Robot mechanical arm inverse kinematics optimization method and system based on quantum machine learning and Grovor search
By employing quantum machine learning and Grover search methods, and utilizing parameterized quantum circuits and the Grover algorithm to optimize robot inverse kinematics, the problems of high computational complexity and local optima were solved, achieving efficient and accurate inverse kinematics solutions.
Patent Information
- Application Number
- CN202511736045.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-25
- Publication Date
- 2026-02-27
AI Technical Summary
Existing technologies suffer from high computational complexity and limited interpretability in solving robot inverse kinematics, making it difficult to meet real-time control requirements. Furthermore, traditional methods are prone to getting trapped in local optima.
A method based on quantum machine learning and Grover search is adopted to optimize the inverse kinematics of the robotic arm through parameterized quantum circuits and Grover's algorithm. Quantum parallelism and superposition states are used for global search, and classical optimizers are combined for parameter updates to achieve efficient inverse kinematics solution.
It achieves efficient inverse kinematics solution for high-degree-of-freedom robotic arms, avoids local optima traps, improves solution accuracy and reliability, and demonstrates good scalability and practicality.
Smart Images
Figure CN121572293A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of quantum computing and robotics, in particular to a robot manipulator inverse kinematics optimization method and system based on quantum machine learning and Grover search. BACKGROUND
[0002] Robot inverse kinematics solving is the core problem of determining whether the end effector can accurately reach the target pose. Traditional solving methods include analytical method, numerical iteration method (such as Jacobian iteration), gradient-based optimization algorithm (such as Newton method) and various heuristic search algorithms. These methods have limitations: analytical solution is only suitable for specific configuration manipulators; numerical method and gradient method are prone to local optimal solution and sensitive to initial value; and the computational complexity of exhaustive search increases exponentially with the increase of manipulator degrees of freedom (DoF) ), which cannot meet the real-time control requirements.
[0003] In recent years, machine learning and reinforcement learning (RL) have been introduced to solve the IK problem in a data-driven manner. However, deep neural networks (DNN) require a large amount of training data, the training process is time-consuming, and their generalization ability and interpretability are limited, with performance improvement only at a polynomial level, making it difficult to cope with extremely complex and high-dimensional configuration spaces.
[0004] Quantum computing provides a revolutionary paradigm for solving such combinatorial optimization problems. The superposition state and entanglement characteristics of quantum bits enable quantum computers to naturally parallel process vast possibilities. Grover's algorithm provides a theoretical quadratic speedup (from to ) for searching unstructured databases. At the same time, quantum machine learning (QML) uses the strong expressive power and high information density of parameterized quantum circuits (PQC) to effectively approximate complex functions with fewer parameters, laying the foundation for building efficient forward kinematics quantum models.
[0005] Currently, the existing technology lacks a complete technical solution that deeply integrates QML and Grover's algorithm, fully utilizes the advantages of quantum parallelism, and can be practically applied to robot inverse kinematics solving. SUMMARY
[0006] In view of the limitations, high computational complexity, and limited interpretability of the existing technology, the present application provides a robot manipulator inverse kinematics optimization method and system based on quantum machine learning and Grover search, with the following technical solutions:
[0007] Step 1, collect the joint angle vector of the manipulator and the corresponding end effector pose to form a training data set, and normalize the data;
[0008] Step 2, encode the training dataset into quantum states using qubits;
[0009] Step 3, construct a parameterized quantum circuit;
[0010] Step 4, train the parameterized quantum circuit in a hybrid quantum-classical optimization loop;
[0011] Step 5, execute the Grover algorithm on the quantum processor with the parameterized quantum circuit as an Oracle, measure the quantum state and decode to obtain the joint configuration that brings the end effector to the target pose.
[0012] Further, the step 2 uses angle encoding based on rotation gates, for a single joint angle vector in the training dataset, high-precision encoding is performed using multiple qubits and applying rotation gates, mapping the normalized angle value to the amplitude or phase of the quantum state.
[0013] Further, the parameterized quantum circuit of step 3 is composed of multiple layers of entanglement layers and parameterized rotation layers, the entanglement layer is a linear entanglement layer composed of CNOT gates; the parameterized rotation layer is composed of parameterized RY and RZ gates.
