Preset time safety control method for unmanned vehicle with unknown disturbance
By establishing an uncertain nonlinear affine state system model and loose controllability conditions, a robust adaptive trajectory tracking controller is designed to solve the problems of unknown disturbances and model uncertainty in the trajectory tracking control of unmanned vehicles, and achieve stability and safety control of unmanned vehicles in complex environments.
Patent Information
- Application Number
- CN202510746669.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-05
- Publication Date
- 2025-09-26
AI Technical Summary
Due to unknown disturbances and model uncertainties, traditional methods for trajectory tracking control of unmanned vehicles rely on precise models and have high computational costs. They are difficult to effectively control in complex environments, and the flexibility of controller design is limited.
An uncertain nonlinear affine state system model is established. By introducing loose controllability conditions, a robust adaptive trajectory tracking controller is designed. The preset time safety control framework (PTSS) is adopted to transform the safety set from the output space to the tracking error space, decoupling the output constraints and performance guarantees.
It ensures that the system state stabilizes to a safe area within a preset time, overcomes the limitations of traditional methods, and provides a robust, efficient and low-complexity control solution suitable for unmanned vehicle trajectory tracking in complex environments.
Smart Images
Figure CN120704126A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of automatic control of unmanned vehicles, and more specifically, relates to a preset time safety control method for an unmanned vehicle with unknown disturbances. Background Art
[0002] Over the past few decades, unmanned vehicles (UAVs), owing to their autonomy and flexibility, have been widely used in a variety of fields, including logistics and transportation, intelligent transportation, environmental monitoring, and military reconnaissance. As these applications continue to expand, trajectory tracking control for UAVs has become a key research focus. Trajectory tracking control is a core issue in UAV motion control, directly impacting their driving stability and mission execution capabilities.
[0003] However, unmanned vehicles are strongly coupled, highly nonlinear, and underactuated systems with multiple inputs and degrees of freedom. These complex dynamics make trajectory tracking control extremely challenging. Traditional control methods typically rely on linearization or approximation of the system model, but these methods have significant limitations. For example, linearization methods are only applicable to small-scale trajectory changes, while approximation methods often result in high computational costs and complex control structures, making them difficult to generalize in practical applications.
[0004] Furthermore, the control input gain matrices for autonomous vehicles are often complex and, in some cases, unknown, further complicating control design. Early studies proposed some controllability conditions, but these were often overly conservative, limiting the flexibility of controller design and resulting in many practical systems being unable to be effectively controlled. Summary of the Invention
[0005] Based on the aforementioned background technology, this paper establishes an uncertain nonlinear affine state system model for unmanned vehicles with unknown external disturbances and model uncertainty. By verifying the existence of the auxiliary matrix, a more relaxed controllability condition for the unmanned vehicle model is introduced. Based on this, a robust adaptive trajectory tracking controller is proposed.
[0006] To solve the above technical problems, the technical solution adopted by the present invention is: a preset time safety control method for an unmanned vehicle with unknown disturbances, comprising the following steps:
[0007] S1: Establish the control system model of the unmanned vehicle;
[0008] S2: Based on the control system model of the unmanned vehicle, a time controller model for preset time control is established;
[0009] S3: Based on the controller model of preset time control, a safety controller model of preset time safety control is established;
[0010] S4: Perform stability analysis on the time controller model and safety controller model and verify feasibility.
[0011] Preferably, in step S1, the control system model is expressed as follows:
[0012]
[0013] in, is the state vector of the system, is the state vector The derivative of , which represents the dynamic behavior of the system, Represents the state vector No. Quantity is a nonlinear vector function, is a reversible nonlinear matrix; is the actual control input vector, and is the unknown external disturbance vector; is a real vector space; represents the time variable, Indicates the initial time;
[0014] The actual control input vector Designed to:
[0015]
[0016] in, is the transformed control input vector; the actual control input vector The transformed control input vector Recovery, based on the control system model makes two assumptions:
[0017] Hypothesis 1: External interference There are known upper and lower bounds and ,Right now ;
[0018] Assumption 2: Security Function and and upper and lower bounds and satisfy:
[0019] .
