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Smooth real-time motion planning based on a cascade dual-quaternion screw-geometry MPC

Ainoor Teimoorzadeh, Frederico Fernandes Afonso Silva, Luis F. C. Figueredo, Sami Haddadin

TL;DR

The paper addresses real-time, coordinate-invariant trajectory tracking for robotic manipulators under end-effector twist, acceleration, and jerk constraints. It couples screw-linear interpolation (ScLERP) in a dual-quaternion framework with a discrete-time MPC to enforce kinodynamic bounds along the path, producing a smooth, constraint-satisfying trajectory on $Spin(3)⋉R^3$. The key contributions are the integration of ScLERP with a QP-based MPC over horizons $n_c$ and $n_p$, a cascade architecture with outer twist-smoothing and inner-pose-tracking, and experimental validation on a $7$-DoF Franka Emika Panda showing constraint enforcement in real time. The approach enables safe, smooth real-time motion planning in cluttered or human-shybrid environments by preserving coordinate invariance and avoiding representation singularities.

Abstract

This paper investigates the tracking problem of a smooth coordinate-invariant trajectory using dual quaternion algebra. The proposed architecture consists of a cascade structure in which the outer-loop MPC performs real-time smoothing of the manipulator's end-effector twist while an inner-loop kinematic controller ensures tracking of the instantaneous desired end-effector pose. Experiments on a $7$-DoF Franka Emika Panda robotic manipulator validate the proposed method demonstrating its application to constraint the robot twists, accelerations and jerks within prescribed bounds.

Smooth real-time motion planning based on a cascade dual-quaternion screw-geometry MPC

TL;DR

The paper addresses real-time, coordinate-invariant trajectory tracking for robotic manipulators under end-effector twist, acceleration, and jerk constraints. It couples screw-linear interpolation (ScLERP) in a dual-quaternion framework with a discrete-time MPC to enforce kinodynamic bounds along the path, producing a smooth, constraint-satisfying trajectory on . The key contributions are the integration of ScLERP with a QP-based MPC over horizons and , a cascade architecture with outer twist-smoothing and inner-pose-tracking, and experimental validation on a -DoF Franka Emika Panda showing constraint enforcement in real time. The approach enables safe, smooth real-time motion planning in cluttered or human-shybrid environments by preserving coordinate invariance and avoiding representation singularities.

Abstract

This paper investigates the tracking problem of a smooth coordinate-invariant trajectory using dual quaternion algebra. The proposed architecture consists of a cascade structure in which the outer-loop MPC performs real-time smoothing of the manipulator's end-effector twist while an inner-loop kinematic controller ensures tracking of the instantaneous desired end-effector pose. Experiments on a -DoF Franka Emika Panda robotic manipulator validate the proposed method demonstrating its application to constraint the robot twists, accelerations and jerks within prescribed bounds.
Paper Structure (10 sections, 28 equations, 6 figures)

This paper contains 10 sections, 28 equations, 6 figures.

Table of Contents

  1. INTRODUCTION
  2. Problem Formulation
  3. Mathematical Preliminaries
  4. Overview of the Problem
  5. ScLERP-MPC: A Motion Planner based on Screw-linear Interpolation & Model-Predictive Control
  6. Experimental Results
  7. Experimental setup
  8. Simulations
  9. Experiments
  10. Conclusions and Future Works

Figures (6)

  • Figure 1: Schematic block diagram of the ScLERP-MPC.
  • Figure 2: Trajectories for the simulated scenario. Solid blue curves correspond to the SCLERP-MPC resulting trajectory whereas Dashed blue correspond a system without kinodynamic constraints. The Dashed red curves refer to the reference.
  • Figure 3: Twist trajectory for the simulation scenario. Solid blue curves correspond to the SCLERP-MPC resulting trajectory whereas the Dashed red curves refer to the reference. The shadowed areas depict picks of acceleration and jerk above the robot limits.
  • Figure 4: Acceleration trajectory for the simulation scenario. Solid blue curves correspond to the SCLERP-MPC resulting trajectory. The shadowed areas depict picks of acceleration and jerk above the robot limits.
  • Figure 5: Real-world experiment trajectories with SCLERP-MPC. Solid blue curves correspond to measured output, whereas the Dashed red refers to the reference.
  • ...and 1 more figures