[0014] Further, the step 4 refers to a cost function defined as the difference between the predicted pose of the parameterized quantum circuit and the true target pose, the calculation method uses mean square error, this calculation is completed on the quantum processor, and the result is read by a classical computer for optimization.
[0015] Further, the step 4 optimization process uses quantum natural gradient descent or stochastic gradient descent algorithm with momentum to update the parameters of the parameterized quantum circuit, and iterates until it converges to a predetermined threshold.
[0016] Further, the Oracle in step 5 is a quantum operator realized by the parameterized quantum circuit, which calculates the predicted pose for a given configuration and compares it with the target pose, if the error is small, the phase is flipped for accurate marking.
[0017] Further, the step 5 prepares the quantum register representing all possible joint configurations as a uniform superposition state by applying Hadamard gates before executing the Grover algorithm, which accesses the entire solution space in parallel.
[0018] Further, the step 5 applies the Grover iteration operator after executing the Grover algorithm, which contains an Oracle call and a diffusion operation in each iteration.
[0019] Further, the diffusion operation: reflects the quantum state to the average amplitude plane, combines the Oracle to amplify the quantum state amplitude corresponding to the optimal joint configuration, while reducing the quantum state amplitude corresponding to the non-optimal joint configuration.
[0020] A robot manipulator inverse kinematics optimization system based on quantum machine learning and Grover search, comprising the following modules:
[0021] A classical data processing unit: prepares and pre-processes the kinematics dataset;
[0022] A parameterized quantum circuit training unit: performs a hybrid optimization loop on a quantum processor or simulator;
[0023] A Grover algorithm execution unit: configures and executes a quantum search on a quantum processor;
[0024] A classical control unit: coordinates the entire process and resolves quantum measurement results.
[0025] Beneficial effects:
[0026] The advantage of the present application is that the Grover algorithm is used to achieve quadratic acceleration, and for a solution space of size , only queries are needed to find the solution, compared with of the classical exhaustive search, the computational efficiency is fundamentally improved when processing high-degree-of-freedom manipulators; based on the parallel global search characteristics of quantum superposition states, this method can effectively avoid the problem of falling into local optimization caused by convexity assumption or improper initial value selection in classical gradient optimization methods, so as to find the global optimal or approximate optimal joint configuration with a higher probability, significantly improving the accuracy and reliability of motion planning; the PQC structure and Grover algorithm framework proposed in the present application are decoupled from the specific configuration of the manipulator, and by increasing the number of quantum bits and adjusting the circuit depth, this method can be flexibly adapted to simple 4-DOF SCARA robots to complex 7-DOF humanoid robots and even multi-robot cooperation systems, showing excellent scalability; the variational quantum algorithm framework used in the present application is the most promising paradigm for medium-scale quantum processors with noise at present, and by combining error mitigation techniques, this method is expected to be deployed practically on actual quantum hardware in the near future. BRIEF DESCRIPTION OF DRAWINGS
[0027] Figure 1 It is the overall flowchart of the robot manipulator inverse kinematics optimization method based on quantum machine learning and Grover search;
[0028] Figure 2 It is a schematic diagram of high-precision encoding of joint angle discrete states of quantum bits;
[0029] Figure 3A schematic diagram of the specific structure of a parameterized quantum circuit;
[0030] Figure 4 This is a schematic diagram of the Grover algorithm component that incorporates parameterized quantum circuits. Detailed Implementation
[0031] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.
[0032] like Figure 1 As shown, the inverse kinematics optimization method for robotic arms based on quantum machine learning and Grover search of the present invention includes the following steps:
[0033] Step 1: Collect the joint angle vectors of the robotic arm and their corresponding end effector poses to form a training dataset, and normalize the data.
[0034] Step 2: Encode the training dataset into quantum states using qubits. Use rotation gate-based angle encoding. For a single joint angle vector in the training dataset, use multiple qubits for high-precision encoding and apply a rotation gate to map the normalized angle value to the amplitude or phase of the quantum state.