[0020] Preferably, in step S2, the time controller model is established as follows:
[0021]
[0022] in, represents the time controller model, is the control gain parameter used to adjust the convergence speed of the controller; is the design parameter, used for the weight of disturbance compensation; ; is the state vector after transformation.
[0023] Preferably, in step S3, the security controller model is established as follows:
[0024] In the set S The robustness of the control system model is established on the basis of the following barrier function:
[0025]
[0026] in Represents the state vector No. A quantity, represents the barrier function.
[0027] Assume that In the case At the time node, the control system model is robust and safe on S, and the construction and , as well as The differential equation form between the unknowns is established, the obstacles are added to the control system model, and the safety controller model is constructed. ,Right now Satisfy the obstacle constraints, where is a design parameter, and ,let , we get the following equation:
[0028]
[0029] in, represents the control barrier function, Indicates the The barrier function of the state, The first control input after transformation A quantity, The unknown external disturbance A quantity, Indicates the system status A quantity, Indicates the safety controller Quantity
[0030] Security Controller Model Expressed as:
[0031]
[0032] Denotes the time controller input of the i-th dimension, using the sufficient condition Replace the barrier constraint, according to assumption 2, in hour, , indicating sufficient conditions are feasible, and the safety controller is designed by solving the quadratic programming
[0033]
[0034] in, Represents the safety controller input of the i-th dimension, which is used to correct the time control input while ensuring system safety Applying the Karush-Kuhn-Tucker optimality condition to equation (8) yields:
[0035]
[0036]
[0037]
[0038]
[0039] in, and are the upper and lower limits, It means that the state of the safety control system is close to the safety lower limit. It means that the state of the safety control system is close to the upper limit of safety; When , it means that the constraint is not activated, that is, the safety margin is sufficient; or When ≠0, the safety margin is insufficient and the constraint is activated; the safety controller model is obtained. as follows:
[0040] .
[0041] Preferably, step S4 specifically includes the following steps:
[0042] S41. Analysis and verification of the time controller model and the safety controller model:
[0043] The result to be verified is: Assumption 1 is established and the time controller model is applied, for :
[0044] 1) All closed-loop signals are uniformly bounded;
[0045] 2) System state x at time When it stabilizes to zero, ;
[0046] Verification process: When ,and and T are known positive / non-negative constants, which are verified from formula (4). Lemma (1) is the same as The limited range shows that , V(t) is bounded; for all ,have and ; From formula (4) and the fact Know, in Down, ; The uniform boundedness of comes from the uniform boundedness of d(t) under the following assumption: all internal signals are uniformly bounded;
[0047] use Calculated by the uniform boundedness of:
[0048]
[0049] S42. Analysis and verification of control system model:
[0050] The result to be verified is: Assumptions 1 and 2 are valid and the safety controller model is applicable. and , the preset time security control is resolved;
[0051] Verification includes the following:
[0052] Part 1: The security system model is robust and secure within the specified time T on the set S:
[0053] The comparison lemma given by formula (6) is hour, Establishment, combined scope , and set , then the time derivative F is calculated as follows:
[0054] (12)
[0055] make , we can conclude , F is monotonically decreasing with respect to t, so
[0056]
[0057] exist , , Under the conditions, , And formula (6) is established; through formula (10), the obstacle constraint condition is established , which is the necessary and sufficient condition of formula (6), and the verification is completed;
[0058] Part II: Proof :
[0059] Verification process: Formula (10) is a segmented design, and the time interval It is divided into several time periods:
[0060]
[0061] in, and is defined as , if present , then in the time interval Inside, because and are continuous and in time hour , formula (10) is continuous; for , Equation (10) must satisfy one of the three conditions; define the following barrier function in each time interval :
[0062]
[0063] The three situations are as follows:
[0064] )if ,when , by step S41 and the actual , It can be seen that from the first part, the limit ;
[0065] )if ,have
[0066]
[0067] )if ,have
[0068]
