Geometric Slosh-Free Tracking for Robotic Manipulators

TL;DR

This paper addresses the challenge of slosh-free liquid transport via robotic manipulators by introducing a real-time, singularity-free tracking pipeline. It replaces the traditional pendulum-based model with a virtual quadrotor to generate a slosh-free reference pose using differential flatness, then applies a cascaded PD controller in task space followed by a convex RAC-based QP to map accelerations to feasible joint commands. The approach is shown to be capable of tracking arbitrary 3D references while ensuring slosh suppression and respecting kinematic constraints, and is validated in both simulations and real-world experiments on a 7-DOF Franka Emika Panda with a cup of water. The combination of differential-flatness-based reference generation, lightweight task-space control, and efficient joint-space optimization yields a real-time, system-agnostic solution for agile, spill-free liquid handling with robotic manipulators.

Abstract

This work focuses on the agile transportation of liquids with robotic manipulators. In contrast to existing methods that are either computationally heavy, system/container specific or dependant on a singularity-prone pendulum model, we present a real-time slosh-free tracking technique. This method solely requires the reference trajectory and the robot's kinematic constraints to output kinematically feasible joint space commands. The crucial element underlying this approach consists on mimicking the end-effector's motion through a virtual quadrotor, which is inherently slosh-free and differentially flat, thereby allowing us to calculate a slosh-free reference orientation. Through the utilization of a cascaded proportional-derivative (PD) controller, this slosh-free reference is transformed into task space acceleration commands, which, following the resolution of a Quadratic Program (QP) based on Resolved Acceleration Control (RAC), are translated into a feasible joint configuration. The validity of the proposed approach is demonstrated by simulated and real-world experiments on a 7 DoF Franka Emika Panda robot. Code: https://github.com/jonarriza96/gsft Video: https://youtu.be/4kitqYVS9n8

Figures (3)

• Figure 1: A planar diagram showcasing the slosh-free condition and its equivalence to the quadrotor. Similar to the existing literature our method couples the longitudinal and rotational accelerations in the container to ensure that the resultant translational acceleration acting on the liquid (in magenta) is perpendicular to the liquid's surface. This implies that the slosh-free angle error $e_{sf}$ (in yellow) is desired to be $0$. For this purpose, we emulate the motion of the container with a virtual quadrotor, whose resultant acceleration aligns with the vertical component (in red), and thus, guarantees to be slosh-free.
• Figure 2: Block diagram of the presented slosh-free tracking method. "Quad. DF." stands for Quadrotor based differential flatness, "TSC" for task space control and "JSC" for joint space control
• Figure 3: Top (above legend box): A comparison between the presented geometric slosh-free tracker (blue) against a non-slosh-free standard tracker (red) with a Franka Emika Panda robot for three different case-studies: A) Loop (left col.), B) Lissajous (middle col.), C) Helix (right col.). The motions of the robot along these trajectories are shown in the first row. The cyan arrows result from the differential flatness based reference generation and refer to the required acceleration's direction to ensure the motion to be slosh-free. Each case-study has been evaluated for different trajectory execution times. The respective position errors $E_p$, slosh-free angle errors $E_{sf}$ and maximum slosh-free angle errors $\max{e_{sf}}$ are depicted in the second, third and fourth rows respectively. The slacks resulting from the slosh-free motions are shown in the fifth row. The gray areas refer to the infeasible regions, i.e, the cases where QP \ref{['eq:QP']} would fail to find a solution if slacks would not be activated. Bottom (below legend box): The motions (left to right) resulting from running the proposed slosh-free tracker in a real Franka Emika Panda robot for trajectories (A) and (B) with a cup filled of water attached to its end-effector.