An IMU-based lower limb joint dynamics parameter prediction method and system

Abstract

This invention discloses an IMU-based method and system for predicting lower limb joint dynamic parameters. The method includes the following steps: acquiring kinematic data of key rigid bodies in the lower limb kinetic chain using four inertial measurement units (IMUs) configured at specific locations on the lower limb; preprocessing the kinematic data to construct a temporal input feature tensor; inputting the temporal input feature tensor into a pre-trained deep learning prediction model to obtain a fused feature vector; the deep learning prediction model performing split decoding on the fused feature vector, mapping it to different task branches; the multi-task branches simultaneously outputting the joint contact forces and torques of the hip, knee, and ankle joints; and the system integrating the aforementioned IMU-based method for predicting lower limb joint dynamic parameters. This invention achieves real-time, high-precision synchronous prediction of contact forces and torques of the hip, knee, and ankle joints using only IMU sensors, and is suitable for rehabilitation assessment and motion monitoring.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary fields of biomechanical monitoring, wearable technology and artificial intelligence, and specifically relates to a method and system for predicting lower limb joint dynamic parameters based on IMU. Background Technology

[0002] Lower limb joint contact forces and torques are important indicators for quantifying the biomechanical characteristics of human movement, reflecting the internal load state of the musculoskeletal system. Accurate acquisition of these parameters has significant application value in fields such as clinical gait analysis, sports rehabilitation assessment, human-machine interaction control of exoskeleton robots, and competitive sports training monitoring.

[0003] Traditional measurement methods rely on a combination of optical motion capture systems and ground reaction force tables, using inverse dynamics algorithms for calculation. This approach is expensive, complex to operate, and limited to indoor laboratory environments, making it unsuitable for real-time continuous monitoring outdoors or in daily life.

[0004] To address the portability issue, wearable measurement methods based on inertial measurement units (IMUs) and pressure insoles have emerged in recent years. However, existing wearable methods still have the following problems: Firstly, the wearing process is cumbersome. To meet the requirements of inverse dynamics calculations, it is usually necessary to wear a dense array of sensor nodes (more than 10), which seriously affects the user's natural movement experience. Secondly, existing models mostly predict for a single joint and cannot identify compensatory problems in adjacent joints caused by pathological changes in a single joint. Third, the generalization and multi-task balance are poor. Existing models are mostly trained for a single horizontal walking pattern, which makes it difficult to adapt to action switching. Moreover, the difficulty of predicting contact force and torque is inconsistent. Gradient dominance is prone to occur when predicting multiple tasks, resulting in inaccurate prediction of small-scale tasks.

[0005] Therefore, there is an urgent need for a technical solution that utilizes sparse sensing configuration to adapt to multiple motion modes and predict the contact forces and torques of multiple joints in the lower limbs in a balanced manner. Summary of the Invention

[0006] This invention is proposed to address the problems existing in the prior art, and its purpose is to provide a method and system for predicting lower limb joint dynamic parameters based on IMU.

[0007] The technical solution of this invention is: a method for predicting lower limb joint dynamic parameters based on IMU, comprising the following steps: A. Kinematic data of key rigid bodies in the human lower limb kinetic chain are collected by four inertial measurement units (IMUs) configured at specific locations in the human lower limb. B. Preprocess the acquired kinematic data to construct a temporal input feature tensor; C. Input the constructed temporal input feature tensor into the pre-trained deep learning prediction model to obtain the fused feature vector; D. Deep learning prediction models split and decode the fused feature vectors, mapping them to different task branches respectively; E. Multi-task branch simultaneously outputs the joint contact force and joint torque of the hip, knee and ankle joints.

[0008] Step A involves acquiring kinematic data of key rigid bodies in the human lower limb kinetic chain using four inertial measurement units (IMUs) configured at specific locations on the lower limb. The specific process is as follows: First, four inertial measurement units (IMUs) form a sparse inertial sensing unit, with the four IMUs respectively located on the sacrum, thigh, calf, and dorsum of the foot; Then, the kinematic data includes the three-axis acceleration, three-axis angular velocity, and three-axis attitude angle at four nodes.

