An unmanned aerial vehicle safety model predictive control method and system based on conditional value at risk

Abstract

The present application relates to a kind of unmanned plane safety model predictive control method and system based on conditional risk value, belong to unmanned plane control technical field.The method specifically includes the following steps: S1: the state estimation of unmanned plane is obtained and reference trajectory as input;S2: based on the input, the uncertainty of unmanned plane system is estimated, and the basic optimal control signal is calculated using model predictive path integral (MPPI) algorithm;S3: based on the uncertainty and basic optimal control signal, risk is sampled and evaluated using Monte Carlo method, and risk constraint is constructed using conditional risk value (CVaR), and the optimal safety control signal is calculated by MPPI algorithm;S4: the optimal safety control signal and basic optimal control signal are fused, generate final control signal and send to unmanned plane execution, then return step S1 and carry out cyclic update.The technical scheme provided by the present application has more excellent performance under environmental uncertainty compared with prior art.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) control technology, and relates to a UAV safety model predictive control method and system based on conditional value of risk. Background Technology

[0002] In recent years, drones have been widely used in tasks such as industrial inspection, low-altitude logistics, and emergency rescue. Ensuring the safety of drones in executing their planned trajectories is crucial. However, in these tasks, drones face numerous uncertainties, such as environmental wind disturbances and inaccurate modeling. Furthermore, due to the nonlinear and underactuated characteristics of drone systems, ensuring the safety of drones under uncertainties presents many challenges.

[0003] Model Predictive Control (MPC) solves optimal control problems using a moving horizon approach. Model Predictive Path Integral (MPPI), a sampling-based MPC method, has demonstrated excellent performance in UAV control. Existing safe MPC methods can be categorized into deterministic and stochastic methods. Deterministic methods include robust control and adaptive control. Robust control methods ensure system safety by assuming the boundedness of uncertain external disturbances. However, robust control methods can lead to overly conservative control strategies, sacrificing dynamic performance. Adaptive control improves tracking performance by estimating the uncertainty of linear parameters in the dynamic model in real time, thus ensuring system safety under uncertainty. In UAV flight control, recent advancements have employed adaptive control methods that directly estimate unknown aerodynamic forces without relying on underlying physical model assumptions, but this method requires a high-frequency, low-latency control system. Stochastic methods, such as those based on chance constraints, ensure system safety by limiting the probability of unsafe events. However, due to the non-convex nature of chance constraints, these methods often require approximation techniques or specific probability distributions to ensure computational feasibility. Conditional value-at-risk (CVaR), as a risk metric conforming to the consistency axiom, distinguishes risky events by measuring the expected value exceeding the risk value (VaR). Furthermore, due to its convexity, it has recently been widely applied in the safe motion planning of robots.

[0004] Therefore, it is necessary to study how to use CVaR for the safe control of UAVs and ensure their flight safety under uncertainty, so as to overcome the shortcomings of existing methods. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a safety model predictive control (MPC) method and system for unmanned aerial vehicles (UAVs) based on Conditional Value at Risk (CVaR). This method and system address many problems in existing control methods, such as the lack of risk perception means, the overly conservative nature of deterministic methods such as robust control, and the lack of perception of tail events in stochastic methods. By introducing CVaR into the decision-making process of MPPI, the flight control safety of UAVs is guaranteed.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A predictive control method for unmanned aerial vehicle (UAV) safety model based on conditional value of risk, the method specifically includes the following steps:

[0008] S1: Obtain the UAV's state estimate and reference trajectory as input;

[0009] S2: Based on the input, estimate the uncertainty of the UAV system and use the Model Predictive Path Integral (MPPI) algorithm to calculate the basic optimal control signal;

[0010] S3: Based on the aforementioned uncertainties and the basic optimal control signal, the Monte Carlo method is used to sample and assess the risks, and risk constraints are constructed using Conditional Value at Risk (CVaR). The optimal safety control signal is then calculated using the MPPI algorithm.

