input parameters of a previous period, calculating steady-state parameters based on the system state parameters and the input parameters, and correcting initial amplitude limiting boundaries of a first execution end and a second execution end by using the steady-state parameters to obtain a first constraint boundary; and a load transfer module, which is used for determining an inverse mapping matrix based on the system state parameters and determining a space base vector according to the inverse mapping matrix; the wheel-leg balance robot MPC control system has the beneficial effects that the saturation deadlock and the risk of thermal damage caused by long-time high pressure anti-interference of a single node are resolved, trajectory distortion caused by conventional hard cutting is avoided, and high-robustness adaptive balance control under extreme disturbance working conditions is realized.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and in particular to the MPC control system for a wheel-legged balancing robot. Background Technology

[0002] In recent years, tandem wheel-legged balancing robots have attracted widespread attention due to their combination of the high efficiency of wheeled robots and the obstacle-crossing capabilities of legged robots. However, in practical engineering applications, existing control schemes face many challenges. Firstly, there is the error problem between the theoretical model and the actual robot. For example, centroid offset, joint friction, wheel hub and gearbox friction, ground friction, and assembly errors can all cause model mismatch, necessitating a mechanism that can accurately estimate the equivalent disturbance torque online and map it to the control channel for compensation. Secondly, there is the instability problem caused by external shocks and transient disturbances. When the robot encounters ground protrusions, steps, or lands on ramps, it generates transient impacts. The system is highly susceptible to misinterpreting these transient impacts as long-term model biases, thus triggering control divergence.

[0003] Furthermore, traditional linear quadratic regulator (LQR) control schemes cannot handle the problem of hard limiting of motors. Under large error conditions, they are prone to outputting control quantities that exceed the actual capabilities of the motor, while simple truncation will destroy the original optimal control trajectory. To solve the constraint and limiting problem, restricted nonlinear optimization schemes have been introduced. However, this leads to a severe contradiction between the excessive computational load of online optimization and the real-time requirements of embedded hardware platforms. How to complete matrix solving and rolling optimization within an extremely limited computing cycle (e.g., 2ms) has become a major engineering challenge.

[0004] When dealing with a single actuator (such as a hub motor) approaching its physical saturation limit, existing technologies can typically only perform local constraint truncation or overall derating at the algorithmic mathematical level. They cannot utilize the redundancy of the multi-degree-of-freedom nature of the wheel-leg system itself to compensate for and transfer the underlying load between actuators. Especially when long-term disturbance rejection leads to thermal overload of local joint motors, existing control systems lack a deep interactive feedback mechanism that bridges the mathematical control law and the robot's physical configuration. They cannot proactively reconstruct the robot's balance posture (such as changing the leg length configuration) to eliminate environmental bias disturbances from a physical source. Ultimately, this can easily lead to actuator thermal runaway or dynamic dimensional reduction instability of the entire robot under extreme terrain. Therefore, it is necessary to design an MPC control system for wheel-leg balancing robots to solve the above problems. Summary of the Invention

[0005] In view of the above-mentioned prior art, this application is hereby proposed. Embodiments of this application provide an MPC control system for a wheel-legged balancing robot, which mitigates the risks of saturation deadlock and thermal damage caused by long-term high-voltage disturbance suppression at a single node, avoids trajectory distortion caused by conventional hard truncation, and achieves highly robust adaptive balance control under extreme disturbance conditions.

[0006] According to one aspect of this application, a wheel-legged balancing robot MPC control system is provided, comprising:

[0007] The boundary correction module is used to obtain the system state parameters of the current cycle and the input parameters of the previous cycle, calculate the steady-state parameters based on the system state parameters and the input parameters, and use the steady-state parameters to correct the initial amplitude limiting boundary between the first execution terminal and the second execution terminal to obtain the first constraint boundary.

[0008] The load transfer module is used to determine the inverse mapping matrix based on the system state parameters, and to determine the spatial basis vector based on the inverse mapping matrix. The spatial basis vector is the adjustment direction vector in the torque space of the execution end that keeps the net virtual support force of the leg unchanged. When the first constraint boundary of the first execution end reaches the preset lower limit threshold, the module generates transfer parameters based on the spatial basis vector, uses the transfer parameters to transfer the steady-state load of the first execution end to the second execution end, and updates the corresponding first constraint boundary to obtain the second constraint boundary.

[0009] The state update module is used to perform time integration on the output power of the second execution terminal to obtain an integral parameter. When the integral parameter exceeds a preset energy consumption threshold, the offset parameter is calculated based on the system state parameter, and the offset parameter is superimposed with a preset first reference state to obtain a second reference state.

[0010] The solution and execution module is used to perform optimization solution based on the second constraint boundary and the second reference state, extract the generated first-cycle control parameters as actual output parameters to perform feedback adjustment, and use the actual output parameters as input parameters for the next cycle.

[0011] According to another aspect of this application, an electronic device is provided, including a memory and a processor, the memory for storing computer-executable instructions, and the processor for executing the computer-executable instructions, which, when executed by the processor, implement the functions of the system as described above.

[0012] According to another aspect of this application, a computer-readable storage medium is provided that stores computer-executable instructions thereon, which, when executed by a processor, implement the functions of the system described above.

[0013] Compared with the prior art, the MPC control system of the wheel-legged balancing robot according to the embodiments of this application can reflect the actual available motion margin of each drive node when the robot faces terrain undulations or continuous external disturbances by correcting the initial limit boundary of the actuator. This reduces the risk of control quantity overflow caused by physical boundary evaluation deviation. When the constraint boundary of the first actuator reaches the lower limit threshold, the system can generate transfer parameters based on the spatial basis vector and transfer the steady-state load that the first actuator can no longer bear to the second actuator in a proportional manner. Thus, while maintaining the overall dynamic balance of the robot, the system uses the multi-degree-of-freedom redundancy characteristics of the body to distribute the local high-pressure load and ensure the motion stability of the system under single-node restricted working conditions.

[0014] By integrating the output power of the second actuator over time, the energy accumulation and thermal fatigue state of the actuator are quantitatively evaluated. The system actively adjusts the first reference state by solving the offset parameters to reconstruct the target attitude. The underlying physical energy consumption is directly fed back to the upper-level reference trajectory planning. By changing the physical configuration, the continuous load is unloaded from the mechanical source, preventing thermal damage caused by the actuator being in a high-load disturbance rejection state for a long time. The solution and execution module incorporates the updated second constraint boundary and the second reference state into the optimization solution domain for calculation. This architecture integrates dynamic physical constraints directly as preconditions into the optimization solution process, avoiding the trajectory distortion and control divergence problems caused by solving the optimal control quantity first and then performing amplitude limiting hard truncation in conventional algorithms. Attached Figure Description

[0015] The above and other objects, features, and advantages of this application will become more apparent from the more detailed description of the embodiments of this application in conjunction with the accompanying drawings. The drawings are provided to further illustrate the embodiments of this application and form part of the specification. They are used together with the embodiments of this application to explain this application and do not constitute a limitation thereof. In the drawings, the same reference numerals generally represent the same components or steps.