[0009] Furthermore, step B preprocesses the acquired kinematic data to construct a temporal input feature tensor, as detailed below: First, a low-pass filter is used to remove high-frequency noise from the acquired kinematic data; Then, the denoised data is subjected to Z-score normalization. Finally, a sliding window is used to cut the continuous time series data into time window samples of fixed length.

[0010] Furthermore, the step size of the sliding window is smaller than the window length to achieve overlapping sampling of data.

[0011] Furthermore, step C inputs the constructed temporal input feature tensor into a pre-trained deep learning prediction model to obtain a fused feature vector. The specific process is as follows: First, deep learning prediction models include feature extraction networks and multi-task decoding networks; Then, the feature extraction network extracts the temporal dependency features of the data through a temporal convolutional network (TCN); Finally, a task-specific attention mechanism is used to weight the feature channels to obtain the fused feature vector.

[0012] Furthermore, the deep learning prediction model is generated based on a multi-task dynamic loss weighting strategy, and the specific process is as follows: First, construct a total loss function that includes multiple task sub-loss functions; Then, during the backpropagation of the model, the weight parameters of each task sub-loss in the total loss function are adaptively adjusted according to the homoscedasticity uncertainty of each task sub-loss function, so as to balance the impact of the difference in the difficulty of predicting contact force and torque at different joints on the gradient.

[0013] Furthermore, the Temporal Convolutional Network (TCN) in the feature extraction network contains multiple stacked residual blocks, each containing an expanded causal convolutional layer; the expanded causal convolutional layer is used to expand the receptive field of the model without revealing future information in order to capture long-term historical motion trends.

[0014] Furthermore, the task-specific attention mechanism adaptively filters features from the shared feature space for each task decoder at each joint.

[0015] Furthermore, in step D, the deep learning prediction model performs split decoding on the fused feature vectors, mapping them to different task branches. The specific process is as follows: First, the multi-task decoding network of the deep learning prediction model contains three parallel fully connected layer branches, corresponding to the hip joint prediction branch, the knee joint prediction branch, and the ankle joint prediction branch, respectively. Then, each branch independently outputs the contact force and torque of the corresponding joint.

[0016] A lower limb joint dynamic parameter prediction system based on IMU is provided, wherein the system implements the aforementioned lower limb joint dynamic parameter prediction method based on IMU.

[0017] The beneficial effects of this invention are as follows: This invention employs a sparse inertial sensing layout, which greatly improves portability and wearing comfort while eliminating reliance on dense sensors. By combining a temporal convolutional network (TCN) with a task-specific attention mechanism, and utilizing the broad receptive field and feature adaptive focusing capability of expanded causal convolution, it achieves accurate capture of long-term historical motion trends. Furthermore, it introduces a dynamic loss weighting strategy based on homoscedastic uncertainty, which effectively solves the gradient-dominated problem caused by differences in prediction difficulty among multiple tasks. This enables balanced, real-time, and high-precision prediction of contact forces and torques at various joints of the lower limbs, significantly enhancing the robustness of the model in complex multi-motion modes. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall process of the method for predicting contact force and torque of lower limb joints in an embodiment of the present invention; Figure 2 This is a schematic diagram of the wearing position of the sparse inertial sensing unit in an embodiment of the present invention; Figure 3 This is a schematic diagram of the network architecture of the deep learning prediction model in an embodiment of the present invention; Figure 4 This is a hardware structure block diagram of the system in an embodiment of the present invention. Detailed Implementation

[0019] The present invention will now be described in detail with reference to the accompanying drawings and embodiments: like Figures 1 to 4 As shown, a method for predicting lower limb joint dynamic parameters based on IMU includes the following steps: A. Kinematic data of key rigid bodies in the human lower limb kinetic chain are collected by four inertial measurement units (IMUs) configured at specific locations in the human lower limb. B. Preprocess the acquired kinematic data to construct a temporal input feature tensor; C. Input the constructed temporal input feature tensor into the pre-trained deep learning prediction model to obtain the fused feature vector; D. Deep learning prediction models split and decode the fused feature vectors, mapping them to different task branches respectively; E. Multi-task branch simultaneously outputs the joint contact force and joint torque of the hip, knee and ankle joints.

