Modern collaborative robotic applications require robot motions that are predictable for human coworkers. Therefore, trajectories often need to be planned in task space rather than configuration space ($\mathcal{C}$-space). While the interpolation of translations in Euclidean space is straightforward, the interpolation of rotations in$SO(3)$is more complex. Most approaches originating from computer graphics do not exhibit the often desired$\mathcal{C}^{2}$-continuity in robotics. Our main contribution is a$\mathcal{C}^{2}$-continuous, zero-clamped interpolation scheme for quaternions that computes a fast synchronized motion given a set of waypoints. As a second contribution, we present modifications to two state-of-the-art quaternion interpolation schemes, Spherical Quadrangle Interpolation (SQUAD) and Spherical Parabolic Blends (SPB), to enable them to compute$\mathcal{C}^{2}$-continuous, zero-clamped trajectories. In experiments, we demonstrate that for the time optimization of trajectories, our approach is computationally efficient and at the same time computes smooth trajectory profiles.

Modern collaborative manipulators operate in unknown environments and share the work space with human coworkers. To ensure flexibility, their kinematic design is redundant which increases the solution space of the inverse kinematics (IK). We propose a real-time capable Predictive Kinematics Controller (PKC) that tracks task space trajectories as a first priority and computes optimal joint trajectories w.r.t. secondary objectives based on model predictive control (MPC). Therefor, the PKC solves a MPC problem in the nullspace of the task space trajectory. We benchmark a direct shooting, a direct collocation and an indirect gradient method in simulation and we identify the direct shooting method as the most efficient. We demonstrate the superior performance of the PKC compared to state-of-the-art local redundancy resolution approaches. In experiments, we show the real-time capability of our implementation.

Over the past decade we have been able to vastly improve the control algorithms of our biped walking robot LOLA. Further enhancements, however, are limited by vibration problems caused by the dynamics of LOLA's mechanical structure. In this work, we present small examples how structural dynamics limit our control design for walking control as well as low level position control of the joints. We also provide a procedure to identify weaknesses in the structural design of our biped using Experimental Modal Analysis. Using this method, we could successfully identify the structural modes of the system. Furthermore, we were able to use a closed-loop identification method to show a connection between the control loop resonances and the structural resonances of our robot.

In order to fulfill conflicting requirements in the development of industrial robots, such as increased accuracy of a weightreduced manipulator with lower mechanical stiffness, the robot's dynamical behavior must be evaluated early in the development process. This leads to the need of accurate multibody models of the manipulator under development.This paper deals with multibody models that include flexible bodies, which are exported from the corresponding Finite Element model of the structural parts. It is shown that such a flexible link manipulator model, which is purely based on development and datasheet data, is suitable for an accurate description of an industrial robot's dynamic behavior. No stiffness parameters need to be identified by experimental methods, making this approach especially relevant during the development of new manipulators. This paper presents results of experiments in time and frequency domain for analyzing the modeling approach and for validating the model performance against real robot behavior.

Because of their large workspace, robot manipulators have the potential to be used for high precision non-contact manufacturing processes, such as laser cutting or welding, on large complex work pieces. However, most industrial manipulators are not able to provide the necessary accuracy requirements. Mainly because of their flexible structures, they are subject to point to point positioning errors and also vibration errors on a smaller scale. The vibration issues are especially hard to deal with. Many published solutions propose to modify the robot's own control system to deal with these problems. However, most modern control techniques require high fidelity models of the underlying system dynamics, which are quite difficult to obtain for robot manipulators. In this work, we propose an external stabilization unit with an additional set of actuators/sensors to stabilize the process tool, similar to Optical Image Stabilization systems. We show that, because of collocated control, a model of the robot's own dynamic behavior is not needed to achieve high tracking accuracy. We also provide testing results of a prototype stabilizing a dummy tool in two degrees of freedom on a UR10 robot, which reduced its tracking error by two orders of magnitude below 20 micrometers.

