Robotics: Theory and Examples

8. Error Handling and Limits in Robotic Arms

In this article, we will discuss the limitations of robotic arms, such as their workspace and the possibility of singularities. We will also encourage students to modify the code to include error handling or change the robot arm’s configuration to see how it affects the simulation. Understanding these limitations is crucial for designing safe and efficient robotic systems. Please refer to the 2R pick-and-place robot simulation on GitHub.

8.1. Workspace Limitations

The workspace of a robotic arm refers to the space in which it can reach and perform tasks. It is defined by the robot’s configuration, the length of its links, and the range of motion of its joints. However, the workspace is often not a simple geometric shape, making it challenging to determine its boundaries precisely.

To understand the workspace limitations, students can experiment with different robot configurations and observe the changes in the workspace. For example, they can change the length of the links or the joint limits to see how these modifications affect the robot’s reachability.

8.2. Singularities

A singularity in a robotic arm occurs when the manipulator loses one or more degrees of freedom due to a particular joint configuration. In such cases, the robot may become uncontrollable or lose its ability to generate the required forces and velocities at the end-effector.

Singularities can lead to unexpected behavior and potential damage to the robotic system. Therefore, it is essential to implement error handling and avoid such configurations during trajectory planning.

8.3. Modifying the Code for Error Handling

Students can modify the code to include error handling to detect and manage workspace limitations and singularities. Here are some suggestions for error handling in robotic arm simulations:

Add checks for joint limit violations: Ensure that the joint angles remain within their specified limits during trajectory planning and execution.
Implement singularity detection: Monitor the robot’s configuration and detect singularities to prevent undesired behavior.
Integrate workspace boundary checks: Verify that the desired end-effector positions are within the robot’s workspace before planning and executing trajectories.

8.4. Changing the Robot Arm’s Configuration

To gain a deeper understanding of the limitations of robotic arms, students can change the robot arm’s configuration and observe its impact on the simulation. Some possible modifications include:

Adjusting the link lengths: Observe how longer or shorter links affect the workspace and the robot’s performance.
Changing the joint types: Explore the differences between revolute, prismatic, and spherical joints and their impact on the robot’s capabilities.
Modifying the joint limits: Experiment with different joint angle limits to see how they influence the robot’s reachability and dexterity.

8.5. Error Handling and Limits: A Case in Point

The following aspects of the 2R robot arm simulation apply to the topic of Error Handling and Limits in Robotic Arms:

Inverse Kinematics Calculation:

def inverse_kinematics(x, y, offset=0):
    d = np.sqrt(x**2 + (y + offset)**2)
    a = np.arccos((L1**2 + L2**2 - d**2) / (2 * L1 * L2))
    b = np.arctan2(y + offset, x) - np.arctan2(L2 * np.sin(a), L1 + L2 * np.cos(a))
    return b, a + b

This function calculates the joint angles for a given end-effector position (x, y). It does not include error handling for situations where the target position is out of the workspace or when the robot encounters a singularity. This can be modified to check for these scenarios and return an error message or handle the error gracefully.

Workspace Limitations:

L1 = 6  # Adjust link length
L2 = 6  # Adjust link length

These variables define the lengths of the robot arm links (L1 and L2). They determine the robot arm’s workspace, which is the area the end-effector can reach. Modifying the link lengths will change the robot arm’s workspace, which can help students understand how it affects the robot arm’s limitations.

Updating the Robot Arm’s Joint Angles:

if frame < num_frames / 6:
    t = frame / (num_frames / 6)
    theta1_diff = shortest_angle_diff(theta1_home, theta1_initial)
    theta2_diff = shortest_angle_diff(theta2_home, theta2_initial)
    theta1 = theta1_home + t * theta1_diff
    theta2 = theta2_home + t * theta2_diff

This part of the update function updates the joint angles based on the frame number during the simulation. It can be modified to include error handling in cases when the robot arm is moving towards an unreachable position or approaching a singularity. Proper error handling can help ensure the robot arm operates smoothly and safely during the simulation.

8.6. Conclusion

Understanding the limitations of robotic arms, such as workspace boundaries and singularities, is essential for designing safe and efficient robotic systems. By modifying the code to include error handling and experimenting with different robot configurations, students can develop a deeper understanding of these limitations and learn how to address them in their projects.

8.7. Exercise

Example 1

What is the significance of understanding the workspace of a robotic arm, and how can altering the robot’s configuration impact the workspace?