[0016] Figure 1 This is a schematic diagram of the overall process of the MPC control system for the wheel-legged balancing robot of the present invention.

[0017] Figure 2 This is a schematic diagram of the logic framework of the MPC control system for the wheel-legged balancing robot of the present invention.

[0018] Figure 3 This is an extended schematic diagram of the MPC control system for the wheel-legged balancing robot of the present invention. Detailed Implementation

[0019] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0020] Example 1:

[0021] To address the issues in existing wheeled robot control systems, such as the susceptibility to torque saturation and overheating fatigue caused by single-node disturbance rejection, the lack of multi-joint collaborative compensation and active attitude unloading mechanisms, and the tendency for conventional amplitude limiting to easily lead to optimal trajectory distortion and control divergence, this application dynamically corrects the amplitude limiting boundary by calculating steady-state parameters. When the first actuator touches the boundary, the load is smoothly transferred to the second actuator using the spatial basis vectors of the inverse mapping matrix. Simultaneously, power integral monitoring is introduced, and when energy consumption at the actuator exceeds the limit, offset parameters are calculated to reconstruct the initial reference state of the robot. Finally, the updated physical constraint boundary and reconstructed reference state are directly incorporated into the MPC optimization solution domain, and the first-shot control parameters are extracted to execute closed-loop feedback.

[0022] This application utilizes the dual mechanisms of spatial load transfer and active attitude reconstruction, leveraging the multi-degree-of-freedom redundancy of the entire machine, to mitigate the risks of saturation deadlock and thermal damage caused by long-term high-voltage disturbances at a single node from a physical and mechanical perspective. Simultaneously, by placing dynamic boundary constraints directly at the bottom-level optimization process, it avoids trajectory distortion caused by conventional hard truncation, achieving highly robust adaptive balance control under extreme disturbance conditions.

[0023] Reference Figures 1-3 As an embodiment of the present invention, a wheel-legged balancing robot MPC control system is provided, including: a boundary correction module, a load transfer module, a state update module, and a solution and execution module.

[0024] For ease of understanding, the following example illustrates the operation of a tandem wheel-legged balancing robot on a slope. Each leg of the robot is driven by a hub motor and two joint motors (front and rear). These two joint motors, via a five-bar linkage and virtual model control (VMC), jointly generate the virtual support force and virtual torque for that leg. The control system operates with a control cycle of approximately 2ms. Assume the robot is maintaining balance and moving forward at a low speed on a slope of approximately 15°. Its right leg is in an extended support state. Due to gravity torque and continuous disturbance rejection, the steady-state load of the right leg's front joint motor is high, gradually approaching its torque output limit. The following explanation uses the right leg's front joint motor as the first actuator and the right leg's rear joint motor as the second actuator. It should be noted that the first and second actuators can also be combinations of other redundant actuators associated with the same inverse mapping matrix (e.g., the left and right legs); this selection is merely an example and not a limitation.

[0025] Before describing each module, the system state parameters that run through all modules will be explained. The system state parameters are state vectors representing the robot's current motion and attitude. In this embodiment, they are 10-dimensional state vectors, composed of components such as the body pitch angle, roll angle, yaw angle and their angular velocities calculated by the inertial measurement unit (IMU), gravity-compensated acceleration, leg length and leg angles calculated by the virtual model control of the five-bar linkage, and chassis speed estimates obtained by fusing wheel speed, leg swing speed, and IMU data. At the beginning of each control cycle, these components are processed from asynchronous, noisy sensor data into a unified state vector, which serves as the input for subsequent module calculations.

[0026] Figure 1 and Figure 2 The figure illustrates the MPC control system for a wheel-legged balancing robot according to an embodiment of this application, specifically including:

[0027] Reference Figure 1 In the boundary correction module, the system state parameters of the current cycle and the input parameters of the previous cycle are obtained. The steady-state parameters are calculated based on the system state parameters and the input parameters, and the specific formula is as follows:

[0028] ;

[0029] in, For steady-state parameters ( ), The state feedback gain coefficient characterizes the linear adjustment ratio of the system state deviation to the steady-state torque. ), The system state parameter (rad) for the current period. The preset input coupling ratio coefficient, The input parameters for the previous cycle ( );

[0030] In this module, the steady-state parameter characterizes the low-frequency equivalent perturbation torque acting on the actuator in the current cycle, caused by model mismatch and persistent disturbances. Its source is the mapping of the low-frequency steady-state component of the equivalent disturbance estimated by the extended state observer to the torque domain of the actuator, reflecting the steady-state differences between the theoretical model and the real robot (such as center of mass offset, joint friction, ground friction, etc.). The input parameter of the previous cycle is the torque actually applied to the actuator in the previous control cycle. Incorporating it into the solution of the steady-state parameter reflects the coupling effect of the input history on the current steady-state load. It should be noted that... The first control cycle after system power-on or reset has no actual input from the previous cycle. At this time, the input parameters of the previous cycle take a preset initial value, which can be set to zero torque or an initial control guess composed of gravity feedforward. From the second control cycle onwards, the input parameters of the previous cycle take the torque actually output in the previous control cycle. The state feedback gain coefficient and the input coupling ratio coefficient are determined based on the estimation relationship of the extended state observer for the steady-state equivalent disturbance and are calibrated offline during the modeling stage. Since the robot dynamics change with the leg length, the above coefficients are updated online according to the interval in which the leg length is located.

[0031] The initial limiting boundaries between the first and second execution terminals are then corrected using steady-state parameters to obtain the first constraint boundary, as shown in the following formula:

[0032] ;

[0033] in, For the first constraint boundary ( ), For the initial amplitude limit boundary ( );

[0034] In this module, the initial limiting boundary is the upper limit of the torque that the actuator can continuously output without considering steady-state disturbances. It is determined by the rated continuous torque or peak torque of the actuator motor. The first constraint boundary is obtained by subtracting the steady-state parameters from the initial limiting boundary. It reflects the torque margin that the actuator can still use after bearing the current steady-state disturbance torque. Since the steady-state parameters are updated online with the working conditions, the first constraint boundary can reflect the actual motion margin of each actuator of the robot under terrain undulations or continuous external disturbances, thereby reducing the risk of control quantity overflow caused by physical boundary evaluation deviation.