[0069] For the scene , solve equation (16), study The limit of the divergence of is obtained according to the comparison criterion and L'Hôpital's rule:
[0070]
[0071] is positive, defined by construction, and there exists an unknown positive constant and ,like ,in , , and is an unknown constant, and using the squeeze theorem we can get:
[0072]
[0073] For the scene , Equation (19) still holds, and by following the similar analytical procedure in the above proof, according to The definition of ;
[0074] Part III: Prove that the closed-loop signal is Uniform boundedness of an interval:
[0075] For the scene , From Theorem 1, we can conclude that both are bounded; for the scenario and , The uniform boundedness of ,when and By constructing uniformly bounded, through the scene ,get
[0076]
[0077] when When , it can be concluded from (20) that for , is bounded; when When , apply the Lagrange mean value theorem twice to the first term on the right side of Equation (20), and then multiply by , and finally, through L'Hôpital's rule and formula (18), we can get:
[0078]
[0079] It can be seen that exist Convergent when , you can also check exist is bounded, and when It converges when ; therefore, exist is uniformly bounded; moreover, , guaranteed uniformly bounded; due to It is bounded. It is also uniformly bounded.
[0080] The beneficial effects of adopting the above technical solution are: the present invention uses a preset time safety and stability control framework (PTSS) to convert the safety set from the output space to the tracking error space and plan the performance boundary, effectively decoupling the output constraints and performance guarantees, ensuring that the system state is strictly in the safety area and stabilizes to zero within the preset time T, solving the problems of traditional methods relying on precise models, high computational costs and inability to effectively handle dynamic safety constraints. At the same time, by relaxing the controllability conditions, the scope of applicable systems is expanded, providing a robust, efficient and low-complexity control solution for the trajectory tracking of unmanned vehicles in complex environments, effectively addressing the safety, stability and real-time challenges in the motion control of unmanned vehicles. BRIEF DESCRIPTION OF THE DRAWINGS
[0081] Figure 1 is the numerical example response of the time controller model;
[0082] Figure 2 is an example of a numerical response of the safety controller model;
[0083] Figure 3 It is a simulation of the safety controller response of the actual application. DETAILED DESCRIPTION
[0084] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.
[0085] The present invention provides a robust safety trajectory tracking control scheme for a multi-input multi-output nonlinear system with unknown external human disturbance. The specific implementation steps are as follows:
[0086] S1: Select the unmanned vehicle as the research object and analyze its control system model.
[0087] The control system model of the unmanned vehicle is expressed as follows:
[0088]
[0089] in, is the state vector of the system, is the state vector The derivative of , which represents the dynamic behavior of the system, Represents the state vector No. Quantity is a nonlinear vector function, is a reversible nonlinear matrix; is the actual control input vector, and is the unknown external disturbance vector; is a real vector space; represents the time variable, Indicates the initial time.
[0090] In the present invention, and can be used to design the control system model. Therefore, the actual control input vector Can be designed as:
[0091]
[0092] in, is the transformed control input vector. Obviously, the actual control input vector The transformed control input vector Recovery. Based on the constructed control system model, two assumptions can be made for subsequent design.
[0093] Hypothesis 1: External interference There are known upper and lower bounds and ,Right now .
[0094] Assumption 2: Security Function and and upper and lower bounds and satisfy:
[0095] .
[0096] S2: Based on the control system model, design a time controller model for preset time control.
[0097] We are in time Under the condition that the control system model in step 1 is stable without considering the safety constraints, let .right Taking the derivatives of equations (1) and (2), we can get: , combined with the derived time derivative of V, and then using assumption 1 and Young's inequality to design the time controller model as follows:
[0098]
[0099] in, represents the time controller model, is the control gain parameter used to adjust the convergence speed of the controller; is the design parameter, which is used as the weight of disturbance compensation to ensure that the control system is stable within the preset time T; ; is the state vector after transformation.
