Impedence Control for Variable Stiffness Mechanisms with Nonlinear Joint Coupling

The current discussion on physical human robot interaction and the related safety aspects, but also the interest of neuro-scientists to validate their hypotheses on human motor skills with bio-mimetic robots, led to a recent revival of tendondriven robots. In this paper, the modeling of tendon-driven elastic systems with nonlinear couplings is recapitulated. A control law is developed that takes the desired joint position and stiffness as input. Therefore, desired motor positions are determined that are commanded to an impedance controller. We give a physical interpretation of the controller. More importantly, a static decoupling of the joint motion and the stiffness variation is given. The combination of active (controller) and passive (mechanical) stiffness is investigated. The controller stiffness is designed according to the desired overall stiffness. A damping design of the impedance controller is included in these considerations. The controller performance is evaluated in simulation

Sampling-Based Trajectory (re)planning for Differentially Flat Systems: Application to a 3D Gantry Crane

In this paper, a sampling-based trajectory planning algorithm for a laboratory-scale 3D gantry crane in an environment with static obstacles and subject to bounds on the velocity and acceleration of the gantry crane system is presented. The focus is on developing a fast motion planning algorithm for differentially flat systems, where intermediate results can be stored and reused for further tasks, such as replanning. The proposed approach is based on the informed optimal rapidly exploring random tree algorithm (informed RRT*), which is utilized to build trajectory trees that are reused for replanning when the start and/or target states change. In contrast to state-of-the-art approaches, the proposed motion planning algorithm incorporates a linear quadratic minimum time (LQTM) local planner. Thus, dynamic properties such as time optimality and the smoothness of the trajectory are directly considered in the proposed algorithm. Moreover, by integrating the branch-and-bound method to perform the pruning process on the trajectory tree, the proposed algorithm can eliminate points in the tree that do not contribute to finding better solutions. This helps to curb memory consumption and reduce the computational complexity during motion (re)planning. Simulation results for a validated mathematical model of a 3D gantry crane show the feasibility of the proposed approach.Comment: Published at IFAC-PapersOnLine (13th IFAC Symposium on Robot Control

Singularity Avoidance with Application to Online Trajectory Optimization for Serial Manipulators

This work proposes a novel singularity avoidance approach for real-time trajectory optimization based on known singular configurations. The focus of this work lies on analyzing kinematically singular configurations for three robots with different kinematic structures, i.e., the Comau Racer 7-1.4, the KUKA LBR iiwa R820, and the Franka Emika Panda, and exploiting these configurations in form of tailored potential functions for singularity avoidance. Monte Carlo simulations of the proposed method and the commonly used manipulability maximization approach are performed for comparison. The numerical results show that the average computing time can be reduced and shorter trajectories in both time and path length are obtained with the proposed approachComment: 8 pages, 2 figures, Accepted for publication at IFAC World Congress 202

Machine Learning-based Framework for Optimally Solving the Analytical Inverse Kinematics for Redundant Manipulators

Solving the analytical inverse kinematics (IK) of redundant manipulators in real time is a difficult problem in robotics since its solution for a given target pose is not unique. Moreover, choosing the optimal IK solution with respect to application-specific demands helps to improve the robustness and to increase the success rate when driving the manipulator from its current configuration towards a desired pose. This is necessary, especially in high-dynamic tasks like catching objects in mid-flights. To compute a suitable target configuration in the joint space for a given target pose in the trajectory planning context, various factors such as travel time or manipulability must be considered. However, these factors increase the complexity of the overall problem which impedes real-time implementation. In this paper, a real-time framework to compute the analytical inverse kinematics of a redundant robot is presented. To this end, the analytical IK of the redundant manipulator is parameterized by so-called redundancy parameters, which are combined with a target pose to yield a unique IK solution. Most existing works in the literature either try to approximate the direct mapping from the desired pose of the manipulator to the solution of the IK or cluster the entire workspace to find IK solutions. In contrast, the proposed framework directly learns these redundancy parameters by using a neural network (NN) that provides the optimal IK solution with respect to the manipulability and the closeness to the current robot configuration. Monte Carlo simulations show the effectiveness of the proposed approach which is accurate and real-time capable ($\approx$ \SI{32}{\micro\second}) on the KUKA LBR iiwa 14 R820

Optimal control of quasi-1D Bose gases in optical box potentials

In this paper, we investigate the manipulation of quasi-1D Bose gases that are trapped in a highly elongated potential by optimal control methods. The effective meanfield dynamics of the gas can be described by a one-dimensional non-polynomial Schr\"odinger equation. We extend the indirect optimal control method for the Gross-Pitaevskii equation by Winckel and Borzi (2008) to obtain necessary optimality conditions for state and energy cost functionals. This approach is then applied to optimally compress a quasi-1D Bose gase in an (optical) box potential, i.e., to find a so-called short-cut to adiabaticity, by solving the optimality conditions numerically. The behavior of the proposed method is finally analyzed and compared to simple direct optimization strategies using reduced basis functions. Simulations results demonstrate the feasibility of the proposed approach.Comment: 6 pages, 5 figures, 2 tables, accepted for IFAC World Congress 202

Real-time 6-DoF Pose Estimation by an Event-based Camera using Active LED Markers

Real-time applications for autonomous operations depend largely on fast and robust vision-based localization systems. Since image processing tasks require processing large amounts of data, the computational resources often limit the performance of other processes. To overcome this limitation, traditional marker-based localization systems are widely used since they are easy to integrate and achieve reliable accuracy. However, classical marker-based localization systems significantly depend on standard cameras with low frame rates, which often lack accuracy due to motion blur. In contrast, event-based cameras provide high temporal resolution and a high dynamic range, which can be utilized for fast localization tasks, even under challenging visual conditions. This paper proposes a simple but effective event-based pose estimation system using active LED markers (ALM) for fast and accurate pose estimation. The proposed algorithm is able to operate in real time with a latency below \SI{0.5}{\milli\second} while maintaining output rates of \SI{3}{\kilo \hertz}. Experimental results in static and dynamic scenarios are presented to demonstrate the performance of the proposed approach in terms of computational speed and absolute accuracy, using the OptiTrack system as the basis for measurement.Comment: 14 pages, 12 figures, this paper has been accepted to WACV 202