[0035] Continuing with the aforementioned scenario, let's assume the initial limiting boundary of the first actuator (right leg anterior joint motor). 30 The steady-state parameter acting on this execution end, calculated from the current state and the input of the previous cycle, is approximately 20. Then the corrected first constraint boundary That is, after the execution end bears the steady-state disturbance, only about 10 remain. Available margin.

[0036] Through the above scheme, the boundary correction module incorporates the steady-state disturbance torque that varies with the operating conditions into the online evaluation of the limiting boundary, providing a first constraint boundary that reflects the true availability margin for the subsequent load transfer triggering determination and the constraint solution of the solution and execution module.

[0037] After the boundary correction module obtains the first constraint boundary reflecting the true available margin, the load transfer module further addresses the situation where the margin of a single actuator is insufficient. The core of this module is that when the available margin of a certain actuator drops to a preset lower limit, the redundant degrees of freedom in the direction of net virtual support force of multiple actuators in the wheel-leg mechanism associated with the same inverse mapping matrix are used to distribute the steady-state load that the actuator can no longer bear to the actuator to the actuators that still have margin, without changing the net virtual support force of the leg.

[0038] return Figure 1 In the load transfer module, the inverse mapping matrix is ​​determined based on the system state parameters, and the spatial basis vector is determined based on the inverse mapping matrix. The spatial basis vector is the adjustment direction vector in the torque space of the execution end that keeps the net virtual support force of the leg unchanged.

[0039] In this module, the inverse mapping matrix is ​​a mapping matrix derived from the virtual support force and virtual torque to the torques of each actuator. It is determined online by the virtual model control based on current system state parameters (such as leg length and leg angle), and thus updates with changes in robot posture. The spatial basis vectors are the basis vectors of the subspace formed by redundant directions in the actuator torque space. This subspace (i.e., the null space) is defined by the following condition: when the torques of each actuator are synchronously adjusted along any direction, the net virtual support force of that leg remains unchanged; only the torque is redistributed among the actuators. In numerical implementation, the mapping relationship from the torques of each actuator to the net virtual support force of that leg can be obtained from the inverse mapping matrix. Singular value decomposition is performed on this mapping relationship, and the direction vector corresponding to its zero singular value (the smallest singular value in the numerical implementation) is taken as the spatial basis vector. It is a dimensionless direction vector, and each component corresponds to the participation ratio of an actuator in that redundant direction.

[0040] When the first constraint boundary of the first execution end reaches the preset lower limit threshold, the transfer parameter is generated based on the spatial basis vector. The steady-state load of the first execution end is transferred to the second execution end using the transfer parameter, and the corresponding first constraint boundary is updated to obtain the second constraint boundary.

[0041] The lower limit threshold is the lower limit of the available margin for triggering load transfer. Its value can be set as a preset proportion of the initial limiting boundary, as shown in the following formula:

[0042] ;

[0043] in, The lower threshold is... For the initial amplitude limit boundary ( ), The lower limit ratio coefficient is a preset value (range 0 < λ < 1). The lower limit ratio coefficient is set according to the continuous load level and safety margin requirements allowed by the execution end. The larger the value of λ, the earlier the load transfer is triggered and the more safety margin is reserved for the execution end.

[0044] The process of transferring the steady-state load from the first execution terminal to the second execution terminal includes:

[0045] Extract the first vector element associated with the first execution end from the spatial basis vectors;

[0046] Specifically, each component of the spatial basis vector corresponds one-to-one with each execution end, and each component represents the proportion of torque participation of the corresponding execution end in the redundant direction; the first vector element associated with the first execution end is extracted, that is, the component of the spatial basis vector corresponding to the first execution end is taken as the first vector element. Its numerical value represents the torque participation ratio corresponding to the unit adjustment amount of the first execution end in the redundant direction;

[0047] Using preset regularization factors For the first vector element Perform bias correction to obtain the corrected vector elements. : Based on the modified vector elements, the steady-state load to be transferred at the first execution end is proportionally mapped to obtain the load scaling factor, as shown in the following formula:

[0048] ;

[0049] in, Load scaling factor ( ), The steady-state load to be transferred at the first execution end ( ), To correct vector elements (dimensionless);

[0050] In this module, the regularization factor is a dimensionless small positive constant, whose magnitude is more than an order of magnitude lower than the typical amplitude of each component of the spatial basis vector. Its function is to avoid division by zero and suppress numerical distortion of the load scaling factor when the first vector element approaches zero. Its value can be set in conjunction with the numerical range of the spatial basis vector and the numerical precision of the solver. The steady-state load to be transferred at the first execution end is the portion of the steady-state load at that execution end that needs to be unloaded. Its value can be set as the difference between the steady-state parameter corresponding to the first execution end and its lower threshold, as shown in the following formula:

[0051] ;

[0052] in, The steady-state load to be transferred at the first execution end ( ), For the steady-state parameters corresponding to the first execution end, The lower limit threshold;

[0053] The spatial basis vectors are adjusted for gain based on the load scaling factor to generate transfer parameters, as shown in the following formula:

[0054] ;

[0055] in, To transfer parameters, Spatial basis vectors;

[0056] The first transfer component corresponding to the first execution end and the second transfer component corresponding to the second execution end are parsed from the transfer parameters;

[0057] Specifically, the transfer parameters are a set of actuator torque adjustment quantities along the spatial basis vector direction, and each component corresponds one-to-one with each actuator in the same order as the spatial basis vector; the component corresponding to the first actuator is taken from the transfer parameters as the first transfer component. Take the component corresponding to the second execution end as the second transfer component. These two are the torque adjustment amounts undertaken by the first and second execution ends in this load transfer, respectively. Since the transfer parameters are generated along the zero space direction, the contributions of the first transfer component and the second transfer component to the net virtual support force of the leg cancel each other out. Therefore, the load unloaded by the first execution end is equally borne by the second execution end.

[0058] Using the first transfer component and the second transfer component, the first constraint boundaries of the first execution end and the second execution end are updated respectively, as shown in the following formula:

[0059] ;

[0060] in, The first constraint boundary of the updated first execution end ( ), For the first constraint boundary ( ), For the first transfer component ( );

[0061] In this module, the transfer parameters are a set of execution end torque adjustment quantities along the spatial basis vector direction. The first transfer component acts on the first execution end, and the second transfer component acts on the second execution end. Since the transfer parameters are generated along the null space direction of the inverse mapping matrix, each transfer component forms a combination with zero influence on the net virtual support force between each execution end. Therefore, the steady-state load unloaded by the first execution end is taken over by the second execution end, while the net virtual support force of this leg remains unchanged. Accordingly, the constraint boundaries of the first and second execution ends are updated respectively to obtain the second constraint boundary, so that the available margin of the first execution end rises back to above the lower limit threshold, while the available margin of the second execution end decreases accordingly.