[0020] Step A involves acquiring kinematic data of key rigid bodies in the human lower limb kinetic chain using four inertial measurement units (IMUs) configured at specific locations on the lower limb. The specific process is as follows: First, four inertial measurement units (IMUs) form a sparse inertial sensing unit, with the four IMUs respectively located on the sacrum, thigh, calf, and dorsum of the foot; Then, the kinematic data includes the three-axis acceleration, three-axis angular velocity, and three-axis attitude angle at four nodes.

[0021] Step B involves preprocessing the acquired kinematic data to construct a temporal input feature tensor. The specific process is as follows: First, a low-pass filter is used to remove high-frequency noise from the acquired kinematic data; Then, the denoised data is subjected to Z-score normalization. Finally, a sliding window is used to cut the continuous time series data into time window samples of fixed length.

[0022] The step size of the sliding window is smaller than the window length to achieve overlapping sampling of data.

[0023] Step C involves inputting the constructed temporal input feature tensor into a pre-trained deep learning prediction model to obtain a fused feature vector. The specific process is as follows: First, deep learning prediction models include feature extraction networks and multi-task decoding networks; Then, the feature extraction network extracts the temporal dependency features of the data through a temporal convolutional network (TCN); Finally, a task-specific attention mechanism is used to weight the feature channels to obtain the fused feature vector.

[0024] Deep learning prediction models are generated based on a multi-task dynamic loss weighting strategy, and the specific process is as follows: First, construct a total loss function that includes multiple task sub-loss functions; Then, during the backpropagation of the model, the weight parameters of each task sub-loss in the total loss function are adaptively adjusted according to the homoscedasticity uncertainty of each task sub-loss function, so as to balance the impact of the difference in the difficulty of predicting contact force and torque at different joints on the gradient.

[0025] The temporal convolutional network (TCN) in the feature extraction network contains multiple stacked residual blocks, each containing an dilated causal convolutional layer. The dilated causal convolutional layer is used to expand the receptive field of the model without revealing future information. The receptive field of the model is expanded by an exponentially increasing dilation coefficient, thereby effectively capturing long-span temporal dependencies and implicit nonlinear dynamic features.

[0026] The task-specific attention mechanism adaptively selects features from the shared feature space for each task decoder.

[0027] Step D: The deep learning prediction model performs split decoding on the fused feature vectors, mapping them to different task branches. The specific process is as follows: First, the multi-task decoding network of the deep learning prediction model contains three parallel fully connected layer branches, corresponding to the hip joint prediction branch, the knee joint prediction branch, and the ankle joint prediction branch, respectively. Then, each branch independently outputs the contact force and torque of the corresponding joint.

[0028] Specifically, in step C, the specific attention mechanism, each prediction task is equipped with an independent attention module that adaptively selects key features from shared features.

[0029] Furthermore, each of the above tasks is equipped with an independent regression head that maps weighted features to the target physical quantity.

[0030] Furthermore, the task-specific attention mechanism performs global average pooling on the feature map output by the TCN to obtain channel descriptors; it learns the dependencies between channels through a fully connected layer to generate channel weight coefficients; and it multiplies these channel weight coefficients with the original feature map. This task-specific attention mechanism can automatically enhance the feature responses of key sensor channels and suppress the features of irrelevant noise channels based on the current motion state.

[0031] Specifically, the inertial sensing unit (IMU) fully considers the portability and low cost requirements of daily life scenarios; each sensor node adopts an ergonomic flexible strap design to fit the limbs and reduce sway artifacts during movement; each sensor node has a built-in low-power Bluetooth transmission module, which can directly connect to smart mobile terminals or personal computers for data transmission without the need for additional base stations or cables; the sparse inertial sensing unit adopts a low-power design to support long-term continuous biomechanical monitoring, thereby achieving migration from laboratory environments to daily application scenarios at extremely low cost.

[0032] Specifically, to address the imbalance in the difficulty of predicting multi-joint contact forces and moments, the deep learning prediction model employs a dynamic loss weighting strategy based on homoscedastic uncertainty during the training phase, namely: A total loss function containing multiple task sub-loss functions is constructed; during model backpropagation, a trainable log-variance parameter is learned for each task, and the loss weights of each task are dynamically calculated during training; this method enables the model to automatically balance the gradient contributions of contact force and torque, avoiding the optimization direction being dominated by tasks with high prediction difficulty.