Collaborating robots face rising challenges with respect to autonomy and safety as they are deployed in flexible automation applications. The ability to perform the required tasks in the presence of humans and obstacles is key for the integration of these machines in industry. In this work we introduce a framework for motion planning of manipulators that builds upon the most promising existing approaches by combining them in an advantageous way. It includes a new Obstacle-related Sampling Rejection Probabilistic Roadmap planner (ORSR-PRM) that represents the free workspace in an efficient way. Using this representation, dynamic obstacles can be avoided in real-time using an attractor-based online trajectory generation. The resulting motions satisfy kinematic and dynamic joint limits, ensuring a safe human-robot interaction. We validate the functionality and performance of the presented framework in simulations and experiments.

Collision-free walking in cluttered environments is still an open issue for humanoids. Most current approaches use heuristics with large safety margins to plan the robot's motion. That way, the chance of collisions can be greatly reduced but the robot movements are artificially limited. In this context, we extend our framework for motion generation and whole-body collision-avoidance by an on-line predictive kinematic parameter evaluation and optimization: we propose to evaluate the parameter set describing the walking pattern by integrating the full kinematic model of the robot. Initial parameter sets, which are kinematically infeasible due to kinematic limits or collisions, can be identified and adapted before the motion is executed. Starting with a feasible solution, the parameter set is optimized using a gradient method. Since the method is applied before each step, while the robot is executing the previous step, it is very reactive to changes in the environment or in the user input. The optimization method is not limited to a specific walking pattern representation, but it is applicable to different representations. We want to emphasize its suitability for real-time control. The optimization can be stopped if it exceeds a predetermined time budget. In that case, an executable but suboptimal result is used. The method is presented with simulation results obtained with our multi-body simulation. We have also validated the real-time performance in experiments with our humanoid Lola.

In this paper we present a step-planner embedded in a framework which enables a humanoid robot to navigate among obstacles, exploiting its overall capacities. The system allows the robot to react to changes of user input or changes in a dynamic environment in real-time while walking at reasonable speeds. The proposed method relies neither on external sensors nor on color coding or textured surfaces. The key idea is to use a fast collision model based on swept-sphere-volumes (SSVs) for real-time generation of collision-free footsteps and whole-body trajectories. Using a SSV-based 3D approximation in all control modules enables the robot to avoid collisions with itself and the environment. Obstacles are detected with an on-board RGB-D sensor while the robot navigates through an environment which is not known in advance. A step-planner reacts to high-level user commands like desired velocity and direction or changes in the environment within less than a step. Instead of investigating only the footholds an articulated 3D approximation of the lower leg and the foot is considered to find feasible and optimal footstep locations. Additionally, it provides an initial solution for the swing-foot movement. Finally, collision-free swing-foot trajectories are created in real-time in the feedback control layer using all the foot's degrees of freedom. We validated this approach in experiments with our robot Lola.

The exploitation of new fields of application in addition to traditional industrial production for robot manipulators (e.g. agriculture, human areas) requires extensions to the sensor as well as to the planning capabilities. Motion planning solely based on visual information performs poorly in cluttered environments since contacts with obstacles might be inevitable and thus a distinction between hard and soft objects has to be made. In our contribution we present a novel intrinsic tactile sensing module mounted on a multipurpose 9 DOF agricultural manipulator. With its innovative sensor arrangement we consider it to be a low-cost, easily manageable and efficient solution with a reasonable abstraction layer in comparison to complex torque sensing or tactile skins. The sensor provides information about the resulting force and torque. In the second part of our paper, the tactile information is used for minimizing contact forces while pursuing the end-effector tasks as long as reasonable. Hence, we present robust and efficient extensions to Resolved Motion Rate Control for real-time application. We introduce a general formulation providing control inputs in task-space, joint-space and nullspace. Thus, we design a suitable controller by feedback linearization and feed-forward terms. Results from real-world experiments show the potential of our approach. A discussion of the different control schemes completes the paper.

This paper introduces a new state estimator for biped robots fusing encoder, inertial and force torque measurements. The estimator is implemented as a Kalman filter that uses the dynamical model of the linear inverted pendulum with the center of mass (CoM) state as output. In order to compensate for disturbances and model errors we extend the model by a state for the external force and an additional input which is calculated from the dynamics error in pattern generation. Several simulation results underline the effectiveness of the proposed filter and show its robustness against disturbances. Experimental results and an application example validate the method under real world conditions.