[0062] Continuing with the aforementioned scenario, the first constraint boundary of the first execution end for When the preset lower limit ratio coefficient λ is 0.4, the lower limit threshold is... , The load has fallen below the lower threshold, triggering load transfer; the steady-state load to be transferred is... ,about The steady-state load is redistributed to the second actuator (right leg rear joint motor) via the spatial basis vector, and the constraint boundary of the first actuator rises back to above the lower limit threshold, thus obtaining the second constraint boundary.

[0063] Conventional limiting processes each actuator independently. When a single actuator approaches saturation, the only options are to reduce the overall output of the robot or cut off the output of that actuator individually. However, in a wheel-leg mechanism, multiple actuators associated with the same inverse mapping matrix have redundant degrees of freedom in the direction of the net virtual support force. Redistributing the actuator torque along this redundant direction does not change the net force on the robot body. Therefore, the steady-state load of the actuator approaching saturation can be distributed to the actuators with remaining margin without disrupting the dynamic balance. This allows for the distribution of local high-pressure loads using the redundancy of multiple degrees of freedom while maintaining the overall balance of the robot, delaying the saturation deadlock of a single node, and maintaining the motion stability of the robot under single-actuator-constrained conditions.

[0064] As alternatives, overall derating, hard truncation at the output end, or individual limiting of the saturated actuator end can also prevent the actuator end from going out of bounds to some extent. However, overall derating comes at the cost of sacrificing the overall machine output, hard truncation will destroy the optimized control trajectory, and individual limiting will fail to utilize the redundancy between actuator ends. The reason for choosing to transfer the load along the spatial basis vector is that it only operates in the redundant direction with zero impact on the net virtual support force, and the transfer amount can be continuously adjusted by the load scaling factor, which is convenient for connecting with subsequent constraint solutions.

[0065] The load transfer module distributes the steady-state load among the actuators. However, if the second actuator that receives the load maintains a high output for a long time, it will face the risk of overheating due to the continuous accumulation of energy and heat. Furthermore, the distribution of torque cannot eliminate the continuous load (such as the gravitational torque generated by the center of mass offset) from the mechanical source. Therefore, the state update module monitors the energy accumulation state of the second actuator and reconstructs the reference attitude of the machine when it exceeds the preset energy consumption level, thereby unloading the continuous load from the mechanical source.

[0066] return Figure 1 In the state update module, the output power of the second execution end is integrated over time to obtain the integral parameter, and the specific formula is as follows:

[0067] ;

[0068] in, J is the integral parameter. This is the lower limit (s) for the start time of integration. This represents the upper limit (s) of the current time. The output power (W) of the second actuator at time t;

[0069] In this module, the integral parameter is the integral of the output power of the second actuator over time within a set time interval. It represents the energy accumulated by the actuator within this interval and is related to the heating and temperature rise of the actuator winding. Compared with instantaneous power, the accumulated energy better reflects the overheating fatigue trend of the actuator due to long-term load. The integration start time is the starting point of the current monitoring interval. After each attitude reconstruction is triggered, the integral parameter is reset to zero and re-accumulated, so that the integral parameter reflects the accumulated energy of the receiving end in the most recent continuous load interval, rather than the unbounded accumulation since the system started.

[0070] When the integral parameter exceeds a preset energy consumption threshold, the offset parameter is calculated based on the system state parameters. The offset parameter is then superimposed with a preset first reference state to obtain a second reference state, including:

[0071] First, it should be noted that the energy consumption threshold is a limit characterizing the upper limit of cumulative energy that the second actuator can withstand. Its value can be determined based on the equivalent heat capacity and allowable temperature rise of the actuator winding, as shown in the following formula:

[0072] ;

[0073] in, Energy consumption threshold The equivalent heat capacity (J / ℃) of the second actuator winding. The allowable temperature rise (°C) is set based on the thermal parameters and safe temperature limit of the actuator motor, and the energy consumption threshold is determined accordingly.

[0074] The center of gravity offset data representing the current body posture is extracted from the system state parameters. Specifically, the center of gravity offset data is the offset of the body's center of mass relative to the actuator axis, obtained from the system state parameters. It reflects the magnitude of the lever arm that generates the continuous gravitational torque. The extraction of the center of gravity offset data is as follows: the pitch angle representing the body posture and the leg length and leg angle representing the leg configuration are taken from the system state parameters. Combined with the mass distribution geometry of the body, the projection length of the vector pointing from the actuator axis to the body's center of mass in the horizontal direction is calculated. This horizontal projection length is the center of gravity offset data. When the body's center of mass is directly above the actuator axis, the projection length is zero. The greater the pitch deviation of the body and the longer the lever arm, the greater the projection length.

[0075] Based on the preset attitude unloading mapping function, the center of gravity offset data is spatially transformed to generate displacement compensation components corresponding to each actuator. These displacement compensation components are then combined into offset parameters, as shown in the following formula:

[0076] ;

[0077] in, The offset parameter is in mm. This is the preset attitude unloading ratio coefficient. The data is the center of gravity offset (mm). The attitude unloading mapping function is used to convert the center of gravity offset into displacement compensation components for each actuator. The preset attitude unloading ratio coefficient represents the reference attitude translation amount corresponding to a unit center of gravity offset, which is calibrated based on the mapping relationship between the center of gravity offset and the reference attitude adjustment amount according to the body geometry.

[0078] The offset parameter is dimensionally aligned with the preset first reference state and then superimposed to obtain the second reference state, as shown in the following formula:

[0079] ;

[0080] in, This is the second reference state (mm). This is the first reference state (mm). The offset parameter is (mm); the first reference state is a reference quantity consisting of the target attitude reference given by the upper-level motion planning or operation command, such as the target leg length, the target body position, etc. When there is no attitude unloading requirement, the second reference state is the same as the first reference state.

[0081] Continuing with the aforementioned scenario, the second actuator (right leg posterior joint motor) continuously outputs power at approximately 15W after absorbing the load; assuming the equivalent heat capacity of this actuator... 8J / ℃, allowable temperature rise If the temperature is 40℃, then the energy consumption threshold is... This corresponds to a continuous output of approximately 21 seconds; when the integral parameter When the value exceeds 320J, attitude reconstruction is triggered: set the center of gravity offset data. The preset attitude unloading ratio coefficient is 12mm. If it is 0.5, then the offset parameter Second reference state The target orientation is shifted by about 6mm in the direction of reducing the gravitational lever arm in order to reduce the continuous gravitational torque acting on the receiving end.

