🤖 adam

Automatic Differentiation for rigid-body-dynamics Algorithms

adam computes rigid-body dynamics for floating-base robots. Built on Featherstone's algorithms and available across multiple backends:

🔥 JAX – compile, vectorize, and differentiate with XLA
🎯 CasADi – symbolic computation for optimization and control
🔦 PyTorch – GPU acceleration and batched operations
🐍 NumPy – simple numerical evaluation

All backends share the same interface and produce numerically consistent results, letting you pick the tool that fits your use case.

📦 Installation

With pip

# JAX backend
pip install adam-robotics[jax]

# CasADi backend
pip install adam-robotics[casadi]

# PyTorch backend
pip install adam-robotics[pytorch]

# MuJoCo support
pip install adam-robotics[mujoco]

# OpenUSD support
pip install adam-robotics[usd]

# All backends
pip install adam-robotics[all]

With conda

# CasADi backend
conda create -n adamenv -c conda-forge adam-robotics-casadi

# JAX backend (Linux/macOS only)
conda create -n adamenv -c conda-forge adam-robotics-jax

# PyTorch backend (Linux/macOS only)
conda create -n adamenv -c conda-forge adam-robotics-pytorch

# OpenUSD support
conda install -n adamenv -c conda-forge openusd

# All backends (Linux/macOS only)
conda create -n adamenv -c conda-forge adam-robotics-all

From source

git clone https://github.com/ami-iit/adam.git
cd adam
pip install .[jax]  # or [casadi], [pytorch], [mujoco], [usd], [all]

🚀 Quick Start

Load a robot model and compute dynamics quantities:

JAX

[!NOTE] Check the JAX installation guide

import adam
from adam.jax import KinDynComputations
import icub_models
import numpy as np
import jax.numpy as jnp
from jax import jit, vmap

# if you want to icub-models https://github.com/robotology/icub-models to retrieve the urdf
model_path = icub_models.get_model_file("iCubGazeboV2_5")
# The joint list
joints_name_list = [
    'torso_pitch', 'torso_roll', 'torso_yaw', 'l_shoulder_pitch',
    'l_shoulder_roll', 'l_shoulder_yaw', 'l_elbow', 'r_shoulder_pitch',
    'r_shoulder_roll', 'r_shoulder_yaw', 'r_elbow', 'l_hip_pitch', 'l_hip_roll',
    'l_hip_yaw', 'l_knee', 'l_ankle_pitch', 'l_ankle_roll', 'r_hip_pitch',
    'r_hip_roll', 'r_hip_yaw', 'r_knee', 'r_ankle_pitch', 'r_ankle_roll'
]

kinDyn = KinDynComputations(model_path, joints_name_list)
# Set velocity representation (3 options available):
# 1. MIXED_REPRESENTATION (default) - time derivative of base origin position (expressed in world frame) + world-frame angular velocity
kinDyn.set_frame_velocity_representation(adam.Representations.MIXED_REPRESENTATION)
# 2. BODY_FIXED_REPRESENTATION - both linear & angular velocity in body frame
# kinDyn.set_frame_velocity_representation(adam.Representations.BODY_FIXED_REPRESENTATION)
# 3. INERTIAL_FIXED_REPRESENTATION - world-frame linear & angular velocity
# kinDyn.set_frame_velocity_representation(adam.Representations.INERTIAL_FIXED_REPRESENTATION)

w_H_b = np.eye(4)
joints = np.ones(len(joints_name_list))
M = kinDyn.mass_matrix(w_H_b, joints)
print(M)
w_H_f = kinDyn.forward_kinematics('frame_name', w_H_b, joints)

# JAX functions can also be jitted!
# For example:

def frame_forward_kinematics(w_H_b, joints):
    # This is needed since str is not a valid JAX type
    return kinDyn.forward_kinematics('frame_name', w_H_b, joints)

jitted_frame_fk = jit(frame_forward_kinematics)
w_H_f = jitted_frame_fk(w_H_b, joints)

# JAX natively supports batching
joints_batch = jnp.tile(joints, (1024, 1))
w_H_b_batch = jnp.tile(w_H_b, (1024, 1, 1))
w_H_f_batch = kinDyn.forward_kinematics('frame_name', w_H_b_batch, joints_batch)

[!NOTE] The first call of the jitted function can be slow, since JAX needs to compile the function. Then it will be faster!

CasADi

import casadi as cs
import adam
from adam.casadi import KinDynComputations
import icub_models
import numpy as np

# if you want to icub-models https://github.com/robotology/icub-models to retrieve the urdf
model_path = icub_models.get_model_file("iCubGazeboV2_5")
# The joint list
joints_name_list = [
    'torso_pitch', 'torso_roll', 'torso_yaw', 'l_shoulder_pitch',
    'l_shoulder_roll', 'l_shoulder_yaw', 'l_elbow', 'r_shoulder_pitch',
    'r_shoulder_roll', 'r_shoulder_yaw', 'r_elbow', 'l_hip_pitch', 'l_hip_roll',
    'l_hip_yaw', 'l_knee', 'l_ankle_pitch', 'l_ankle_roll', 'r_hip_pitch',
    'r_hip_roll', 'r_hip_yaw', 'r_knee', 'r_ankle_pitch', 'r_ankle_roll'
]

kinDyn = KinDynComputations(model_path, joints_name_list)
# Set velocity representation (3 options available):
# 1. MIXED_REPRESENTATION (default) - time derivative of position + world-frame angular velocity
kinDyn.set_frame_velocity_representation(adam.Representations.MIXED_REPRESENTATION)
# 2. BODY_FIXED_REPRESENTATION - both linear & angular velocity in body frame
# kinDyn.set_frame_velocity_representation(adam.Representations.BODY_FIXED_REPRESENTATION)
# 3. INERTIAL_FIXED_REPRESENTATION - world-frame linear & angular velocity
# kinDyn.set_frame_velocity_representation(adam.Representations.INERTIAL_FIXED_REPRESENTATION)

w_H_b = np.eye(4)
joints = np.ones(len(joints_name_list))
M = kinDyn.mass_matrix_fun()
print(M(w_H_b, joints))