[0100] S3: Based on the time controller model in step S2, a safety controller model for preset time safety control is designed.
[0101] In order to be in the set S To establish the robustness of the control system, we introduce the following barrier function:
[0102]
[0103] Assume that Under this condition, the control system model is robust and secure on S. Combining equations (1), (2) and (5), we construct the equation and , as well as The differential equation form between the unknowns is established, and the differential relationship between the unknowns is established. The obstacles are added to the control system model to test the stability of the control system model under interference. Therefore, we design a safety controller model By force The differential with time, Satisfy the obstacle constraints, where is a design parameter, and . Let Simplify to the following equation:
[0104]
[0105] In order to make the above formula (6) valid, the safety controller model The design is based on the following online quadratic programming problem:
[0106]
[0107] However, d(t) in the formula is unknown, which makes it impossible to solve the quadratic programming problem (7). We can use the sufficient condition: To replace the obstacle constraint, according to assumption 2, Under the conditions, , which means that the above sufficient conditions are always feasible. Therefore, we can design the safety controller model by solving the quadratic programming .
[0108]
[0109] Applying the Karush-Kuhn-Tucker (KKT) optimality condition to equation (8) yields:
[0110]
[0111]
[0112]
[0113]
[0114] In the formula and Are the upper and lower limits. This means that the state of the safety control system is close to the safety lower limit, and the time controller must apply additional control force to avoid crossing the limit. This means that the state of the entire control system is close to the upper limit of safety, and the time controller needs to be adjusted in the opposite direction. When , the constraint is not activated, that is, the safety margin is sufficient. At this time, the safety controller delays the control input with the preset time control. or When ≠0, the safety margin is insufficient, the constraint is activated, and the time controller needs to sacrifice some performance to meet the safety requirements. The various situations considered in this invention all meet the upper and lower limit ranges, so the safety controller model can be Designed for
[0115]
[0116]
[0117] S4: Perform stability analysis on the time controller model and safety controller model of the present invention to verify the feasibility of the invention. The specific steps are as follows:
[0118] S41. Analysis and verification of the time controller model and the safety controller model
[0119] Considering a control system model with unknown external disturbances, if the assumption in step S1 holds and the time controller model is applied, then for :
[0120] 1) All closed-loop signals are uniformly bounded;
[0121] 2) System state x at time When it stabilizes to zero, .
[0122] Proof: When ,and and T are known positive / non-negative constants, which can be verified from formula (4). Lemma (1) is consistent with The limited range shows that , V(t) is bounded. Therefore, for all , we have and From (4) and the fact We know that in Down, .Then, The uniform boundedness of follows from the uniform boundedness of d(t) under the assumption that all internal signals are uniformly bounded.
[0123] Finally, we can use Calculated by the uniform boundedness of:
[0124]
[0125] S42. Analysis and verification of control system model
[0126] Consider a MIMO nonlinear control system model with unknown external disturbances. If Assumptions 1 and 2 are satisfied and the safety controller model is applicable, then for all and , the preset time security control is resolved.
[0127] The proof consists of three parts. The first part is to prove that the control system model is robust and secure within the specified time T on the set S; the second part is to prove that ; The last part is to prove that all closed-loop signals are are uniformly bounded.
[0128] Part I: We prove that the control system model is robust and secure within the specified time T on the set S. Obviously, the comparison lemma given by Equation (6) is hour, Established, then combined with the scope , and set , then the time derivative F is calculated as follows:
[0129] (12)
[0130] By selecting , we conclude , that is, F is monotonically decreasing with respect to t. Therefore, we have
[0131]
[0132] This means that ,Right now , Under the conditions , And (6) holds. Through the safety controller model, the obstacle constraint condition is established , which is a necessary and sufficient condition for formula (6). The first part is completed.