[0082] Through the above scheme, the state update module feeds back the energy accumulation state of the lower execution end to the upper reference trajectory. By reconstructing the reference attitude, the continuous load is reduced from the mechanical source, providing the solution and execution module with a second reference state that takes into account both disturbance resistance and load unloading.

[0083] While load transfer can distribute steady-state loads between the execution ends, prolonged high loads at the receiving end can lead to energy and heat accumulation. Furthermore, simple torque-level distribution cannot eliminate the load continuously generated at the mechanical source due to factors such as center-of-mass offset. By integrating the output power of the receiving end over time, its accumulated energy can be quantified. When a threshold is exceeded, the gravitational lever arm can be shortened by changing the reference attitude (such as target leg length or target body position), thus unloading the continuous load from the mechanical source. This allows the energy consumption and heat generation status of the lower layer to be directly fed back to the upper-level reference trajectory planning. By changing the physical configuration, the continuous gravitational torque can be reduced, preventing thermal damage to the receiving end caused by prolonged high loads.

[0084] As an alternative, one could rely solely on the thermal protection derating of the actuator itself, or simply increase the attitude-related cost weights to suppress attitude deviations. However, the former is a passive response and comes at the cost of lost output, while the latter, due to the derivative of the quadratic cost near zero, has limited suppressive effect from simply increasing the weights and may cause body oscillations. The reason for choosing to drive attitude reconstruction with power time integration is that power time integration represents accumulated energy rather than instantaneous value, which corresponds to the heat accumulation of the actuator. Driving the reference attitude translation with center of gravity offset can directly act on the lever arm that generates continuous torque.

[0085] After the boundary correction module and load transfer module obtain the second constraint boundary and the state update module obtains the second reference state, the solution and execution module incorporates the above dynamic physical constraints and reconstructed reference state into the optimization solution domain for calculation, and converts the solution result into an executable torque command.

[0086] return Figure 1 In the solution and execution module, optimization is performed based on the second constraint boundary and the second reference state. The generated first-step control parameters are extracted as actual output parameters for feedback adjustment, including:

[0087] First, it should be noted that the optimization solution employs an iterative linear quadratic regulator (iLQR) that performs a rolling solution within the prediction time domain. It uses the second reference state as the objective and the second constraint boundary as the torque feasible region to optimize the quadratic cost function. The quadratic cost function consists of a state deviation weighting term and a control deviation weighting term. The control deviation weighting term uses the low-frequency steady-state disturbance as its zero point, i.e., it is constructed as the square of the difference between the control quantity and the low-frequency steady-state disturbance. Its determination method is as follows: the equivalent disturbance estimated by the extended state observer is decomposed; the low-frequency steady-state component is used to shift the control zero point and the amplitude limit zero point of the cost function (corresponding to the processing of correcting the constraint boundary with steady-state parameters in the boundary correction module); the high-frequency fast component enters the forward prediction process and decays exponentially with the prediction step size. The weight matrices of the state deviation weighting term and the control deviation weighting term are tuned according to the relative importance of each state quantity and control quantity and their physical dimensions after normalization.

[0088] It should be noted that the quadratic cost function targeted by the optimization is the overall objective consisting of the sum of the running costs of each node and the terminal cost within the prediction time domain; the first and second derivatives of the cost function with respect to the control torque in the subsequent backward recursion refer to the first and second derivatives of the control torque of the current prediction node with respect to the node, derived from the overall quadratic cost function, from the current prediction node to the end of the prediction time domain (i.e., the cost to be optimized of the node); the two originate from the same quadratic cost function, only differing in their scope of application—the former is the optimization objective for the entire prediction time domain, while the latter is a local sensitivity characterization of the objective at a single node in the backward recursion.

[0089] Based on the system state parameters and the second reference state, an initial optimization sequence is constructed in the prediction time domain. In this module, the initial optimization sequence is the initial value for iterative optimization. It is constructed by shifting the optimal control sequence obtained in the previous control cycle one time step to the left along the time axis and using it as the initial value for the current cycle, i.e., hot start. If there is no optimal control sequence from the previous cycle in the first control cycle, the initial optimization sequence is taken from a preset initial sequence, such as an all-zero sequence or an initial guess sequence composed of gravity feedforward. Compared with searching from zero, hot start can reduce the convergence pressure of iterative optimization and is beneficial to obtain a usable solution within a limited control cycle.

[0090] Iterative optimization is performed based on the initial optimization sequence. In the reverse recursive calculation stage, the predicted input data of the current prediction node is numerically compared with the amplitude limit threshold of the second constraint boundary.

[0091] In this context, the prediction nodes are the discrete time-series nodes within the prediction time domain. The state deduction within the prediction time domain is based on the system's state transition relationship, which maps the system state parameters and control variables of the current node to the system state parameters of the next node. This relationship is obtained by linearizing the robot dynamics in the neighborhood of the current working point, and its coefficients are updated online according to the interval where the leg length is located. Using the current system state parameters as initial values, the prediction time domain is pushed forward node by node along this state transition relationship to obtain the system state of each prediction node and the prediction input data of that node. In the reverse recursive calculation stage, the prediction time domain is pushed back node by node from the end node to the initial node. At each node, the first and second derivatives of the control torque of the cost to be optimized with respect to that node are calculated. The prediction input data is the control torque value of the forward trajectory at that node in the current iteration.

[0092] When the predicted input data is determined to have reached the amplitude limit threshold, and the numerical sign of the optimization gradient data corresponding to the current node points outside the amplitude limit threshold, the optimization gradient data is masked and frozen. The constrained descent step size is then calculated using the unmasked optimization gradient data, including:

[0093] In this module, the optimization gradient data is the first derivative of the cost function with respect to the control torque. Its numerical sign indicates the direction of descent of the cost function. When the predicted input data has reached the limit threshold and the optimization gradient data points outside the limit threshold (i.e., continuing to update along this direction will cause the control quantity to go out of the feasible region), the optimization gradient data of this dimension is subjected to a masking and freezing process to make the update direction fall within the feasible region, thereby satisfying the torque constraint inside the solution process, rather than truncating the result after the solution.

[0094] Extract the second-order cost feature matrix corresponding to the current node; specifically, the second-order cost feature matrix of each prediction node is obtained in the above reverse recursion process. It is composed of the second derivative of the node's running cost with respect to the control torque and the second-order cost term passed back from subsequent nodes through the state transition relationship. Therefore, it is a square matrix with each control dimension as the row and column. Its diagonal elements represent the second-order sensitivity of each control dimension itself, and the off-diagonal elements represent the cross-coupling between different control dimensions. The second-order cost feature matrix is ​​the second-order derivative matrix of the cost function with respect to the control torque, which reflects the second-order influence of each control dimension itself and its cross-coupling on the cost.

