# Source code for skbot.inverse_kinematics.gradient_descent

```
from .. import transform as tf
from .targets import Target
from typing import List
import numpy as np
from scipy.optimize import minimize, OptimizeResult, Bounds
import warnings
[docs]def gd(
targets: List[Target],
joints: List[tf.Joint],
*,
rtol: float = 1e-6,
maxiter: int = 500,
):
"""L-BFGS-B based Gradient Descent.
.. note::
This function will modify the objects in ``joints`` as a side effect.
Use L-BFGS-B to find values for ``joints`` such that the sum of all target
scores is minimal. L-BFGS-B is a quasi-Newton method that approximates both
the targets Jacobian and Hessian.
Parameters
----------
targets : List[Target]
A list of quality measures that a successful pose minimizes.
joints : List[joint]
A list of 1DoF joints which should be adjusted to minimize ``targets``.
rtol : float
Relative tolerance for termination. If, after one iteration, the sum of
scores has not improved by more than rtol the algorithm terminates and
assumes that a local optimum has been found.
maxiter : int
The maximum number of iterations to perform.
Returns
-------
joint_values : List[float]
The final parameters of each joint.
Notes
-----
Joint limits (min/max) are enforced as hard constraints throughout the
optimization.
A common cause of IK faulure is that the chosen initial condition is too far
away from the desired target position. One indicator for this is that
:func:`gd` converges based on ``rtol``, but the score of one or more targets
isn't below ``atol``.
"""
joint_values = np.array([l.param for l in joints])
for target in targets:
target._chain = tf.simplify_links(target._chain, keep_links=joints)
atols = np.array([x.atol for x in targets])
bounds = Bounds(
[x.lower_limit for x in joints],
[x.upper_limit for x in joints],
keep_feasible=True,
)
def objective_function(joint_config: np.ndarray) -> float:
for joint, value in zip(joints, joint_config):
joint.param = value
normalized_scores = np.array([x.score() / x.atol for x in targets])
return np.sum(normalized_scores)
# return np.max(normalized_scores)
# check if optimization is needed
skip = False
for target in targets:
if target.score() > target.atol:
break
else:
skip = True
if not skip:
result: OptimizeResult = minimize(
objective_function,
joint_values,
bounds=bounds,
method="L-BFGS-B",
options={"maxiter": maxiter, "ftol": rtol},
)
if not result.success:
warnings.warn(
f"L-BFGS-B terminated abnormally with message `{result.message}`."
)
scores = np.array([x.score() for x in targets])
if np.any(scores > atols):
raise RuntimeError(
f"IK failed. Reason: Local minimum doesn't reach one or more targets."
)
for joint, value in zip(joints, result.x):
joint.param = value
joint_values = np.array([j.param for j in joints])
return joint_values
```