[0011] S4: The optimal safety control signal is fused with the basic optimal control signal to generate the final control signal and sent to the UAV for execution. Then, the process returns to step S1 for cyclical updates.

[0012] Furthermore, in step S2, the uncertainty is estimated using a piecewise constant adaptive law, and the uncertainty parameters are updated in real time based on the dynamic model of the UAV.

[0013] Furthermore, in step S2, the loss function calculation of the MPPI algorithm introduces a loss discount factor, propagates the loss forward from the last time step, and assigns different weights at different time steps to enhance control stability under long field of view.

[0014] Furthermore, in step S3, when the Monte Carlo method samples the risk, the risk value is defined by the following formula:

[0015]

[0016] Where, p k p represents the actual location of the drone. k ref For reference position, δ f,k and δ τ,kLet be force and torque disturbances, respectively, γ be the discount factor, and λ be the weighting coefficient.

[0017] Furthermore, in step S3, the construction of the CVaR constraint includes the following steps: sorting the risk values ​​of the Monte Carlo sampling, selecting samples that exceed the Value at Risk (VaR) threshold to calculate the expected value, forming the CVaR constraint condition, and incorporating the constraint into the cost function of MPPI through a soft penalty function.

[0018] Furthermore, the UAV is a quadcopter UAV, and its dynamic model is discretized using the fourth-order Runge-Kutta method. The control inputs include thrust and torque, and the optimal control sequence is solved by optimizing the KL divergence.

[0019] Furthermore, the final control signal mentioned in step S4 is generated by weighted averaging the optimal safety control signal and the basic optimal control signal, with the weights determined by the trajectory cost distribution of Monte Carlo sampling.

[0020] The present invention also provides a UAV safety model prediction and control system based on conditional value at risk, which employs the method described above.

[0021] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the UAV safety model predictive control method based on conditional value of risk as described above.

[0022] The present invention also provides a drone control system, comprising: a sensor module for acquiring drone status information in real time; a processor module configured to execute the control method described above; and an execution module for converting the final control signal into drone drive commands.

[0023] The beneficial effects of this invention are as follows:

[0024] Compared with existing methods, the model predictive control method based on conditional value of risk proposed in this invention exhibits superior performance under environmental uncertainty. Specifically: 1. By incorporating the Monte Carlo CVaR evaluation method into the model predictive control method, risk perception is achieved, improving the tracking accuracy of the controller under uncertainty. 2. By optimizing the update strategy of the sampling-based model predictive path integral controller, the stability of the control system under long-field-of-view conditions is ensured.

[0025] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0026] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0027] Figure 1 This is a pseudocode diagram of the method described in this invention;

[0028] Figure 2 A schematic diagram of a UAV safety model predictive control method based on conditional value at risk;

[0029] Figure 3 The figure shows the experimental results comparing the method of this invention with the baseline method;

[0030] Figure 4 The diagram shows the method of this invention and L1-MPC tracking a figure-eight trajectory under wind disturbance.

[0031] Figure 5 The figure shows the observation results of the piecewise constant disturbance observer under wind disturbance. Detailed Implementation

[0032] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0033] Figure 1 This is a pseudocode diagram illustrating the method described in this invention. Figure 2 This is a schematic diagram of a UAV safety model predictive control method based on conditional value at risk. In this embodiment, a quadcopter UAV system is used as an example, and its dynamic model is expressed as follows:

[0034]

[0035] Where: the subscript W represents the world frame, B represents the machine frame, p, q, v, ω represent the UAV's position, attitude, velocity, and angular velocity, respectively, and g is the acceleration due to gravity. The symbol represents the rotation of a vector by a quaternion, ⊙ represents the multiplication of quaternions, J is the moment of inertia of the UAV, and T... B With M B Here, represents the thrust and torque generated by the drone's motor, and mass represents the mass of the drone.

