Troubleshooting IK: Why Isn't My Pink Example Working?

by Alex Johnson 55 views

Are you grappling with an inverse kinematics (IK) simulation that just won't converge? You're not alone! Many robotics enthusiasts and developers face similar challenges when implementing IK, especially with libraries like Pinocchio and Pink. This article delves into a common issue where a simple IK example runs indefinitely without meeting the desired error threshold, using a specific case with a Piper robot model. We'll break down the problem, examine the code, and provide actionable suggestions to get your IK simulation back on track. Let's dive in!

Understanding the Problem: Infinite Loops in IK Simulations

Inverse kinematics is the process of calculating the joint angles required for a robot to reach a specific pose (position and orientation) in its workspace. It's a fundamental problem in robotics, with applications ranging from robot arm control to character animation. However, IK solutions aren't always straightforward. Several factors can lead to an IK solver failing to converge, resulting in an infinite loop.

  • Singularities: These are configurations where the robot loses one or more degrees of freedom, making it impossible to move in certain directions. Attempting to reach a target near a singularity can cause the solver to oscillate or diverge.
  • Joint Limits: Every physical robot has limits on how far its joints can rotate. If the target pose requires joint angles beyond these limits, the solver will struggle to find a valid solution.
  • Target Reachability: The target pose might simply be unreachable given the robot's physical constraints and geometry. Think of trying to touch your elbow with the same hand – it's physically impossible!
  • Solver Parameters: The IK solver itself might have parameters that need fine-tuning, such as the step size (dt) or damping factor. Inappropriate values can lead to instability.
  • Task Definition: The way the IK task is defined, including the choice of frames and weights, can significantly impact convergence. A poorly defined task might lead the solver down the wrong path.

Analyzing the Pink IK Example

Let's examine the provided Python code snippet, which uses the Pinocchio and Pink libraries for IK. The code aims to move the end-effector of a Piper robot arm to a specified target pose. The script sets up a FrameTask to control the end-effector position and orientation and then iteratively solves for joint velocities using pink.solve_ik. The core of the problem lies in the while loop, which continues until the error norm (the distance between the current end-effector pose and the target pose) falls below a threshold (stop_thres). When the IK solver fails to converge, this loop can run indefinitely.

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
#
# SPDX-License-Identifier: Apache-2.0
#
# /// script
# dependencies = ["daqp", "pin-pink", "qpsolvers", "robot_descriptions"]
# ///

"""Move the end-effector of a UR10 arm to a prescribed target."""

import numpy as np
import pinocchio
import pinocchio as pin
import qpsolvers
from robot_descriptions.loaders.pinocchio import load_robot_description

import pink
from pink.tasks import FrameTask
from scipy.spatial.transform import Rotation as R

# IK parameters
dt = 1e-2
stop_thres = 1e-8

if __name__ == "__main__":
    # robot = load_robot_description("ur10_description")
    # urdf_path = "assets/piper_description_v100_test2.urdf"
    urdf_path = "data/rynn_models/3.robot_arm/22.piper/urdf/piper.urdf"
    model = pin.buildModelFromUrdf(urdf_path)

    # Frame details
    joint_name = model.names[-1]
    parent_joint = model.getJointId(joint_name)
    # parent_frame = model.getFrameId(joint_name)
    print(f"parent: {parent_joint}")
    # placement = pin.SE3.Identity()

    FRAME_NAME = "joint6"
    # ee_frame = model.addFrame(
    #     pin.Frame(
    #         FRAME_NAME,
    #         parent_joint,
    #         parent_frame,
    #         placement,
    #         pin.FrameType.OP_FRAME,
    #     )
    # )
    data = pin.Data(model)
    low = model.lowerPositionLimit
    high = model.upperPositionLimit
    model.q0 = pin.neutral(model)

    print(model)