[0095] The masking and freezing process for the optimization gradient data is simultaneously applied to the second-order cost feature matrix block, freezing the cross-coupling parameters of the associated dimensions to obtain the dimensionality-reduced feature matrix block.

[0096] Perform positive definite matrix decomposition and inversion on the dimensionality-reduced feature matrix block to obtain the inverse optimization operator, the specific formula of which is as follows:

[0097] ;

[0098] in, For the reverse optimization operator ( ), The feature matrix block is a reduced-dimensionality matrix that reflects the second derivative of the cost function with respect to the control torque. The cross-coupling parameters of the frozen dimensions are simultaneously frozen to obtain a dimensionality-reduced feature matrix block that retains only feasible dimensions. This avoids interference from constrained dimensions on the update directions of other dimensions. Specifically, the simultaneous freezing is achieved by setting the off-diagonal elements of the row and column containing the frozen control dimension in the second-order cost feature matrix (i.e., the cross-coupling terms between this dimension and other dimensions) to zero, so that the frozen dimension no longer participates in the solution of the update directions of other dimensions. The dimensionality-reduced feature matrix block is then formed by the submatrices corresponding to the remaining unfrozen dimensions. The inversion of positive definite matrix decomposition can be implemented using Choleski decomposition, which obtains the inverse optimization operator while ensuring that the matrix is ​​positive definite.

[0099] The inverse optimization operator is used to perform mapping calculations on the unmasked optimization gradient data to generate the constrained descent step size, as shown in the following formula:

[0100] ;

[0101] in, To constrain the descent step size ( ), For the reverse optimization operator ( ), This is the unmasked optimization gradient data, reflecting the first derivative of the cost function with respect to the control torque. );

[0102] The initial optimization sequence is updated using the constrained descent step size, and an optimized control sequence satisfying the second constraint boundary is iteratively generated, as shown in the following formula:

[0103] ;

[0104] in, For the updated optimized control sequence ( ), For the initial optimization sequence ( ), To constrain the descent step size ( );

[0105] When the iterative calculation reaches the preset termination condition, the optimization solution is stopped, and the first control parameter in the optimization control sequence is extracted as the actual output parameter to perform feedback adjustment.

[0106] It should be noted that the termination condition is the stopping criterion for iterative optimization, and it is determined as follows: when the number of iterations reaches the preset maximum number of iterations, or when the decrease in the cost function between two adjacent iterations is less than the preset convergence threshold, the termination condition is satisfied. The maximum number of iterations and the window length of the prediction time domain are set based on the available computing power within a single control cycle to ensure that the solution is completed within the control cycle. In one example, the window length of the prediction time domain is set to 20 steps and the maximum number of iterations is set to 2.

[0107] The actual output parameters are used as input parameters for the next cycle. Specifically, the first control parameter is the first control quantity in the optimized control sequence corresponding to the current cycle, which includes the left wheel torque, right wheel torque, left leg virtual torque, and right leg virtual torque. The wheel torque is applied to the hub motor after output protection, and the leg virtual torque is mapped to the torque of the front and rear joint motors through the virtual model control and then applied to the corresponding joint motors. This transforms the abstract control quantity output by the optimization solution into a torque command that can be executed by each execution end. The torque command is the target torque value sent to the motor driver of each execution end. The driver converts it into a target current based on the torque-current relationship of the motor, and it is tracked by the current closed loop of the motor, so that each execution end outputs the target torque. The actual output parameters are recorded at the same time and used as input parameters for solving the steady-state parameters and constructing the initial optimization sequence in the next cycle.

[0108] If the torque exceeding the limit is truncated after the solution is completed, it will destroy the optimal control sequence obtained by optimization and may cause trajectory distortion. Therefore, the torque constraint needs to be handled internally in the optimization solution. In the reverse recursion process of the iterative linear quadratic regulator, when the predicted input reaches the limit threshold and the optimization gradient points outside the limit, the corresponding gradient components and the associated coupling terms in the second-order cost feature matrix are frozen, so that the descent direction constraint is within the feasible region. The advantage of this operation is that the constraint is satisfied internally in the solution, avoiding the trajectory distortion caused by solving the non-executable torque first and then forcibly truncating it. Combined with the second constraint boundary that has deducted the steady-state disturbance bias, it enables the solver to optimize within the truly usable control boundary.

[0109] As alternatives, constraints can be handled by methods such as hard truncation at the output end, penalty function method or interior point method, and effective set quadratic programming. However, hard truncation will destroy the optimal trajectory, penalty function method requires tuning of penalty weights and constraints are not strictly satisfied, and interior point method and effective set quadratic programming have large computational costs and are not conducive to real-time solutions within short control cycles. The reason for choosing the projection solution with simultaneous freezing of gradient and second-order matrix is ​​that it satisfies box moment constraints while maintaining Newton-type iterative convergence, and the computational cost is comparable to that of unconstrained iterative solutions.

[0110] Furthermore, to ensure that the load transferred from the load transfer module to the second execution terminal does not exceed the available margin of that execution terminal, refer to... Figure 3 Before generating the transition parameters based on the spatial basis vectors, this system also imposes constraints on the upper limit of the transition, as follows: Before generating the transition parameters based on the spatial basis vectors, the following also applies:

[0111] Based on the system state parameters, the predictive control sequence of the second execution terminal within the preset sliding window is deduced, and the difference sequence between the predictive control sequence and the initial limiting boundary of the second execution terminal is extracted.

[0112] Specifically, the derivation of the predictive control sequence is based on the state transition relationship of the aforementioned system: taking the current system state parameter as the initial value, the predictive control quantity acting on the second execution terminal at each time node is obtained by advancing node by node along the state transition relationship within the preset sliding window. The predictive control quantity of each node is arranged in time sequence to form the predictive control sequence of the second execution terminal within the sliding window. The difference sequence is a sequence composed of the difference between the initial limiting boundary of the second execution terminal and the corresponding value of its predictive control sequence at each time node within the preset sliding window. It represents the remaining available amount of the second execution terminal from its limiting boundary at each time point within the sliding window.

