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.

This paper presents a method to compute differentiable collision-free parametric corridors. In contrast to existing solutions that decompose the obstacle-free space into multiple convex sets, the continuous corridors computed by our method are smooth and differentiable, making them compatible with existing numerical techniques for learning and optimization. To achieve this, we represent the collision-free corridors as a path-parametric off-centered ellipse with a polynomial basis. We show that the problem of maximizing the volume of such corridors is convex, and can be efficiently solved. To assess the effectiveness of the proposed method, we examine its performance in a synthetic case study and subsequently evaluate its applicability in a real-world scenario from the KITTI dataset.

This work focuses on spatial time-optimal motion planning, a generalization of the exact time-optimal path following problem that allows a system to plan within a predefined space. In contrast to state-of-the-art methods, we drop the assumption of a given collision-free geometric reference. Instead, we present a three-stage motion planning method that solely relies on start and goal locations and a geometric representation of the environment to compute a time-optimal trajectory that is compliant with system dynamics and constraints. The proposed scheme first finds collision-free navigation corridors, second computes an obstacle-free Pythagorean Hodograph parametric spline along each corridor, and third, solves a spatially reformulated minimum-time optimization problem at each of these corridors. The spline obtained in the second stage is not a geometric reference, but an extension of the free space associated with its corridor, and thus, time-optimality of the solution is guaranteed. The validity of the proposed approach is demonstrated by a well-established planar example and benchmarked in a spatial system against state-of-the-art methodologies across a wide range of scenarios in highly congested environments. Video: https://youtu.be/zGExvnUEfOY

Minimum-time navigation within constrained and dynamic environments is of special relevance in robotics. Seeking time-optimality, while guaranteeing the integrity of time-varying spatial bounds, is an appealing trade-off for agile vehicles, such as quadrotors. State-of-the-art approaches, either assume bounds to be static and generate time-optimal trajectories offline, or compromise time-optimality for constraint satisfaction. Leveraging nonlinear model predictive control and a path parametric reformulation of the quadrotor model, we present a real-time control that approximates time-optimal behavior and remains within dynamic corridors. The efficacy of the approach is evaluated by simulated results, showing itself capable of performing extremely aggressive maneuvers as well as stop-and-go and backward motions. Video: https://youtu.be/Apc8MCu7Yvo