[0033] A system for predicting lower limb joint dynamic parameters based on IMU, wherein the system implements the aforementioned method for predicting lower limb joint dynamic parameters based on IMU.

[0034] Specifically, the system includes a data acquisition module, a data processing module, a model prediction module, and a result output module.

[0035] The data acquisition module is used to acquire kinematic data through sparse inertial sensing units configured on the sacrum, outer thigh, outer calf, and dorsum of the foot. The data processing module is used to filter, normalize, and perform sliding window segmentation on the collected data. The model prediction module internally deploys a multi-task prediction model based on a temporal convolutional network and a task-specific attention mechanism, which is used to extract spatiotemporal features of data and perform multi-objective regression; the model is generated by training based on a dynamic loss weighting strategy. The result output module is used to output and display the predicted curves of contact force and torque of each joint of the lower limb in real time. Example

[0036] This embodiment abandons the reliance on dense sensor arrays in traditional methods, adopting an optimized sparse layout scheme. It contains only 4 inertial measurement units (IMUs), and their specific wearing positions and biomechanical functions are defined as follows: Sacral node: worn on the sacral plane of the subject, that is, the midpoint of the line connecting the two posterior superior iliac spines. This node is used to establish the proximal boundary conditions of the lower limb kinetic chain, capture the translational acceleration and rotational angular velocity of the pelvis, and reflect the trajectory of the body's center of gravity.

[0037] Thigh node: Worn on the middle of the outer thigh, at the midpoint of the line connecting the greater trochanter and the lateral condyle of the knee joint, it is used to capture the postural changes of the femur during movement, mainly related to the dynamic state of the hip and knee joints.

[0038] Lower leg node: worn on the middle of the outer side of the lower leg, at the midpoint of the line connecting the fibular head and the lateral malleolus, to capture tibial movement. Its data is crucial for knee joint load transfer and ankle joint kinematics.

[0039] Foot node: Worn on the instep. This node is located at the end of the kinetic chain and is mainly used to capture transient impact characteristics and high-frequency oscillation signals when the heel strikes the ground and the toes leave the ground.

[0040] The sensor's local coordinate system is defined as follows: the Z-axis is upward along the long axis of the limb, the X-axis faces the forward direction, and the Y-axis is perpendicular to the sagittal plane of the human body, satisfying the right-hand rule.

[0041] Before data acquisition begins, a static calibration procedure is performed: the subject maintains an upright, static posture for 3-5 seconds. The system records the data during this period, calculates the initial posture of each sensor using a quaternion algorithm, and maps all the dispersed local coordinates of the sensors to human anatomical coordinates using a rotation matrix, thus eliminating installation angle deviations.

[0042] Each IMU node integrates a three-axis accelerometer, a three-axis gyroscope, and a microprocessor. In step A, all nodes synchronously acquire motion data at a sampling frequency of 100Hz via a wireless synchronization protocol (such as RF or Bluetooth Low Energy). The acquired data vector... Includes: triaxial acceleration and triaxial angular velocity The data is transmitted in real time via Bluetooth to a host computer or mobile terminal for further processing.

[0043] To fully utilize prior biomechanical knowledge and construct inputs suitable for deep learning models, step B includes the following processing sub-steps: b1. Joint angle fusion calculation: This embodiment introduces an extended Kalman filter algorithm, fusing accelerometer and gyroscope data to estimate the absolute orientation quaternions of each limb segment in real time. .

[0044] Subsequently, based on the relative quaternions of adjacent segments, the flexion-extension angles of the hip, knee, and ankle joints in the sagittal plane are calculated.

[0045] Input Feature Construction: The final constructed input feature vector contains 27 channels. : 4 IMUs (3-axis acceleration + 3-axis angular velocity) = 24 dimensions; The flexion and extension angles of the three joints (hip, knee, and ankle) = 3D.

[0046] b2. Signal Processing and Standardization: Low-pass filtering: A fourth-order Butterworth low-pass filter with a cutoff frequency of 15Hz is used to perform zero-phase filtering on the raw IMU data to remove skin soft tissue artifacts and high-frequency electronic noise.

[0047] Z-score standardization: The data for each channel is standardized independently, i.e. ,in The mean, The standard deviation is used to ensure the stability of network training convergence.