# If you want to use the symbolic version
w_H_b = cs.SX.eye(4)
joints = cs.SX.sym('joints', len(joints_name_list))
M = kinDyn.mass_matrix_fun()
print(M(w_H_b, joints))

# This is usable also with casadi.MX
w_H_b = cs.MX.eye(4)
joints = cs.MX.sym('joints', len(joints_name_list))
M = kinDyn.mass_matrix_fun()
print(M(w_H_b, joints))

PyTorch

import adam
from adam.pytorch import KinDynComputations
import icub_models
import numpy as np

# if you want to icub-models https://github.com/robotology/icub-models to retrieve the urdf
model_path = icub_models.get_model_file("iCubGazeboV2_5")
# The joint list
joints_name_list = [
    'torso_pitch', 'torso_roll', 'torso_yaw', 'l_shoulder_pitch',
    'l_shoulder_roll', 'l_shoulder_yaw', 'l_elbow', 'r_shoulder_pitch',
    'r_shoulder_roll', 'r_shoulder_yaw', 'r_elbow', 'l_hip_pitch', 'l_hip_roll',
    'l_hip_yaw', 'l_knee', 'l_ankle_pitch', 'l_ankle_roll', 'r_hip_pitch',
    'r_hip_roll', 'r_hip_yaw', 'r_knee', 'r_ankle_pitch', 'r_ankle_roll'
]

kinDyn = KinDynComputations(model_path, joints_name_list)
# choose the representation you want to use the body fixed representation
kinDyn.set_frame_velocity_representation(adam.Representations.BODY_FIXED_REPRESENTATION)
# or, if you want to use the mixed representation (that is the default)
kinDyn.set_frame_velocity_representation(adam.Representations.MIXED_REPRESENTATION)
w_H_b = np.eye(4)
joints = np.ones(len(joints_name_list))
M = kinDyn.mass_matrix(w_H_b, joints)
print(M)

PyTorch Batched

Use pytorch.KinDynComputations to process also multiple configurations.

[!NOTE] There is a class pytorch.KinDynComputationsBatch that has the functionality of pytorch.KinDynComputations. It exists to avoid API changes in existing code. New users should prefer pytorch.KinDynComputations for both single and batched computations.

import adam
from adam.pytorch import KinDynComputations
import icub_models

# if you want to icub-models
model_path = icub_models.get_model_file("iCubGazeboV2_5")
# The joint list
joints_name_list = [
    'torso_pitch', 'torso_roll', 'torso_yaw', 'l_shoulder_pitch',
    'l_shoulder_roll', 'l_shoulder_yaw', 'l_elbow', 'r_shoulder_pitch',
    'r_shoulder_roll', 'r_shoulder_yaw', 'r_elbow', 'l_hip_pitch', 'l_hip_roll',
    'l_hip_yaw', 'l_knee', 'l_ankle_pitch', 'l_ankle_roll', 'r_hip_pitch',
    'r_hip_roll', 'r_hip_yaw', 'r_knee', 'r_ankle_pitch', 'r_ankle_roll'
]

kinDyn = KinDynComputations(model_path, joints_name_list)
# choose the representation you want to use the body fixed representation
kinDyn.set_frame_velocity_representation(adam.Representations.BODY_FIXED_REPRESENTATION)
# or, if you want to use the mixed representation (that is the default)
kinDyn.set_frame_velocity_representation(adam.Representations.MIXED_REPRESENTATION)
w_H_b = np.eye(4)
joints = np.ones(len(joints_name_list))

num_samples = 1024
w_H_b_batch = torch.tensor(np.tile(w_H_b, (num_samples, 1, 1)), dtype=torch.float32)
joints_batch = torch.tensor(np.tile(joints, (num_samples, 1)), dtype=torch.float32)

M = kinDyn.mass_matrix(w_H_b_batch, joints_batch)
w_H_f = kinDyn.forward_kinematics('frame_name', w_H_b_batch, joints_batch)

MuJoCo

adam supports loading models directly from MuJoCo MjModel objects. This is useful when working with MuJoCo simulations or models from robot_descriptions.

import mujoco
import numpy as np
from adam import Representations
from adam.numpy import KinDynComputations

# Load a MuJoCo model (e.g., from robot_descriptions)
from robot_descriptions.loaders.mujoco import load_robot_description
mj_model = load_robot_description("g1_mj_description")

# Create KinDynComputations directly from MuJoCo model
kinDyn = KinDynComputations.from_mujoco_model(mj_model)

# Set velocity representation (default is mixed)
kinDyn.set_frame_velocity_representation(Representations.MIXED_REPRESENTATION)

# Set gravity to match MuJoCo settings
kinDyn.g = np.concatenate([mj_model.opt.gravity, np.zeros(3)])

# Create MuJoCo data and set state
mj_data = mujoco.MjData(mj_model)
mj_data.qpos[:] = your_qpos  # Your configuration
mj_data.qvel[:] = your_qvel  # Your velocities
mujoco.mj_forwar

Adam

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