[0035] Step 3: Construct a parameterized quantum circuit consisting of multiple alternating entangled layers and parameterized rotation layers. The entangled layers are linear entangled layers composed of CNOT gates; the parameterized rotation layers are composed of parameterized RY and RZ gates.
[0036] Step 4: A hybrid optimization framework is adopted. The classical optimizer (such as ADAM or quantum natural gradient optimizer) receives the cost function, which is defined as the difference between the pose predicted by the parameterized quantum circuit and the actual target pose. The calculation method uses mean square error. The parameters of the parameterized quantum circuit are updated using quantum natural gradient descent or stochastic gradient descent algorithm with momentum. The process is repeated iteratively until convergence to a predetermined threshold.
[0037] Step 5: The parameterized quantum circuit is used as the Oracle in the Grover algorithm. The Oracle calculates the predicted pose of a given configuration and compares it with the target pose. If the error is small, the phase is flipped and the position is accurately marked. Then, the quantum registers representing all possible joint configurations are prepared into a uniform superposition state by applying a Hadamard gate, and the entire solution space is accessed in parallel. The Grover algorithm is executed on the quantum processor, and the Grover iterative operator is applied for multiple iterations to amplify the quantum state amplitude corresponding to the optimal joint configuration. The quantum state is measured and decoded to obtain the joint configuration that enables the end effector to reach the target pose.
[0038] Example 1
[0039] Take the inverse kinematics solution of a 6-DOF industrial robot arm as an example.
[0040] 1. System configuration:
[0041] Use a high-performance classical computer (equipped with GPU to accelerate simulation) to run Qiskit or PennyLane quantum computing framework, connect a quantum processor or simulator that supports at least 12 qubits.
[0042] 2. Data preparation and encoding:
[0043] Use the official model of the robot arm or generate a dataset through motion capture, containing 100,000 data pairs, normalize each joint angle to the interval.
[0044] As shown in Figure 2 , the circuit first prepares a superposition state through the Hadamard gate (H), then introduces entanglement and phase operations through the controlled NOT gate (C-NOT) and the controlled Z gate (C-Z), completes the encoding and transformation of information, and finally decodes the quantum information into classical data by measuring the position of the instrument symbol in the diagram. The encoding scheme uses angle encoding based on rotation gates, each joint angle uses 3 qubits for encoding, a total of 18 qubits are used to encode 6 joints, plus 2 auxiliary qubits, a total of 20 qubits, through a series of rotation gates (such as RX, RY, RZ), the normalized angle value is mapped to the amplitude or phase of the quantum state.
[0045] 3. PQC training:
[0046] As shown in Figure 3 , the PQC contains 4 layers of repeated structure, the parameterized rotation layer is composed of parameterized RY, RZ gates, and the D layer is composed of a linear entanglement layer composed of CNOT gates. This structure is used to approximate the forward kinematics.
[0047] On the quantum simulator, use the mean square error cost function and the quantum natural gradient descent optimizer for training. After 3000 iterations, the loss function converges, and the PQC predicts the average error of the pose on the test set is less than 0.005m.
[0048] 4. Inverse kinematics solution:
[0049] Given a new target pose, configure the 18 joint qubits into a uniform superposition state through the Hadamard gate, integrate the trained PQC into Figure 4In the illustrated Grover Oracle, the Oracle applies a phase flip (multiplied by -1) to the solution state, while leaving other states unchanged. The PQC computes the predicted pose for the given configuration and compares it to the target pose, and if the error is small, it flips the phase. The phase flip ensures that the solution state is anti-phase with respect to other states, so that when the diffusion operation reflects the entire state, the solution amplitude constructively interferes, while other states destructively interfere, achieving the identification and marking of good solutions that make the cost function below a certain threshold, i.e. joint configurations that can guide the end effector to approach the target pose.
[0050] The Grover iteration is performed, applying the Grover iteration operator, which contains an Oracle call and a diffusion operation in each iteration. The diffusion operation is: the diffusion operator (also called Grover diffuser) reflects the quantum state to the average amplitude plane, which is equivalent to inverting the amplitude of all states around the average value. In combination with the phase marking of the Oracle, this operation amplifies the amplitude of the solution while reducing the amplitude of other states. After multiple iterations, the quantum state will be highly concentrated around the optimal solution. Finally, the quantum register is measured with 18 qubits, and the result is decoded as a joint angle vector.