[0133] Part II: We now prove . Note the segmented design of the security controller model, we divide the time interval It is divided into several time periods:
[0134]
[0135] in and is defined as , if present , then in the time interval Inside, because and are continuous and in time hour , the security controller model is continuous. , the safety controller model must satisfy one of the three conditions. We define the following barrier function in each time interval :
[0136]
[0137] So consider the following three cases:
[0138] )if .when , by step S41 and the actual , We can see that we have the limit proved from the first part .
[0139] )if , we have
[0140]
[0141] )if , we have
[0142]
[0143] For the scene , we first solve equation (16), and then study The limit of the divergence of , and then according to the comparison criterion and L'Hôpital's rule, we get:
[0144]
[0145] because is positive and bounded by construction, there is an unknown positive constant and ,For example ,in , , and is an unknown constant, and then using the squeeze theorem we can get:
[0146]
[0147] For the scene , (19) still holds, by following the similar analytical procedure in the above proof. According to We have the definition of . The second part is completed.
[0148] Part III: Finally, we prove that the closed-loop signal Uniform boundedness of interval. For the scenario , From step S41, it is concluded that both are bounded. and , The uniform boundedness of ,when and By construction, it is uniformly bounded. We first study the scenario .
[0149]
[0150] when When , we can derive from formula (20) that , is bounded. When , apply the Lagrange mean value theorem twice to the first term on the right side of Equation (20), and then multiply by , and finally, through L'Hôpital's rule and formula (18), we can get:
[0151]
[0152] This means exist For the scene , you can also check exist is bounded, and when By using the same arguments as in the proof above, it converges. Therefore, exist is uniformly bounded. In addition, remember that , which ensures Finally, due to the uniform boundedness of It is bounded. It is also uniformly bounded. The proof is complete.
[0153] Next, the time controller model and the safety controller model are simulated and verified.
[0154] Numerical Example
[0155] We conduct simulation experiments on a two-dimensional numerical example where the system nonlinearity and external disturbance are respectively given by and Then it can be verified that when and Our goal is to enforce robust security of the example on the set S determined by the security function
[0156]
[0157] This obviously makes hypothesis 2 valid.
[0158] In the simulation, we set the initialization and regulation times to and For time controller We choose the design parameters as For safety controllers , we choose the design parameters as In addition, the system initialization condition is .、
[0159] The numerical simulation results are as follows Figure 1 Figure 2 As shown. Figure 1 Describes the time controller System status and actual input From Figure 1 It can be seen that the system state x is at the preset time is stabilized to 0, the actual input It is bounded.
[0160] Figure 2 Describes its use in safety controllers The results show that this numerical example is robust and secure on the set S, and , and the actual input is continuous and bounded. Therefore, the effectiveness of the proposed control scheme is verified.
[0161] Practical Application Example: 2-D Mobile Robot
[0162] To demonstrate the practical applicability of the developed control method, we consider the problem of safe parking of a mobile robot in a predetermined time while performing a task on a two-dimensional plane. According to the sufficient conditions for the design of a safety controller, the kinematic model of the robot is:
[0163]
[0164] in represents the position and posture of the mobile robot in the body coordinate system, Indicates along the attitude direction The translation velocity v and the angular velocity perpendicular to the body coordinate system ,and represents the unknown external disturbance. Here is considered as the control input of Eq. (23). We use the position of the hand and transformation vector Convert Equation (23) into the following equivalent form:
[0165]
[0166] We aim to set the time The mobile robot is parked at the original position of the hand within , while not violating the safety area determined by the set S given in Section G. In the simulation, the system parameters are selected as , the initial state conditions are set as and In addition, all other settings in the simulation are consistent with those adopted in Section G.
[0167] The simulation results are as follows Figure 3 As shown. Figure 3 It can be seen that the mobile robot has robust safety on the set S, and its hand position is stabilized to 0 at the preset time T. This shows that the robot can park safely within the preset time T. In addition, the actual input The boundedness of Figure 2 Thus, the practical capabilities of the control method were tested.