[0113] Extreme value extraction is performed on the difference sequence to obtain a compensation margin parameter representing the available range of the second execution end within a preset sliding window, including:

[0114] Obtain the decay weight sequence that matches the time series length of the preset sliding window; specifically, the decay weight sequence is a weight sequence that decreases with time series node indices, and it is determined by exponential decay according to the time series node indices, as shown in the following formula:

[0115] ;

[0116] in, Let be the decay coefficient value of the decay weight sequence at the i-th node. The attenuation coefficient (value range 0 < 0) <1), the decay coefficient is set according to the reliability of the prediction in time series, so that near-end nodes get higher weight and far-end nodes have exponentially decayed weight;

[0117] The difference sequence and the decay weight sequence are weighted by corresponding terms to obtain the weighted difference sequence, as shown in the following formula:

[0118] ;

[0119] in, The value of the weighted difference sequence at the i-th node ( ), The value of the difference sequence at the i-th node ( ), Let be the decay coefficient value (dimensionless) of the decay weight sequence at the i-th node, where i is the index number of the time-series node within a preset sliding window in the sequence (difference sequence, decay weight sequence, or weighted difference sequence);

[0120] The minimum value is extracted by traversing the weighted difference sequence and used as the compensation margin parameter. Specifically, the minimum value in the weighted difference sequence is taken as the compensation margin parameter. The most unfavorable value of the available amount of the second execution end within the preset sliding window is taken as the upper limit of its load capacity, so as to avoid the second execution end from exceeding its limit boundary at any time within the preset sliding window due to load transfer.

[0121] Extract the steady-state parameters corresponding to the first execution end, compare the steady-state parameters with the compensation margin parameters, and generate a constraint bearing range for limiting the upper limit of load transfer, including:

[0122] The dimension transformation operator is extracted using spatial basis vectors. The steady-state parameters are then mapped to the physical domain of the second execution terminal using the dimension transformation operator, resulting in the mapped steady-state parameters. The specific formula is as follows:

[0123] ;

[0124] in, To map steady-state parameters ( ), This is a dimension transformation scaling operator, representing the deceleration ratio across execution ends. The steady-state parameter corresponding to the first execution end ( The dimension transformation operator is used to convert the steady-state parameters of the first execution end to the torque physical domain of the second execution end; specifically, it takes the ratio of the second execution end component to the first execution end component in the spatial basis vector, which physically corresponds to the cross-end deceleration ratio between the two execution ends; the mapped steady-state parameters are the equivalent torque of the steady-state load to be transferred from the first execution end to the second execution end;

[0125] Calculate the difference parameter between the compensation margin parameter and the mapped steady-state parameter, and obtain the sign characteristic of the difference parameter, as shown below:

[0126] ;

[0127] in, For difference parameters, To map steady-state parameters ( ), For the compensation margin parameter ( );

[0128] A smoothing truncation function is constructed based on the characteristics of positive and negative signs. The specific formula is as follows:

[0129] ;

[0130] in, The activation coefficients are calculated for the smooth cutoff function. The sign function is used to extract the characteristics of positive and negative signs, and its output is a dimensionless constant.

[0131] By applying a smooth truncation function to limit the mapped steady-state parameters, the limited steady-state parameters are obtained, as shown in the following formula:

[0132] ;

[0133] in, For the amplitude-limited steady-state parameter ( ), To map steady-state parameters ( ), For the compensation margin parameter ( );

[0134] The amplitude-limiting steady-state parameter is used as the upper limit to generate the constrained bearing interval; the constrained bearing interval is used as the boundary input condition, and the transfer parameter is generated within the constrained bearing interval based on the spatial basis vector;

[0135] The smoothing cutoff function takes a value between the mapped steady-state parameter and the compensation margin parameter based on the sign of the difference parameter: when the mapped steady-state parameter does not exceed the compensation margin parameter (i.e., the second execution end margin is sufficient to handle the transferred load), the limiting steady-state parameter takes the mapped steady-state parameter; when the mapped steady-state parameter exceeds the compensation margin parameter, the limiting steady-state parameter replaces the compensation margin parameter, thereby limiting the transfer upper limit to within the available margin of the second execution end. After generating the constraint bearing interval with the limiting steady-state parameter as the upper limit, the transfer parameter is generated within this interval, so that the actual transferred load does not exceed the amount that the second execution end can bear within the preset sliding window.

[0136] The upper limit of load transfer is limited by the available margin of the second execution terminal itself. If the transfer amount is not constrained, excessive transfer may cause the second execution terminal to exceed its limit boundary at subsequent times, resulting in secondary saturation. By extrapolating the difference between the predicted control sequence of the second execution terminal and its limit boundary within a preset sliding window, and using the minimum value of the difference sequence after attenuation weighting as the available margin, the upper limit of transfer is set accordingly. The advantages of this operation are: it ensures that the load transfer amount does not exceed the actual available margin of the second execution terminal within the preset sliding window, avoiding secondary saturation of the second execution terminal caused by transfer; attenuation weighting makes the margin assessment focus on near-end nodes with higher confidence, exponential decay reduces the impact of far-end prediction uncertainty on the margin assessment, and the smooth truncation function smoothly takes values ​​between the mapped steady-state parameter and the compensation margin parameter according to the sign of the difference, avoiding abrupt changes in the transfer amount caused by hard switching.

[0137] As an alternative, a fixed upper limit for transfer or only the margin at the current moment can be used as a constraint. However, a fixed upper limit is difficult to adapt to changing operating conditions, and only taking the margin at the current moment ignores the dynamic changes of the margin within the preset sliding window. The reason for choosing the weighted minimum margin constraint based on the preset sliding window is that it evaluates the available range of the second execution end within the entire preset sliding window and takes the most unfavorable value, so that the transfer amount is within the safe range at each moment within the preset sliding window.

[0138] Example 2:

[0139] In one embodiment of the present invention, which differs from the previous embodiment, the electronic device includes one or more processors and a memory.

[0140] A processor can be a central processing unit (CPU) or other form of processing unit with data processing and / or instruction execution capabilities, and can control other components in an electronic device to perform desired functions.

[0141] The memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. Volatile memory may include, for example, random access memory (RAM) and / or cache memory. Non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc.

[0142] In one example, the electronic device may also include input devices and output devices, which are interconnected via a bus system and / or other forms of connection mechanisms (not shown). In addition, depending on the specific application, the electronic device may include any other suitable components.

[0143] Example 3:

[0144] Embodiments of this application may also be computer-readable storage media storing computer program instructions thereon, which, when executed by a processor, cause the processor to perform the steps described in the "Embodiment 1" section of this specification according to the various embodiments of this application.

[0145] Computer-readable storage media may take the form of any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may, for example, include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0146] The basic principles of this application have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this application are merely examples and not limitations, and should not be considered as essential features of each embodiment of this application. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not restrict the application from being implemented using the specific details described above.

[0147] The block diagrams of devices, apparatuses, devices, and systems involved in this application are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0148] It should also be noted that in the apparatus, equipment, and methods of this application, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered as equivalent solutions of this application.