[0051] The above embodiments are only used to illustrate the technical solutions of the present application, but not limit it; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.
Claims
1. A method for optimizing the inverse kinematics of a robotic arm based on quantum machine learning and Grover search, characterized in that... Includes the following steps: Step 1: Collect the joint angle vectors of the robotic arm and their corresponding end effector poses to form a training dataset, and normalize the data. Step 2: Encode the training dataset into quantum states using qubits; Step 3: Construct parameterized quantum circuits; Step 4: Hybrid quantum-classical optimization loop training of parameterized quantum circuits; Step 5: Using the parameterized quantum circuit as the Oracle in the Grover algorithm, execute the Grover algorithm on the quantum processor, measure the quantum state and decode it to obtain the joint configuration that enables the end effector to reach the target pose.
2. The method for optimizing the inverse kinematics of a robotic arm based on quantum machine learning and Grover search as described in claim 1, characterized in that: Step 2 employs rotation gate-based angle encoding. For a single joint angle vector in the training dataset, multiple qubits are used for high-precision encoding and a rotation gate is applied to map the normalized angle value to the amplitude or phase of the quantum state.
3. The method for optimizing the inverse kinematics of a robotic arm based on quantum machine learning and Grover search as described in claim 1, characterized in that: The parameterized quantum circuit in step 3 consists of multiple alternating entangled layers and parameterized rotation layers. The entangled layers are linear entangled layers composed of CNOT gates; the parameterized rotation layers are composed of parameterized RY and RZ gates.
4. The method for optimizing the inverse kinematics of a robotic arm based on quantum machine learning and Grover search as described in claim 1, characterized in that: Step 4 refers to a cost function, which is defined as the difference between the pose predicted by the parameterized quantum circuit and the actual target pose. The calculation method uses mean square error. This calculation is performed on a quantum processor, and the result is read by a classical computer for optimization.
5. The method for optimizing the inverse kinematics of a robotic arm based on quantum machine learning and Grover search as described in claim 1, characterized in that: The optimization process in step 4 uses quantum natural gradient descent or stochastic gradient descent with momentum to update the parameters of the parameterized quantum circuit, and iterates cyclically until it converges to a predetermined threshold.
6. The method for optimizing the inverse kinematics of a robotic arm based on quantum machine learning and Grover search as described in claim 1, characterized in that: In step 5, the Oracle is a quantum operator implemented by a parameterized quantum circuit. The parameterized quantum circuit calculates the predicted pose of a given configuration and compares it with the error of the target pose. If the error is small, the phase is flipped and the pose is accurately marked.
7. The method for optimizing the inverse kinematics of a robotic arm based on quantum machine learning and Grover search as described in claim 1, characterized in that: In step 5, before executing the Grover algorithm, the quantum registers representing all possible joint configurations are prepared into a uniform superposition state by applying a Hadamard gate, allowing parallel access to the entire solution space.
8. The method for optimizing the inverse kinematics of a robotic arm based on quantum machine learning and Grover search as described in claim 1, characterized in that: Step 5 involves performing multiple iterations of the Grover algorithm using the Grover iteration operator. Each iteration of this operator includes an Oracle call and a diffusion operation.
9. The method for optimizing the inverse kinematics of a robotic arm based on quantum machine learning and Grover search as described in claim 8, characterized in that: The diffusion operation involves reflecting the quantum state onto the average amplitude plane, amplifying the quantum state amplitude corresponding to the optimal joint configuration using Oracle, and simultaneously reducing the quantum state amplitude corresponding to the non-optimal joint configuration.
10. A robot arm inverse kinematics optimization system based on quantum machine learning and Grover search, characterized in that... Includes the following modules: Classic data processing unit: preparing and preprocessing kinematic datasets; Parameterized quantum circuit training unit: Executes hybrid optimization loops on a quantum processor or simulator; Grover's algorithm execution unit: Configures and executes quantum searches on a quantum processor; Classical control unit: coordinates the entire process and analyzes the quantum measurement results.