Solution:

Understanding the workspace of a robotic arm is crucial because it defines the region where the robot can reach and perform tasks. Altering the robot’s configuration, such as changing the length of its links or adjusting the joint limits, can directly impact the workspace by expanding or reducing the robot’s reachability.

Example 2

Explain the concept of singularities in robotic arms and discuss their potential impact on the performance of the robot.

Solution:

Singularities in robotic arms occur when the manipulator loses one or more degrees of freedom due to a specific joint configuration. These can lead to unexpected behavior and potential damage to the robotic system, as the robot may become uncontrollable or lose its ability to generate the required forces and velocities at the end-effector.

Example 3

Provide at least two examples of error-handling methods that can be implemented in robotic arm simulations to address workspace limitations and singularities.

Solution:

Two examples of error handling methods in robotic arm simulations are:

Adding checks for joint limit violations: Ensuring that the joint angles remain within their specified limits during trajectory planning and execution can help prevent workspace violations and maintain safe robot operation.
Implementing singularity detection: Monitoring the robot’s configuration and detecting singularities can help prevent undesired behavior and potential damage to the robotic system by allowing the control software to react accordingly.

Example 4

What is the difference between kinematic redundancy and singularities in robotic arms, and how can they affect the robot’s performance?

Solution:

Kinematic redundancy and singularities are two distinct concepts in robotic arms:

Kinematic redundancy occurs when a robotic arm has more degrees of freedom than the task requirements, allowing for multiple solutions to achieve a given end-effector position and orientation. This redundancy can be advantageous for optimizing performance, avoiding obstacles, or compensating for joint limitations.
Singularities, on the other hand, occur when the robotic arm loses one or more degrees of freedom due to a specific joint configuration. Singularities can negatively impact the robot’s performance by causing uncontrollable behavior or loss of the ability to generate required forces and velocities at the end-effector.

In summary, kinematic redundancy can offer additional flexibility and optimization options for a robotic arm, while singularities represent a potential risk to the robot’s performance and safety.

Example 5

How can you modify the inverse kinematics function in the given 2R robot arm simulation to incorporate error handling for situations where the target position is out of the robot arm’s workspace?

Solution:

First, create a function to determine if a given target position is within the robot arm’s workspace. We can then modify the inverse kinematics function to check if the target position is within the workspace before calculating the joint angles. If the target position is outside the workspace, we can return an error message or handle the error gracefully.

Here’s a suggested approach:

Create a function to determine if a given target position is within the robot arm’s workspace:

def is_target_position_reachable(x, y):
    max_reachable_distance = L1 + L2
    min_reachable_distance = abs(L1 - L2)
    distance_to_target = np.sqrt(x**2 + y**2)
    return min_reachable_distance <= distance_to_target <= max_reachable_distance

Modify the inverse_kinematics function to incorporate error handling for unreachable target positions:

def inverse_kinematics(x, y, offset=0):
    # Check if the target position is within the robot arm's workspace
    if not is_target_position_reachable(x, y + offset):
        print("Error: Target position is out of the robot arm's workspace.")
        return None, None

    d = np.sqrt(x**2 + (y + offset)**2)
    a = np.arccos((L1**2 + L2**2 - d**2) / (2 * L1 * L2))
    b = np.arctan2(y + offset, x) - np.arctan2(L2 * np.sin(a), L1 + L2 * np.cos(a))

    return b, a + b

By incorporating error handling for unreachable target positions, the inverse kinematics function can now provide more meaningful feedback when the robot arm is commanded to move to an invalid position. This can help prevent the robot from trying to reach an impossible position, reducing the risk of mechanical failure or other problems.

Comments (2)

New

Amos Munene

Hey there. The sample values used in Example one bring about the following error in the function when executed:

" imeWarning: invalid value encountered in arccos "

I suggest using the following values instead L1 = 2 , L2 = 1 , x=2 , y = 1

2 April 2024 14:19

Kemboi

I'd really like if you would explain to me Inverse Kinematics for a six-DoF robot, because All the tutorials and resources are not for such robots.

17 June 2024 11:18

Robotics: Theory and Examples

8. Error Handling and Limits in Robotic Arms

8.1. Workspace Limitations

8.2. Singularities

8.3. Modifying the Code for Error Handling

8.4. Changing the Robot Arm’s Configuration

8.5. Error Handling and Limits: A Case in Point

8.6. Conclusion

8.7. Exercise

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