[0036] The continuous dynamics model of the UAV is discretized using the fourth-order Runge–Kutta method, resulting in a discrete dynamics model:

[0037] x k+1 =F(x) k u k (2)

[0038] in, The system inputs are T, respectively. B With MB The original MPPI solves the following problem:

[0039]

[0040] Here, x0 represents the current system state. The MPPI algorithm solves this problem by minimizing the KL divergence between the controlled trajectory distribution and the optimal trajectory distribution. It obtains the optimal control output by sampling M trajectories in each control cycle, evaluating and weighting them. The cost S of the m-th trajectory is... m for:

[0041]

[0042] Unlike the original MPPI, for its K time steps, the method of this invention will calculate the cost of the k-th time step for each sampled trajectory.

[0043]

[0044] Where γ represents the cost discount. The optimal control sequence v of the improved MPPI algorithm of this invention. * The following was obtained by weighted averaging of the samples:

[0045]

[0046] in, It is the optimal control quantity at the k-th time step. Weight for:

[0047]

[0048] Then set the next average control sequence v to v = v * .

[0049] Consider the disturbed dynamics model:

[0050]

[0051] Where δ f ,δ τ These represent force and torque disturbances caused by uncertainties, respectively. After obtaining the disturbance estimate through the piecewise constant adaptive law in L1 adaptive control, and considering the random noise caused by other uncertainties, the actual disturbance estimate is:

[0052]

[0053] The risk of the above uncertainties to drones is defined as follows:

[0054]

[0055] The state sequence of the control sequence under uncertainty is as follows: To estimate the random variable r, this invention employs the Monte Carlo method, sampling r N times and using CVaR for estimation, obtaining:

[0056]

[0057] Among them, F r Let C be the cumulative distribution function. For values ​​exceeding the threshold C... u The trajectory is subject to soft constraint penalties, and its cost is updated as follows:

[0058]

[0059] Ultimately, the method proposed in this invention solves the following problem:

[0060]

[0061] The adaptive model predictive path integral control method (RA-MPPI) based on Conditional Value-at-Risk (CVaR) proposed in this invention exhibits significant advantages in robustness and trajectory tracking accuracy under complex disturbance environments compared to existing technologies. To verify the effectiveness of the method, in this embodiment, circular (c), pentagonal (s), and figure-eight (l) trajectory tracking experiments were conducted under four typical disturbance scenarios (no disturbance, constant disturbance, periodic disturbance, and wind disturbance), and compared with benchmark methods such as MPC, L1-MPC, and MPPI. Experimental results are shown in […]. Figure 3 As can be seen, the present invention achieves optimal performance in 80% of the comparison scenarios, especially with a reduction of 55.9% in trajectory tracking error under wind disturbance.

[0062] The control results of the proposed method and the benchmark method were compared in various complex environments. Table 1 shows that in the most challenging wind disturbance scenario, the proposed method achieved a tracking error of 0.089 meters on a pentagram trajectory, representing reductions of 39.0%, 55.9%, and 55.1% compared to MPPI (0.146 meters), MPC (0.202 meters), and L1-MPC (0.198 meters), respectively. In the figure-eight trajectory tracking task, the proposed method performed best with an error of 0.149 meters, a 16.8% improvement over the second-best method, MPPI (0.179 meters). Even in undisturbed scenarios, the proposed method maintained its accuracy advantage, achieving a tracking error of 0.137 meters on a circular trajectory, a 9.3% reduction compared to the traditional MPC (0.151 meters). In the thrust attenuation simulation experiment (constant disturbance), the proposed method achieved an angle tracking error of 0.068 meters on a pentagram trajectory, demonstrating excellent anti-interference capabilities. Experiments also show that the proposed method reduces the overall error by 21.4% compared to the MPC method under periodic perturbation scenarios, verifying its stability under time-varying perturbations. Figure 4 As shown, the method proposed in this invention outperforms L1-MPC in complex environments, and its estimation of disturbances is shown in [reference needed]. Figure 5 .