[0168] The operation results of the above numerical simulation and application examples prove the correctness and effectiveness of the preset time safety control method of the present invention.
[0169] The above are only preferred specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solutions and inventive concepts of the present invention, should be covered by the scope of protection of the present invention.
Claims
1. A preset time safety control method for an unmanned vehicle with unknown disturbances, characterized in that: The following steps are involved: S1: Establish the control system model of the unmanned vehicle; S2: Based on the control system model of the unmanned vehicle, a time controller model for preset time control is established; S3: Based on the controller model of preset time control, a safety controller model of preset time safety control is established; S4: Perform stability analysis on the time controller model and safety controller model and verify feasibility.
2. The preset time safety control method for an unmanned vehicle with unknown disturbance according to claim 1 is characterized in that: In step S1, the control system model is expressed as follows: in, is the state vector of the system, is the state vector The derivative of , which represents the dynamic behavior of the system, Represents the state vector No. Quantity is a nonlinear vector function, is a reversible nonlinear matrix; is the actual control input vector, and is the unknown external disturbance vector; is a real vector space; represents the time variable, Indicates the initial time; The actual control input vector Designed to: in, is the transformed control input vector; the actual control input vector The transformed control input vector Recovery, based on the control system model makes two assumptions: Hypothesis 1: External interference There are known upper and lower bounds and ,Right now ; Assumption 2: Security Function and and upper and lower bounds and satisfy: 。 3. The preset time safety control method for an unmanned vehicle with unknown disturbance according to claim 2, characterized in that: In step S2, the time controller model is established as follows: in, represents the time controller model, is the control gain parameter used to adjust the convergence speed of the controller; is the design parameter, used for the weight of disturbance compensation; ; is the state vector after transformation.
4. The preset time safety control method for an unmanned vehicle with unknown disturbance according to claim 3 is characterized in that: In step S3, the security controller model is established as follows: In the set S The robustness of the control system model is established on the basis of the following barrier function: in Represents the state vector No. A quantity, represents the barrier function; Assume that In the case At the time node, the control system model is robust and safe on S, and the construction and , as well as The differential equation form between the unknowns is established, the obstacles are added to the control system model, and the safety controller model is constructed. ,Right now Satisfy the obstacle constraints, where is a design parameter, and ,let , we get the following equation: in, represents the control barrier function, Indicates the The barrier function of the state, The first control input after transformation A quantity, The unknown external disturbance A quantity, Indicates the system status A quantity, Indicates the safety controller Quantity Security Controller Model Expressed as: Denotes the time controller input of the i-th dimension, using the sufficient condition Replace the barrier constraint, according to assumption 2, in hour, , indicating sufficient conditions are feasible, and the safety controller is designed by solving the quadratic programming in, Represents the safety controller input of the i-th dimension, used to correct the time control input Applying the Karush-Kuhn-Tucker optimality condition to equation (8) yields: in, and are the upper and lower limits, It means that the state of the safety control system is close to the safety lower limit. It means that the state of the safety control system is close to the upper limit of safety; When , it means that the constraint is not activated, that is, the safety margin is sufficient; or When ≠0, the safety margin is insufficient and the constraint is activated; the safety controller model is obtained. as follows: 。 5. The preset time safety control method for an unmanned vehicle with unknown disturbance according to claim 4 is characterized in that: Step S4 specifically includes the following steps: S41. Analysis and verification of the time controller model and the safety controller model: Assumption 1 is established and the time controller model is applied, for : 1) All closed-loop signals are uniformly bounded; 2) System state x at time When it stabilizes to zero, ; S42. Analysis and verification of control system model: Assumptions 1 and 2 are true, and the safety controller model is applicable. For all and , the preset time security control is resolved; The verification content includes: Part 1, the security system model is robust and secure within the specified time T on the set S; Part 2, proof ; Part III, prove that the closed-loop signal is Uniform boundedness of intervals.