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# Inverse Kinematics and Dynamics
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Compute inverse kinematics solutions for robotic manipulation and inverse dynamics for force computation and control. Essential for robotic applications requiring precise end-effector positioning and force control.
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## Capabilities
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### Inverse Kinematics
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```python { .api }
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def calculateInverseKinematics(bodyUniqueId, endEffectorLinkIndex, targetPosition, targetOrientation=None, lowerLimits=None, upperLimits=None, jointRanges=None, restPoses=None, maxNumIterations=20, residualThreshold=1e-4, physicsClientId=0):
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    """
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    Calculate inverse kinematics solution for target end-effector pose.
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    Args:
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        bodyUniqueId (int): Robot body unique ID
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        endEffectorLinkIndex (int): End effector link index
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        targetPosition (list): Target position [x, y, z]
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        targetOrientation (list, optional): Target orientation quaternion [x, y, z, w]
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        lowerLimits (list, optional): Joint lower limits
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        upperLimits (list, optional): Joint upper limits
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        jointRanges (list, optional): Joint ranges for null space optimization
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        restPoses (list, optional): Rest pose joint angles
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        maxNumIterations (int, optional): Maximum IK iterations. Defaults to 20.
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        residualThreshold (float, optional): Convergence threshold. Defaults to 1e-4.
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        physicsClientId (int, optional): Physics client ID. Defaults to 0.
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    Returns:
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        list: Joint angles solution
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    """
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def calculateInverseKinematics2(bodyUniqueId, endEffectorLinkIndices, targetPositions, targetOrientations=None, lowerLimits=None, upperLimits=None, jointRanges=None, restPoses=None, jointDamping=None, solver=0, maxNumIterations=20, residualThreshold=1e-4, physicsClientId=0):
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    """Calculate IK for multiple end effectors simultaneously."""
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```
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### Inverse Dynamics
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```python { .api }
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def calculateInverseDynamics(bodyUniqueId, objPositions, objVelocities, objAccelerations, physicsClientId=0):
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    """
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    Calculate joint torques using inverse dynamics.
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    Args:
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        bodyUniqueId (int): Body unique ID
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        objPositions (list): Joint positions
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        objVelocities (list): Joint velocities
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        objAccelerations (list): Desired joint accelerations
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        physicsClientId (int, optional): Physics client ID. Defaults to 0.
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    Returns:
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        list: Required joint torques
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    """
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```
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### Jacobian Computation
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```python { .api }
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def calculateJacobian(bodyUniqueId, linkIndex, localPosition, objPositions, objVelocities, objAccelerations, physicsClientId=0):
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    """
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    Calculate Jacobian matrices for given configuration.
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    Returns:
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        tuple: (linearJacobian, angularJacobian)
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    """
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def calculateMassMatrix(bodyUniqueId, objPositions, physicsClientId=0):
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    """Calculate mass matrix for given configuration."""
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```
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## Usage Examples
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### Basic Inverse Kinematics
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```python
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import pybullet as p
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p.connect(p.GUI)
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robotId = p.loadURDF("kuka_iiwa/model.urdf")
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# Target end-effector position
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targetPos = [0.5, 0.2, 0.7]
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targetOrn = p.getQuaternionFromEuler([0, -math.pi/2, 0])
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# Calculate IK solution
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jointPositions = p.calculateInverseKinematics(
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    robotId,
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    6,  # End effector link index
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    targetPos,
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    targetOrn
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)
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# Apply solution
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for i, pos in enumerate(jointPositions):
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    p.setJointMotorControl2(robotId, i, p.POSITION_CONTROL, targetPosition=pos)
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```
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[Complete documentation with detailed examples and usage patterns]