[0063] Table 1. Trajectory tracking error (m) under different disturbances

[0064]

[0065] Ablation experiments were conducted on the method proposed in this invention. The ablation experiments verified the effectiveness of the CVaR module by adjusting the risk sensitivity coefficient A (A=0 indicates a risk-free value mechanism). As shown in Table 2, under constant force disturbance scenarios, the optimal tracking performance (0.139 meters) was achieved when A=5, representing a 4.8% improvement over the baseline A=0 scheme (0.146 meters). In wind disturbance scenarios, the A=0.5 configuration (0.153 meters) reduced the tracking error by 3.8% compared to the risk-free sensing scheme (A=0, 0.159 meters), but performance slightly declined when A=5 (0.154 meters). This demonstrates that using conditional value at risk can reduce trajectory tracking errors, verifying the effectiveness of the method proposed in this invention.

[0066] Table 2 Ablation Experiment Results

[0067]

[0068] Although the implementation process of this invention is mainly based on evaluation using unmanned aerial vehicles (UAVs), the proposed method is also applicable to control tasks in other dynamic environments, such as robot navigation, autonomous driving, and industrial automation control, and has broad application prospects.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications should be covered within the scope of the claims of the present invention.

Claims

1. A predictive control method for unmanned aerial vehicle (UAV) safety models based on conditional value at risk, characterized in that: The method specifically includes the following steps: S1: Obtain the UAV's state estimate and reference trajectory as input; S2: Based on the input, estimate the uncertainty of the UAV system and use the Model Predicted Path Integral (MPPI) algorithm to calculate the basic optimal control signal; S3: Based on the aforementioned uncertainties and the basic optimal control signal, the Monte Carlo method is used to sample and assess the risks, and risk constraints are constructed using Conditional Value at Risk (CVaR). The optimal safety control signal is then calculated using the MPPI algorithm. S4: The optimal safety control signal is fused with the basic optimal control signal to generate the final control signal and sent to the UAV for execution. Then, the process returns to step S1 for cyclical updates.

2. The UAV safety model predictive control method based on conditional value of risk according to claim 1, characterized in that: In step S2, the uncertainty is estimated using a piecewise constant adaptive law, and the uncertainty parameters are updated in real time based on the dynamic model of the UAV.

3. The UAV safety model predictive control method based on conditional value at risk according to claim 2, characterized in that: In step S2, the loss function calculation of the MPPI algorithm introduces a loss discount factor, propagates the loss forward from the last time step, and assigns different weights at different time steps to enhance control stability under long field of view.

4. The UAV safety model predictive control method based on conditional value at risk according to claim 3, characterized in that: In step S3, when the Monte Carlo method samples the risk, the risk value is defined by the following formula: in, p k The actual location of the drone. p k ref For reference position, δ f,k and δ τ,k Let be force and torque disturbances, respectively, γ be the discount factor, and λ be the weighting coefficient.

5. The UAV safety model predictive control method based on conditional value at risk according to claim 4, characterized in that: In step S3, risk constraints are constructed using Conditional Value at Risk (CVaR), including the following steps: sorting the risk values ​​sampled in Monte Carlo, selecting samples that exceed the Value at Risk (VaR) threshold to calculate the expected value, forming CVaR constraints, and incorporating the constraints into the cost function of MPPI through a soft penalty function.

6. The UAV safety model predictive control method based on conditional value of risk according to claim 5, characterized in that: The UAV is a quadcopter UAV. Its dynamic model is discretized using the fourth-order Runge-Kutta method. The control inputs include thrust and torque, and the optimal control sequence is solved by optimizing the KL divergence.

7. The UAV safety model predictive control method based on conditional value at risk according to claim 6, characterized in that: The final control signal mentioned in step S4 is generated by weighted averaging the optimal safety control signal and the basic optimal control signal, with the weights determined by the trajectory cost distribution of Monte Carlo sampling.

8. A UAV safety model predictive control system based on conditional value at risk, characterized in that: The system employs the method described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the UAV safety model predictive control method based on conditional risk value as described in any one of claims 1-7.

10. A drone control system, characterized in that, include: The sensor module is used to acquire the drone's status information in real time; The processor module is configured to perform the control method as described in any one of claims 1-7; The execution module is used to convert the final control signals into drone drive commands.

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