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Robot Path and Trajectory Planning Considering a Spatially Fixed TCP

Bernhard Rameder, Hubert Gattringer, Andreas Mueller, Ronald Naderer

TL;DR

The paper addresses robot path planning when the tool center point (TCP) is spatially fixed and the part is moved instead, using a B-spline representation of the processing path on the part to generate a smooth robot trajectory. It maps the part-path to a robot-path through process orientation frames derived from the path geometry, enabling conversion to the robot's inertial frame and yielding a corresponding end-effector path and orientation. Time parameterization via arc-length control ensures adherence to velocity, acceleration, and jerk limits, with the pose and derivatives computed in workspace coordinates; the method also discusses potential cusp formation and smoothing strategies. The approach is validated on an industrial robot with an arbitrarily defined part, and future work includes optimizing path parameterization under joint/workspace limits, refining the mounting and tool positioning, and integrating a thermal model to improve processing quality for tasks like tape laying or sealing.

Abstract

This paper presents a method for planning a trajectory in workspace coordinates using a spatially fixed tool center point (TCP), while taking into account the processing path on a part. This approach is beneficial if it is easier to move the part rather than moving the tool. Whether a mathematical description that defines the shape to be processed or single points from a design program are used, the robot path is finally represented using B-splines. The use of splines enables the path to be continuous with a desired degree, which finally leads to a smooth robot trajectory. While calculating the robot trajectory through prescribed orientation, additionally a given velocity at the TCP has to be considered. The procedure was validated on a real system using an industrial robot moving an arbitrary defined part.

Robot Path and Trajectory Planning Considering a Spatially Fixed TCP

TL;DR

The paper addresses robot path planning when the tool center point (TCP) is spatially fixed and the part is moved instead, using a B-spline representation of the processing path on the part to generate a smooth robot trajectory. It maps the part-path to a robot-path through process orientation frames derived from the path geometry, enabling conversion to the robot's inertial frame and yielding a corresponding end-effector path and orientation. Time parameterization via arc-length control ensures adherence to velocity, acceleration, and jerk limits, with the pose and derivatives computed in workspace coordinates; the method also discusses potential cusp formation and smoothing strategies. The approach is validated on an industrial robot with an arbitrarily defined part, and future work includes optimizing path parameterization under joint/workspace limits, refining the mounting and tool positioning, and integrating a thermal model to improve processing quality for tasks like tape laying or sealing.

Abstract

This paper presents a method for planning a trajectory in workspace coordinates using a spatially fixed tool center point (TCP), while taking into account the processing path on a part. This approach is beneficial if it is easier to move the part rather than moving the tool. Whether a mathematical description that defines the shape to be processed or single points from a design program are used, the robot path is finally represented using B-splines. The use of splines enables the path to be continuous with a desired degree, which finally leads to a smooth robot trajectory. While calculating the robot trajectory through prescribed orientation, additionally a given velocity at the TCP has to be considered. The procedure was validated on a real system using an industrial robot moving an arbitrary defined part.
Paper Structure (7 sections, 9 equations, 5 figures)

This paper contains 7 sections, 9 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Geometric Description of Processing Path on Part
  3. Robot Path Planning
  4. Calculation of the Process Orientation Frames
  5. Calculation of the Robot Path Using the TCP Location and Processing Path Geometry on the Part
  6. Robot Trajectory Calculation
  7. Conclusion and Outlook

Figures (5)

  • Figure 1: Robot with exemplary part. Part borders represent processing path.
  • Figure 2: Process orientation frames $\mathcal{F}_F$ depicted along processing path ${_P}\mathbf{r}_{PF}$
  • Figure 3: Graphical representation of the robot end effector path calculation
  • Figure 4: Calculated robot path ${_I}\mathbf{r}_{0E}$ and corresponding orientation $\mathbf{R}_{IE}$
  • Figure 5: Calculated robot trajectory considering a spatially fixed TCP Legend: ------ x or $\alpha$, ------ y or $\beta$, ------ z or $\gamma$