Unmanned aerial vehicle safety model prediction control method and system based on conditional value-at-risk

Abstract

The invention relates to an unmanned aerial vehicle safety model prediction control method and system based on conditional value-at-risk, and belongs to the technical field of unmanned aerial vehicle control. The method specifically comprises the following steps: S1, obtaining state estimation and a reference trajectory of an unmanned aerial vehicle as input; s2, estimating the uncertainty of the unmanned aerial vehicle system based on the input, and calculating a basic optimal control signal by using a model prediction path integration (MPPI) algorithm; s3, based on the uncertainty and the basic optimal control signal, performing sampling evaluation on the risk by adopting a Monte Carlo method, constructing a risk constraint by utilizing a conditional value-at-risk (CVaR), and calculating an optimal safety control signal through an MPPI algorithm; and S4, fusing the optimal safety control signal with the basic optimal control signal, generating a final control signal, sending the final control signal to the unmanned aerial vehicle for execution, and then returning to the step S1 for cyclic updating. Compared with the prior art, the technical scheme provided by the invention has more excellent performance under an uncertain environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicle (UAV) control, and relates to a UAV safety model predictive control method and system based on conditional value-at-risk (CVaR). Background Art

[0002] In recent years, UAVs have been widely used in tasks such as industrial inspection, low-altitude logistics, and emergency rescue. It is crucial to ensure the safety of UAVs executing the expected planned trajectory. However, in the above tasks, UAVs need to face many uncertainties such as environmental wind disturbances and inaccurate modeling. Moreover, due to the nonlinear and underactuated characteristics of the UAV system, ensuring the safety of UAVs under uncertainties poses many challenges.

[0003] Model Predictive Control (MPC) solves the optimal control problem through the Moving Horizon approach. Model Predictive Path Integral (MPPI), as a sampling-based model predictive control method, has shown excellent performance in UAV control. Existing safety model predictive control methods can be divided into deterministic methods and stochastic methods. Deterministic methods include robust control and adaptive control, etc. Robust control methods ensure the safety of the system by assuming the boundedness of external uncertain disturbances. However, robust control methods will generate overly conservative control strategies and lose the dynamic performance of the system. Adaptive control improves the tracking performance by real-time estimating the linear parameter uncertainties in the dynamic model, thereby ensuring the safety of the system under uncertainties. In the field of UAV flight control, the latest technological progress has adopted an adaptive control method that does not rely on the assumption of the underlying physical model structure and directly estimates unknown aerodynamic forces, but this method requires a high-frequency and low-latency control system to implement. Stochastic methods such as chance-constrained methods ensure the safety of the system by restricting the probability of unsafe events occurring. However, due to the non-convex nature of chance constraints, this method often requires approximation techniques or specific probability distributions to ensure the feasibility of calculation. Conditional value-at-risk (CVaR), as a risk metric that conforms to the consistency axiom, distinguishes risk events by measuring the expectation exceeding the value-at-risk (VaR). And due to its convexity, it has recently been widely applied to the safe motion planning of robots.

[0004] Therefore, it is necessary to study how to use CVaR for UAV safety control to ensure the flight safety of UAVs under uncertainties and overcome the deficiencies of existing methods. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method and system for unmanned aerial vehicle (UAV) safety model predictive control (MPC) based on conditional value at risk (CVaR). The method and system address the problems of existing control methods lacking means for risk perception, deterministic methods such as robust control being too conservative, and stochastic methods lacking perception of tail events. By introducing CVaR into the decision-making process of MPPI, the flight control safety of the UAV is ensured.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for UAV safety model predictive control based on conditional value at risk, the method specifically includes the following steps:

[0008] S1: Obtain the state estimation and reference trajectory of the UAV as inputs;

[0009] S2: Based on the inputs, 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 uncertainty and the basic optimal control signal, use the Monte Carlo method to sample and evaluate the risk, and use conditional value at risk (CVaR) to construct a risk constraint, and calculate the optimal safety control signal through the MPPI algorithm;

[0011] S4: Fuse the optimal safety control signal and the basic optimal control signal to generate a final control signal and send it to the UAV for execution, and then return to step S1 for cyclic update.

[0012] Furthermore, in step S2, the estimation of the uncertainty adopts 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, when calculating the loss function of the MPPI algorithm, a loss discount factor is introduced, and the loss is propagated forward from the last time step, and different weights are assigned at different time steps to enhance the control stability in the long horizon.

[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 is the actual position of the UAV, p k ref is the reference position, δ f,k and δ τ,kThey are force and moment disturbances respectively, γ is the discount factor, and λ is the weight coefficient.

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

[0018] Further, the drone is a quadrotor drone. The discretization of its dynamic model adopts the 4th-order Runge-Kutta method. The control inputs include thrust and moment, and the optimal control sequence is solved by optimizing the KL divergence.

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

[0020] The present invention also provides a drone safety model predictive control system based on conditional value at risk, which adopts the method as described above.

[0021] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the drone safety model predictive control method based on conditional value at risk as described above.