[0048] b3. Timing sliding window segmentation: Considering the temporal dependency of gait cycles, a sliding window technique is used to generate the model input tensor. The window length is set. The timeframe is 85 frames, with a sliding step of 10 frames. At this point, the feature tensor input to the model... Dimensions are ( BatchSize , 27 ,85).

[0049] like Figure 3 As shown, the deep learning model described in step C is the core of this invention, and specifically includes the following modules: c1. Shared temporal feature encoder: It serves as the backbone network for extracting shared features from the lower limb kinetic chain. It consists of three stacked residual blocks, each containing: Dilated causal convolution: The kernel size is set to 7, and the number of filters is 32. The dilation factor of the i-th residual block is set to... (i=0, 1, 2, i.e., the dilation factors are 1, 2, 4 respectively). Dilated convolution expands the receptive field exponentially without increasing the number of parameters, and causal pruning ensures that the output at time t depends only on the input at time t and before, thus meeting the requirements of real-time prediction.

[0050] Nonlinear activation and regularization: Weight normalization, ReLU activation function and Dropout (dropout rate set to 0.5) are applied after each convolution layer to enhance nonlinear expressiveness and prevent overfitting.

[0051] c2. Task-specific attention mechanism: After the shared encoder, the network is split into three branches targeting the hip, knee, and ankle. An attention module is introduced before entering each branch's decoder. This module includes compression and excitation (two fully connected layers) operations to generate channel weight vectors for specific joints.

[0052] Mechanism of action: This allows the model to adaptively select features. For example, when predicting ankle contact force, the foot IMU channel is automatically assigned higher weights; while when predicting hip force, the thigh and sacral IMU channels are assigned higher weights.

[0053] c3. Multi-task decoder: Three parallel decoder branches are used to regress the contact forces and torques of the hip, knee, and ankle joints, respectively. Each decoder consists of two fully connected layers with ReLU activation between them, and the output layer is a linear layer.

[0054] The model training strategies in steps D and E solve the problem of multi-task competition in the model by introducing uncertainty weighting.

[0055] d1. Construction of the total loss function: To simultaneously optimize the prediction accuracy of the three joints while satisfying physical rationality, a total loss function is defined. as follows: ; d2. Dynamic task weighting (homoscedastic uncertainty): : No. The mean square error between the predicted and actual values ​​of the joint contact force (calculated from data obtained by motion capture and force table).

[0056] The task of automatic model learning The observation noise parameters (homoscedasticity uncertainty).

[0057] During training, the model will automatically increase the frequency of tasks with high noise levels, i.e., tasks that are difficult to predict. This reduces the weight of its MSE term, prevents simple tasks from dominating the gradient, and achieves automatic balancing among multiple tasks without the need for manual adjustment of weight hyperparameters.

[0058] c3. Training parameter settings Optimizer: Adam optimizer.

[0059] Learning rate: The initial learning rate is set to .

[0060] Training process: Leave-one-out cross-validation is used. The number of training iterations (Epochs) is set to 100, and an early stopping mechanism is set up to stop training when the validation set loss does not decrease within 10 consecutive Epochs.

[0061] like Figure 4 As shown, the system implementation based on the above method includes: Firstly, the data acquisition front end consists of four miniature IMU nodes, which are fixed to the human body with straps; Secondly, the computing terminal can be a portable laptop, smartphone, or embedded development board (such as the NVIDIA Jetson series). A pre-trained deep learning model is deployed within the terminal. Thirdly, application software: Real-time inference: Receives Bluetooth data packets, performs preprocessing and model inference, and controls single-frame processing latency to the millisecond level.

[0062] Visualization and feedback: Real-time display of contact force and torque waveforms at the hip, knee, and ankle joints on the screen.

[0063] Threshold alarm: Set a safe load threshold. When the predicted contact force and torque continuously exceed the threshold, trigger an audible or vibration alarm for gait retraining or rehabilitation monitoring.

[0064] As can be seen from the above embodiments, the present invention solves the technical problems of cumbersome sensor wearing, weak generalization ability of multiple motion modes, and unbalanced prediction accuracy of multiple tasks in the prior art. In particular, it solves the problem that existing solutions rely on expensive dedicated equipment and are difficult to achieve real-time continuous monitoring in daily life scenarios at low cost.