    # Task details
    np.random.seed(0)
    q_final = np.array(
        # [np.random.uniform(low=low[i], high=high[i], size=(1,))[0] for i in range(6)]
        [
            np.random.uniform(low=low[i], high=high[i], size=(1,))[0]
            for i in range(model.nq)
        ]
    )
    pin.forwardKinematics(model, data, q_final)
    target_pose = data.oMi[parent_joint]
    ee_task = FrameTask(FRAME_NAME, [1.0, 1.0, 1.0], [1.0, 1.0, 1.0])

    target = pin.SE3.Identity()
    target.translation = np.array([0.1, 0.2, 0.3])
    target.rotation = R.from_euler("xyz", [0, 0, 0]).as_matrix()
    # ee_task.set_target(target_pose)
    ee_task.set_target(target)

    configuration = pink.Configuration(model, data, model.q0)
    error_norm = np.linalg.norm(ee_task.compute_error(configuration))
    print(f"Starting from {error_norm = :.2}")
    print(f"Desired precision is error_norm < {stop_thres}")

    nb_steps = 0
    while error_norm > stop_thres:
        dv = pink.solve_ik(
            configuration,
            tasks=[ee_task],
            dt=dt,
            damping=1e-8,
            solver=
                "daqp"
                if "daqp" in qpsolvers.available_solvers
                else qpsolvers.available_solvers[0]
            ,
        )
        q_out = pin.integrate(model, configuration.q, dv * dt)
        q_out = np.clip(q_out, low, high)
        configuration = pink.Configuration(model, data, q_out)
        pin.updateFramePlacements(model, data)
        error_norm = np.linalg.norm(ee_task.compute_error(configuration))
        nb_steps += 1

    print(f"Terminated after {nb_steps} steps with {error_norm = :.2}")

Key Areas to Investigate

  1. Target Pose: The code sets a target pose with a translation of [0.1, 0.2, 0.3] and a zero rotation. While seemingly simple, this target might still be unreachable or close to a singularity, especially considering the robot's initial configuration and joint limits.
  2. Joint Limits: The code clips the joint angles (q_out) to stay within the defined limits. This is good practice, but if the target is far outside the reachable workspace, the clipping might prevent the solver from converging.
  3. Step Size (dt): The step size (dt = 1e-2) determines how much the joint angles are adjusted in each iteration. A small step size can lead to slow convergence, while a large step size might cause oscillations or divergence. Finding the right balance is crucial.
  4. Damping: Damping adds a penalty for large joint velocities, which can help stabilize the solver. However, too much damping can slow down convergence. The code uses a damping value of 1e-8, which is relatively small. Increasing this value might improve stability.
  5. Solver Choice: The code uses the daqp solver if available, otherwise falling back to the first available solver in qpsolvers. Different solvers have different characteristics and might perform better or worse depending on the problem. Experimenting with different solvers could be beneficial.
  6. Task Weights: The FrameTask is initialized with translational and rotational weights of [1.0, 1.0, 1.0]. These weights determine the relative importance of achieving the target position and orientation. Adjusting these weights might improve convergence.

Actionable Suggestions for Debugging

Here are some practical steps you can take to diagnose and fix the infinite loop issue:

1. Visualize the Robot and Target

The most intuitive way to grasp what's happening is to visualize the robot's movements in relation to the target. Pinocchio offers visualization tools, and you can also use external libraries like MeshCat. By visualizing, you can quickly identify if the target is unreachable, if the robot is getting stuck in a singularity, or if joint limits are being violated.

2. Simplify the Target Pose

Start with a target pose that is close to the robot's initial configuration. Gradually move the target further away to see when the solver starts to struggle. This helps isolate the point at which the IK problem becomes difficult.

3. Adjust the Step Size (dt)

Experiment with different values of dt. Try decreasing it (e.g., dt = 1e-3 or dt = 1e-4) to see if it stabilizes the solver. Conversely, try increasing it slightly to potentially speed up convergence, but be cautious of oscillations.

4. Modify the Damping Value

Increase the damping factor (e.g., damping = 1e-4 or damping = 1e-6). Higher damping can help prevent oscillations and improve stability, especially near singularities.

5. Check Joint Limits

Print the joint angles (configuration.q) during the IK iterations. Verify that the joints are not hitting their limits prematurely. If they are, the target might be unreachable, or the initial configuration might need adjustment.

6. Experiment with Different Solvers

Try different solvers available in qpsolvers. Some solvers might be more robust for specific types of IK problems. You can explicitly specify the solver name (e.g., `solver=