[0149] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this application. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of this application. Therefore, this application is not intended to be limited to the aspects shown herein, but rather to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0150] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this application to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. A wheel-legged balancing robot MPC control system, characterized in that, include: The boundary correction module is used to obtain the system state parameters of the current cycle and the input parameters of the previous cycle, calculate the steady-state parameters based on the system state parameters and the input parameters, and use the steady-state parameters to correct the initial amplitude limiting boundary between the first execution terminal and the second execution terminal to obtain the first constraint boundary. The load transfer module is used to determine the inverse mapping matrix based on the system state parameters, and to determine the spatial basis vector based on the inverse mapping matrix. The spatial basis vector is the adjustment direction vector in the torque space of the execution end that keeps the net virtual support force of the leg unchanged. When the first constraint boundary of the first execution end reaches the preset lower limit threshold, the module generates transfer parameters based on the spatial basis vector, uses the transfer parameters to transfer the steady-state load of the first execution end to the second execution end, and updates the corresponding first constraint boundary to obtain the second constraint boundary. The state update module is used to perform time integration on the output power of the second execution terminal to obtain an integral parameter. When the integral parameter exceeds a preset energy consumption threshold, the offset parameter is calculated based on the system state parameter, and the offset parameter is superimposed with a preset first reference state to obtain a second reference state. The solution and execution module is used to perform optimization solution based on the second constraint boundary and the second reference state, extract the generated first-cycle control parameters as actual output parameters to perform feedback adjustment, and use the actual output parameters as input parameters for the next cycle.

2. The MPC control system for the wheel-legged balancing robot according to claim 1, characterized in that, Before generating the transition parameters based on the spatial basis vectors, the process also includes: Based on the system state parameters, the predictive control sequence of the second execution terminal within a preset sliding window is deduced, and the difference sequence between the predictive control sequence and the initial limiting boundary of the second execution terminal is extracted; Extreme value extraction is performed on the difference sequence to obtain a compensation margin parameter that represents the available range of the second execution end within the preset sliding window; Extract the steady-state parameters corresponding to the first execution end, compare the steady-state parameters with the compensation margin parameters, and generate a constraint bearing range for limiting the upper limit of load transfer; Using the constrained bearing interval as the boundary input condition, the transition parameters are generated within the constrained bearing interval based on the spatial basis vectors.

3. The MPC control system for the wheel-legged balancing robot according to claim 2, characterized in that, The acquisition of the compensation margin parameter includes: Obtain a decay weight sequence that matches the time length of a preset sliding window; The difference sequence and the attenuation weight sequence are weighted according to their corresponding terms to obtain a weighted difference sequence; The minimum value is extracted by traversing the weighted difference sequence, and the minimum value is used as the compensation margin parameter.

4. The MPC control system for the wheel-legged balancing robot according to claim 2, characterized in that, The generation of the constraint bearing range includes: The dimension transformation operator is extracted using the spatial basis vectors, and the steady-state parameter is mapped to the physical domain of the second execution terminal through the dimension transformation operator to obtain the mapped steady-state parameter; Calculate the difference parameter between the compensation margin parameter and the mapped steady-state parameter, and obtain the positive and negative sign characteristics of the difference parameter; A smooth truncation function is constructed based on the positive and negative sign characteristics. The smooth truncation function is used to limit the amplitude of the mapped steady-state parameter to obtain the limited steady-state parameter. The limited steady-state parameter is used as the upper limit value to generate the constraint bearing interval.

5. The MPC control system for the wheel-legged balancing robot according to claim 1, characterized in that, The step of transferring the steady-state load from the first execution terminal to the second execution terminal includes: Extract the first vector element associated with the first execution end from the spatial basis vectors; The first vector element is biased and corrected using a preset regularization factor to obtain a corrected vector element. Based on the corrected vector element, the steady-state load to be transferred at the first execution end is proportionally mapped to obtain a load scaling factor. The gain of the spatial basis vector is adjusted according to the load scaling factor to generate the transfer parameters. The first transfer component corresponding to the first execution end and the second transfer component corresponding to the second execution end are parsed from the transfer parameters. The first transition component and the second transition component are used to update the first constraint boundary of the first execution end and the second execution end respectively.

6. The MPC control system for the wheel-legged balancing robot according to claim 1, characterized in that, The execution feedback adjustment includes: Based on the system state parameters and the second reference state, an initial optimization sequence is constructed in the prediction time domain; Iterative optimization is performed based on the initial optimization sequence. In the reverse recursive calculation stage, the predicted input data of the current prediction node is numerically compared with the amplitude limit threshold of the second constraint boundary. When it is determined that the predicted input data reaches the amplitude limit threshold, and the numerical sign of the optimization gradient data corresponding to the current node points outside the amplitude limit threshold, the optimization gradient data is subjected to masking and freezing processing, and the constraint descent step size is calculated using the unmasked optimization gradient data. The initial optimization sequence is updated using the constrained descent step size, and an optimized control sequence that satisfies the second constraint boundary is iteratively generated. When the iterative calculation reaches the preset termination condition, the optimization solution is stopped, and the first control parameter in the optimized control sequence is extracted as the actual output parameter to perform feedback adjustment.

7. The MPC control system for the wheel-legged balancing robot according to claim 6, characterized in that, The calculation of the constraint descent step size includes: Extract the second-order cost feature matrix corresponding to the current node; The masking and freezing process for the optimization gradient data is simultaneously applied to the second-order cost feature matrix block, freezing the cross-coupling parameters of the associated dimensions to obtain the dimensionality-reduced feature matrix block. Perform positive definite matrix decomposition and inversion on the reduced feature matrix block to obtain the inverse optimization operator; The inverse optimization operator is used to perform mapping calculation on the unmasked optimization gradient data to generate the constrained descent step size.

8. The MPC control system for the wheel-legged balancing robot according to claim 1, characterized in that, Obtaining the second reference state includes: Based on the system state parameters, extract the center of gravity offset data that characterizes the current body posture; The center of gravity offset data is spatially transformed according to the preset attitude unloading mapping function to generate displacement compensation components corresponding to each execution end, and the displacement compensation components are combined into the offset parameter. The offset parameter is dimensionally aligned with a preset first reference state and then superimposed to obtain the second reference state.

9. An electronic device comprising a memory and a processor, characterized in that: The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions, which, when executed by the processor, implement the functions of the system as described in any one of claims 1 to 8.

10. A computer-readable storage medium having computer-executable instructions stored thereon, characterized in that: When the computer-executable instructions are executed by the processor, they implement the functions of the system as described in any one of claims 1 to 8.

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