[0065] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Equivalent structural or procedural transformations made by those skilled in the art based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for predicting lower limb joint dynamic parameters based on IMU, characterized in that: Includes the following steps: A. Kinematic data of key rigid bodies in the human lower limb kinetic chain are collected by four inertial measurement units (IMUs) configured at specific locations in the human lower limb. B. Preprocess the acquired kinematic data to construct a temporal input feature tensor; C. Input the constructed temporal input feature tensor into the pre-trained deep learning prediction model to obtain the fused feature vector; D. Deep learning prediction models split and decode the fused feature vectors, mapping them to different task branches respectively; E. Multi-task branch simultaneously outputs the joint contact force and joint torque of the hip, knee and ankle joints.

2. The method for predicting lower limb joint dynamic parameters based on IMU according to claim 1, characterized in that: Step A involves acquiring kinematic data of key rigid bodies in the human lower limb kinetic chain using four inertial measurement units (IMUs) configured at specific locations on the lower limb. The specific process is as follows: First, four inertial measurement units (IMUs) form a sparse inertial sensing unit, with the four IMUs respectively located on the sacrum, thigh, calf, and dorsum of the foot; Then, the kinematic data includes the triaxial accelerations and triaxial angular velocities at the four nodes, as well as the calculated flexion and extension angles of the lower limb joints.

3. The method for predicting lower limb joint dynamic parameters based on IMU according to claim 1, characterized in that: Step B involves preprocessing the acquired kinematic data to construct a temporal input feature tensor. The specific process is as follows: First, a low-pass filter is used to remove high-frequency noise from the acquired kinematic data; Then, the flexion and extension angles of each joint in the lower limb are calculated based on the filtered data; Next, the denoised data is subjected to Z-score normalization. Finally, a sliding window is used to cut the continuous time series data into time window samples of fixed length.

4. The method for predicting lower limb joint dynamic parameters based on IMU according to claim 3, characterized in that: The step size of the sliding window is smaller than the window length to achieve overlapping sampling of data.

5. The method for predicting lower limb joint dynamic parameters based on IMU according to claim 1, characterized in that: Step C involves inputting the constructed temporal input feature tensor into a pre-trained deep learning prediction model to obtain a fused feature vector. The specific process is as follows: First, deep learning prediction models include feature extraction networks and multi-task decoding networks; Then, the feature extraction network extracts the temporal dependency features of the data through a temporal convolutional network (TCN); Finally, a task-specific attention mechanism is used to weight the feature channels to obtain the fused feature vector.

6. The method for predicting lower limb joint dynamic parameters based on IMU according to claim 5, characterized in that: Deep learning prediction models are generated based on a multi-task dynamic loss weighting strategy, and the specific process is as follows: First, construct a total loss function that includes multiple task sub-loss functions; Then, during the backpropagation of the model, the weight parameters of each task sub-loss in the total loss function are adaptively adjusted according to the homoscedasticity uncertainty of each task sub-loss function, so as to balance the impact of the difference in the difficulty of predicting contact force and torque at different joints on the gradient.

7. The method for predicting lower limb joint dynamic parameters based on IMU according to claim 5, characterized in that: The temporal convolutional network (TCN) in the feature extraction network contains multiple stacked residual blocks, each containing an expanded causal convolutional layer; the expanded causal convolutional layer is used to expand the receptive field of the model without revealing future information in order to capture long-term historical motion trends.

8. The method for predicting lower limb joint dynamic parameters based on IMU according to claim 5, characterized in that: The task-specific attention mechanism adaptively selects features from the shared feature space for each task decoder.

9. The method for predicting lower limb joint dynamic parameters based on IMU according to claim 1, characterized in that: Step D: The deep learning prediction model performs split decoding on the fused feature vectors, mapping them to different task branches. The specific process is as follows: First, the multi-task decoding network of the deep learning prediction model contains three parallel fully connected layer branches, corresponding to the hip joint prediction branch, the knee joint prediction branch, and the ankle joint prediction branch, respectively. Then, each branch independently outputs the contact force and torque of the corresponding joint.

10. A lower limb joint dynamics parameter prediction system based on IMU, characterized in that: The system implements any one of the IMU-based methods for predicting lower limb joint dynamic parameters as claimed in claims 1 to 9.

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