[0022] The present invention also provides a drone control system, including: a sensor module for real-time acquisition of the state information of the drone; a processor module configured to execute the control method as described above; and an execution module for converting the final control signal into a drone drive instruction.

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

[0024] Compared with the existing methods, the model predictive control method based on conditional value at risk proposed by the present invention has better performance under uncertain environments. Specifically, it is reflected in: 1. By adding the Monte Carlo CVaR evaluation method to the model predictive control method, the perception of risk is realized, and the tracking accuracy of the controller under uncertainty is improved. 2. By optimizing the update strategy of the sampling-based model predictive path integral controller, the stability of the control system under long horizons is ensured.

[0025] Other advantages, objectives, and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following specification. Description of the Drawings

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

[0027] Figure 1 It is a schematic diagram of the pseudocode of the method described in the present invention;

[0028] Figure 2 It is a schematic diagram of the safety model predictive control method for unmanned aerial vehicles based on conditional value at risk;

[0029] Figure 3 It is a graph of the experimental comparison results between the method of the present invention and the baseline method;

[0030] Figure 4 It is a graph of the method of the present invention and L1-MPC tracking an eight-shaped trajectory under wind disturbance;

[0031] Figure 5 It is a graph of the observation results of the piecewise constant disturbance observer under wind disturbance. Specific Embodiments

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

[0033] Figure 1 It is a schematic diagram of the pseudocode of the method described in the present invention, Figure 2 It is a schematic diagram of the safety model predictive control method for unmanned aerial vehicles based on conditional value at risk. In this embodiment, taking a quadrotor unmanned aerial vehicle system as an example, its dynamic model is expressed as:

[0034]

[0035] Where: the subscript W represents the world frame, B represents the body frame, p, q, v, ω are the position, attitude, velocity, and angular velocity of the unmanned aerial vehicle respectively, g is the acceleration due to gravity, represents the rotation of a quaternion to a vector, ⊙ represents the multiplication of quaternions, J is the moment of inertia of the unmanned aerial vehicle, T B and M B are the thrust and torque generated by the motors of the unmanned aerial vehicle, and mass is the mass of the unmanned aerial vehicle.

[0036] Using the 4th-order Runge–Kutta method to discretize the continuous dynamic model of the unmanned aerial vehicle, the discrete dynamic model is obtained:

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

[0038] Where, is the input of the system, which are T B and M respectivelyB The original MPPI solves the following problem:

[0039]

[0040] where x0 is 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 samples M trajectories in each control period, evaluates and weights them to obtain the optimal control output. The cost S of the m-th trajectory is m as follows:

[0041]

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

[0043]

[0044] where γ is the cost discount. The optimal control sequence v of the improved MPPI algorithm of the present invention * is obtained by weighted averaging of the samples:

[0045]

[0046] where is the optimal control quantity at the k-th time step, the weight is as follows:

[0047]

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

[0049] Consider the perturbed dynamics model:

[0050]

[0051] where δ f , δ τ are the force and moment perturbations caused by uncertainty respectively. After obtaining the perturbation estimate through the piecewise constant adaptation law in L1 adaptive control, considering the random noise caused by the remaining uncertainty, the true perturbation estimate is:

[0052]

[0053] Define the risk of the above uncertainty to the UAV as:

[0054]

[0055] Among them, the state sequence of the control sequence under uncertainty is To estimate the random variable r, the present invention adopts the Monte Carlo method, samples r for N groups, and uses CVaR for estimation to obtain:

[0056]

[0057] Among them, F r is the cumulative distribution function. For trajectories exceeding the threshold C u soft constraint penalties are adopted, and its cost is updated as:

[0058]

[0059] Finally, the method proposed by the present invention solves the following problem:

[0060]

[0061] The proposed Risk-Averse Model Predictive Path Integral control method (RA-MPPI) based on Conditional Value-at-Risk (CVaR) of the present invention shows significant robustness and trajectory tracking accuracy advantages in complex disturbance environments compared with the prior art. To verify the effectiveness of the method, in this embodiment, circular (c), pentagram (s), and figure-eight (l) trajectory tracking experiments are carried out under four typical disturbance scenarios (no disturbance, constant disturbance, periodic disturbance, wind disturbance), and comparative analysis is carried out with benchmark methods such as MPC, L1-MPC, and MPPI. The experimental results are shown in Figure 3 , and it can be seen that the present invention achieves the optimal performance in 80% of the comparison scenarios, and the trajectory tracking error reduction amplitude under wind disturbance reaches 55.9% in particular.

