Experiment 4A: Task Space Path Planning for the Cobot-C1

Explore path planning in Cartesian space where the end-effector moves along straight-line paths between specified points.

Objectives

  • Command the end-effector to move along straight-line paths in Cartesian space
  • Understand and visualize how end-effector paths are calculated and executed
  • Identify challenges such as inverse kinematics and tracking in operational space
  • Analyze trajectory accuracy and path following performance

Key Concepts

  • Task Space Planning: Path planning in Cartesian/operational space coordinates
  • Direct Workspace Control: End-effector movement in workspace coordinates
  • Inverse Kinematics Computation: Real-time calculation of joint angles for trajectory following
  • Trajectory Tracking: Analysis of path accuracy and following performance
  • Workspace Paths: Precise geometric paths for applications like welding and painting

Theory

What is Task Space Path Planning?

Task space path planning generates reference trajectories directly in the manipulator's workspace using Cartesian coordinates (x, y, z). These paths are typically composed of waypoints or continuous curves interpolated between start and goal locations. At each trajectory point, inverse kinematics is used to calculate the corresponding joint angles required for the robot to follow the intended geometric path.

Task space planning is critical for applications where the end-effector must move with precision along prescribed routes in the physical workspace, such as welding seams, painting surfaces, or assembling components.

Advantages of Task Space Planning

  • Ensures prescribed paths in workspace: The robot moves along predictable geometric paths in physical space
  • Direct environmental control: Precise positioning relative to objects and surfaces in the workspace
  • Intuitive path specification: Easier to plan paths in the physical workspace rather than joint space

Limitations of Task Space Planning

  • Requires reliable inverse kinematics: Complex calculations needed to convert Cartesian positions to joint angles
  • Computationally intensive: Real-time IK solving can be demanding
  • Complex joint motions: Even smooth Cartesian paths can produce irregular joint trajectories
  • Singularity issues: May encounter singularities where IK solutions become unstable

Prerequisites

  • Cobot-C1 robot setup in a safe workspace (real or simulated)
  • ROS installed with required packages and communication verified
  • Path planning scripts and Cartesian command utilities accessible
  • Basic familiarity with entering Cartesian coordinates and interpreting simulation output
  • PlotJuggler optionally configured for live observation

Procedure

Step 1: Setup

Prepare Cobot-C1 and verify all ROS nodes and dependencies are operational.

Step 2: Select Start and End Points

Choose desired Cartesian coordinates (x, y, z) as start and goal positions for the end-effector.

Step 3: Launch Task Space Trajectory Script

cd dev/MRL/cobot-C1/src/cobo_control/src/ python3 linear_experiment.py

Step 4: Choose Path Type

When prompted, select 1 for Task Space (Straight Line).

Step 5: Input Points

Enter start and end coordinates as prompted by the script.

Step 6: Observation

  • The robot should move its end-effector along a straight line in Cartesian space
  • Optionally, use PlotJuggler (see Experiment 4C) to visualize actual vs commanded paths

Step 7: Repeat

Perform the experiment with various pairs of start and end points across the robot's workspace.

Step 8: Exit

Press Ctrl+C to terminate the script.

Expected Outcomes and Analysis

Observations to Make

  • Path straightness: Examine whether the end-effector path is truly straight in the workspace
  • Path accuracy: Note any discrepancies between commanded and actual paths
  • IK dependence: Identify potential issues such as unreachable waypoints or abrupt joint changes
  • Motion quality: Consider speed, smoothness, and repeatability of task space trajectories
  • Joint behavior: Observe how joint angles change to maintain the Cartesian path

Analysis Questions

  • Does the end-effector follow a perfectly straight line in Cartesian space?
  • Are there any points where the robot struggles or slows down?
  • How do the joint angles change during the straight-line motion?
  • What happens when you command paths near the edge of the workspace?

Sources of Error and Precautions

Common Sources of Error

  • Incorrectly entered points: Typos in coordinate entry
  • Out-of-reach goals: Targets outside the robot's workspace
  • Inverse kinematics errors: May occur due to singularities or unreachable targets
  • Real-world effects: Calibration error, joint limits, or sensor drift (if using hardware)

Precautions

  • Ensure coordinates are within the robot's workspace
  • Start with slow, short paths before attempting longer trajectories
  • Monitor for unexpected behavior and be ready to stop the robot
  • Verify path endpoints are reachable before executing

Learning Outcomes

  • Understand the principle and implementation challenges of task space path planning
  • Recognize the importance of reliable inverse kinematics in operational space trajectory tracking
  • Appreciate the qualitative appearance of manipulator motion resulting from task space planning
  • Gain practical experience with Cartesian space control for robotic manipulators
  • Identify when task space planning is preferable to joint space planning
Applications: Task space path planning is essential for welding, painting, cutting, assembly tasks, and any application requiring precise geometric paths in the workspace.
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