DynaMapp is a lightweight Python software package designed for the representation and identification of multibody systems. It is optimized for efficient computation and visualization of how static input parameters (such as inertial, geometric, and electromechanical) affect the behavior of these systems.
The primary goal of DynaMapp is to offer an implementation of common rigid body dynamics algorithms and their derivatives using JAX.
It provides tools for computing the state-space representation of these systems.
- Compute the Jacobian tensors of the joint torque vector as a function of the system parameters vector using automatic differentiation.
- Compute the Jacobian of other quantities (such as the global inertia matrix and Coriolis matrix) with respect to the input parameters.
- Implement common identification algorithms for optimizing the multibody system parameters.
The package does not rely on any rigid body dynamics libraries.
Note:
This is an early-stage research software, and many parts still require focus and further implementation.
See the INSTALL file.
This section provides an overview of examples demonstrating the usage of the package's basic functions and mathematical notations. Currently, the documentation lacks detailed and meaningful examples, and these examples do not cover all software functions.
All guidelines will be available in the Tutoriel.
from dynamapp.model import Model
# Define the Inertia matrices (list of 6x6 matrices)
Imats = [jnp.eye(6) for _ in range(3)]
# Define the Denavit-Hartenberg parameters (theta, d, a, alpha)
dhparams = [
[0.0, 0.5, 0.5, jnp.pi / 2],
[0.0, 0.5, 0.5, 0.0],
[0.0, 0.5, 0.5, jnp.pi / 2]
]
# Define the gravity vector
gravity = -9.81
# Define damping coefficients
dampings = [0.1, 0.1, 0.1]
# Create the model instance
model = Model(Imats, dhparams, gravity, dampings)
# Check the generalized torques at initial joint configurations (q, qp, qpp = 0)
torques = model.generalized_torques()from dynamapp.model import Model
# Define joint positions, velocities, and accelerations
q = jnp.array([0.0, 0.0, 0.0]) # Joint positions (rad)
qp = jnp.array([0.0, 0.0, 0.0]) # Joint velocities (rad/s)
qpp = jnp.array([0.0, 0.0, 0.0]) # Joint accelerations (rad/s^2)
# Define the Inertia matrices, DH parameters, and damping coefficients
Imats = [jnp.eye(6) for _ in range(3)]
dhparams = [
[0.0, 0.5, 0.5, jnp.pi / 2],
[0.0, 0.5, 0.5, 0.0],
[0.0, 0.5, 0.5, jnp.pi / 2]
]
gravity = -9.81
dampings = [0.1, 0.1, 0.1]
# Create the model instance
model = Model(Imats, dhparams, gravity, dampings)
# Compute the Generalized Torques at the current joint configuration
generalized_torques = model.generalized_torques(q, qp, qpp)
# Compute the Inertia Matrix at the current joint configuration
inertia_matrix = model.inertia_tensor(q)from dynamapp.model_state import ModelState
# Define system parameters (Inertia matrices, DH parameters, etc.)
Imats = [jnp.eye(6) for _ in range(3)] # Example inertia matrices
dhparams = [
[0.0, 0.5, 0.5, jnp.pi / 2],
[0.0, 0.5, 0.5, 0.0],
[0.0, 0.5, 0.5, jnp.pi / 2]
]
# Initialize the ModelState object
model_state = ModelState(Imats, dhparams)
# Define an example state vector (x)
x = jnp.zeros((2 * model_state.model.ndof, 1)) # Example state vector (2 * ndof)
# Compute the state-space matrices
model_state._compute_matrices(x)
# Access and print the state-space matrices A, B, C, D
print(model_state.model_state_space.a)
print(model_state.model_state_space.b)
print(model_state.model_state_space.c)
print(model_state.model_state_space.d) The last model computation serves as a bridge to state-space identification techniques, subspace identification methods, and other fields.
Note: The stability of the computed matrices is not guaranteed. The intensive computations of derivatives are error-prone, so a new computation method is needed!
from dynamapp.model_state import ModelState
Imats = [jnp.eye(6) for _ in range(3)] # Example inertia matrices
dhparams = [
[0.0, 0.5, 0.5, jnp.pi / 2],
[0.0, 0.5, 0.5, 0.0],
[0.0, 0.5, 0.5, jnp.pi / 2]
]
# Initialize the ModelState object
model_state = ModelState(Imats, dhparams)
# Define an example state vector (x)
x = jnp.zeros((2 * model_state.model.ndof, 1)) # Example state vector (2 * ndof)
# Check if the system is stable
is_stable = model_state._is_stable(x)
eigenvalues = model_state.compute_eigvals(x)
controllability_matrix = model_state.compute_ctlb_matrix(x)
# Compute the observability matrix
observability_matrix = model_state.compute_obs_matrix(x)m = Model(...) # A Model object
q = jnp.array([0.5, 1.0, -0.3]) # Generalized positions (q)
v = jnp.array([0.1, -0.2, 0.3]) # Generalized velocities (v)
a = jnp.array([0.05, 0.1, -0.15]) # Generalized accelerations (a)
t = generalized_torques_wrt_inertia(m, q, v, a)# Example Usage
q = jnp.array([0.5, 1.0, -0.3]) # Generalized positions (q)
v = jnp.array([0.1, -0.2, 0.3]) # Generalized velocities (v)
a = jnp.array([0.05, 0.1, -0.15]) # Generalized accelerations (a)
# Compute the Jacobian of generalized torques with respect to DH parameters
torques_wrt_dhparams = generalized_torques_wrt_dhparams(m, q, v, a)q = jnp.array([0.5, 1.0, -0.3]) # Generalized positions (q)
v = jnp.array([0.1, -0.2, 0.3]) # Generalized velocities (v)
a = jnp.array([0.05, 0.1, -0.15]) # Generalized accelerations (a)
torques_wrt_damping = generalized_torques_wrt_damping(m, q, v, a)The official documentation is avalible at link
please review the following:
- The CHANGELOG for an overview of updates and changes.
- The CONTRIBUTING guide for detailed instructions on how to contribute.
This is an early-stage research software, and contributions are highly welcomed!
If you have any questions or need assistance, feel free to reach out via email.
See the LICENSE file.