[0062] The control results of the method proposed in the present invention and the benchmark method are compared in various complex environments. As can be seen from Table 1, in the most challenging wind disturbance scenario, the tracking error of the present method on the pentagram trajectory is 0.089 m, which is 39.0%, 55.9% and 55.1% lower than that of MPPI (0.146 m), MPC (0.202 m) and L1-MPC (0.198 m) respectively. In the figure-eight trajectory tracking task, the present method performs optimally with an error of 0.149 m, which is 16.8% better than the sub-optimal method MPPI (0.179 m). Even in the non-disturbance scenario, the present method still maintains an accuracy advantage, with a tracking error of 0.137 m on the circular trajectory, which is 9.3% lower than that of the traditional MPC (0.151 m). In the thrust decay simulation experiment (constant disturbance), the angle tracking error of the present method on the pentagram trajectory is 0.068 m, demonstrating excellent anti-interference ability. The experiment also shows that the comprehensive error of the method proposed in the present invention in the periodic disturbance scenario is 21.4% lower than that of the MPC method, verifying the stable performance under time-varying disturbances, as Figure 4 shown, the performance of the method proposed in the present invention in complex environments is better than that of L1-MPC, and its estimated value of the disturbance is shown in Figure 5 .

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

[0064]

[0065] An ablation experiment is conducted on the method proposed in the present invention. The ablation experiment verifies the effectiveness of the CVaR module by adjusting the risk-sensitive coefficient A (A = 0 means no risk value mechanism). As shown in the experimental data in Table 2, in the constant force disturbance scenario, the optimal tracking performance (0.139 m) is obtained when A = 5, which is 4.8% better than the baseline A = 0 scheme (0.146 m); in the wind disturbance scenario, the A = 0.5 configuration (0.153 m) is 3.8% lower than the risk-free perception scheme (A = 0, 0.159 m), but the performance slightly drops when A = 5 (0.154 m). Thus, it can be seen that using conditional value at risk can reduce the trajectory tracking error, verifying the effectiveness of the method proposed in the present invention.

[0066] Table 2 Results of the ablation experiment

[0067]

[0068] Although the implementation process of the present invention is mainly evaluated based on unmanned aerial vehicles, the proposed method is also applicable to control tasks in other dynamic environments, such as robot navigation, autonomous driving, and industrial automation control, etc., 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 not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified without departing from the purpose and scope of the present technical solutions, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for predictive control of an unmanned aerial vehicle safety model based on conditional value at risk, characterized in that: The method specifically includes the following steps: S1: Obtain the state estimation and reference trajectory of the unmanned aerial vehicle (UAV) as inputs; S2: Based on the said inputs, estimate the uncertainty of the UAV system, and use the Model Predictive Path Integral (MPPI) algorithm to calculate the basic optimal control signal; S3: Based on the said uncertainty and basic optimal control signal, use the Monte Carlo method to sample and evaluate the risk, and use Conditional Value at Risk (CVaR) to construct a risk constraint, and calculate the optimal safety control signal through the MPPI algorithm; S4: Fuse the said optimal safety control signal with the basic optimal control signal, generate the final control signal and send it to the UAV for execution, and then return to step S1 for cyclic update.

2. The predictive control method for the UAV safety model based on conditional value at risk according to claim 1, wherein: In step S2, the estimation of the said uncertainty adopts a piecewise constant adaptive law to update the uncertainty parameters in real time based on the dynamic model of the UAV.

3. The predictive control method for an unmanned aerial vehicle safety model based on conditional value at risk according to claim 2, wherein: In step S2, when calculating the loss function of the MPPI algorithm, a loss discount factor is introduced, the loss is propagated forward from the last time step, and different weights are assigned at different time steps to enhance the control stability in the long term.

4. A method for predicting and controlling an unmanned aerial vehicle safety model 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: where p k is the actual position of the UAV, p k ref is the reference position, δ f,k and δ τ,k are force and moment disturbances respectively, γ is the discount factor, and λ is the weight coefficient.

5. The predictive control method for the UAV safety model based on conditional value at risk according to claim 4, wherein: In step S3, the construction of the CVaR constraint includes the following steps: sort the risk values of the Monte Carlo samples, select the samples exceeding the Value at Risk (VaR) threshold to calculate the expected value, form the CVaR constraint condition, and incorporate the constraint into the cost function of the MPPI through a soft penalty function.

6. The predictive control method of an unmanned aerial vehicle safety model based on conditional value at risk according to claim 5, wherein: The said UAV is a quadrotor UAV, and its dynamic model is discretized using the 4th-order Runge-Kutta method. The control inputs include thrust and torque, and the optimal control sequence is solved by optimizing the KL divergence.

7. A method for predictive control of an unmanned aerial vehicle safety model based on conditional value at risk according to claim 6, characterized in that: In step S4, the said final control signal is generated by weighted averaging the optimal safety control signal and the basic optimal control signal, and the weights are determined by the trajectory cost distribution of the Monte Carlo samples.

8. A conditional value-at-risk-based UAV safety model predictive control system, characterized in that: This system adopts 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 said program is executed by a processor, it implements the conditional value at risk-based UAV safety model predictive control method described in any one of claims 1 - 7.

10. A drone control system, characterized in that, It includes: A sensor module for obtaining the state information of the UAV in real time; A processor module configured to execute the control method described in any one of claims 1 - 7; An execution module for converting the final control signal into a UAV drive instruction.

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