Andreas Mueller

Johannes Kepler University Linz | JKU · Institute of Robotics

It is commonly assumed that the singularities of kinematic mappings constitute generically smooth manifolds but this has not yet been proven. Moreover, before this assumption can be verified, the concept of genericity needs to be clarified. In this paper, two different notions of generic properties of kinematic mappings are discussed. One accounts...

The basis for any model-based control of dynamical systems is a numerically efficient formulation of the motion equations, preferably expressed in terms of a minimal set of independent coordinates. To this end the coordinates of a constrained system are commonly split into a set of dependent and independent ones. The drawback of such coordinate pa...

Redundant actuation of parallel manipulators can lead to internal forces without generating end-effector forces (preload). Preload can be controlled in order to prevent backlash during the manipulator motion. Such control is based on the inverse dynamics. The general solution of the inverse dynamics of redundantly actuated parallel manipulators is...

Following the performance and force limitation method of the ISO/TS 15066 standard, human safety is evaluated in a quasi-static impact situation in a human-robot collaboration task. To achieve this, all potentially critical impact situations are first identified and then the corresponding impact forces and pressures are experimentally measured and...

The problem of interpolating a rigid body motion is to find a spatial trajectory between a prescribed initial and terminal pose. Two variants of this interpolation problem are addressed. The first is to find a solution that satisfies initial conditions on the \(k-1\) derivatives of the rigid body twist. This is called the kth-order initial value tr...

The mobility and singularity analysis of linkages comprising helical joints (screw joints with finite pitch) is addressed. The analysis is based on the kinematic tangent cone, which provides the mathematical setting and the computational framework for the higher-order local analysis. The approach is discussed by means of examples. Besides introduci...

This paper addresses the time‐optimal trajectory planning of a redundantly actuated parallel robot driven by series elastic actuators. Here, the actuation redundancy allows prestressing the elastic components of the drives and enables more degrees of freedom in the trajectory planning. To this end, a time‐optimal control problem is formulated that...

This paper presents a method for planning time-optimal trajectories for a formation of multiple nonholonomic (heavy duty) platforms (HDPs) to cooperatively transport an object to a specified pose. The first part addresses the mobile platforms themselves while the second part provides a trajectory planning approach derived from the well-known virtua...

The motions of mechanisms can be described in terms of screw coordinates by means of an exponential mapping. The product of exponentials (POE) describes the configuration of a chain of bodies connected by lower pair joints. The kinematics is thus given in terms of joint screws. The POE serves to express loop constraints for mechanisms as well as th...

The control of free-floating robots requires dealing with several challenges. The motion of such robots evolves on a continuous manifold described by the Special Euclidean Group of dimension 3, known as SE(3). Methods from finite horizon Linear Quadratic Regulators (LQR) control have gained recent traction in the robotics community. However, such a...

Tracking sequences of predefined open and closed paths is of crucial interest for applications like laser cutting and similar production processes. The disconnected paths are connected by non-productive, four times continuously differentiable trajectories, which also account for the overall process time. Heuristic methods are applied in order to fi...

This paper presents a closed-form method to evaluate the inertia-weighted input matrix , which is the map between inputs and system accelerations, using intermediate results from an O(n) method, the Implicit Inversion Method (IIM). This matrix can be used to greatly reduce the calculation times for optimal control problems which include the Equatio...

This paper presents a closed-form method to evaluate the inertia-weighted input matrix , which is the map between inputs and system accelerations, using intermediate results from an O(n) method, the Implicit Inversion Method (IIM). This matrix can be used to greatly reduce the calculation times for optimal control problems which include the Equatio...

Screw and Lie group theory allows for user-friendly modeling of multibody systems (MBS) while at the same they give rise to computationally efficient recursive algorithms. The inherent frame invariance of such formulations allows for use of arbitrary reference frames within the kinematics modeling (rather than obeying modeling conventions such as t...

After three decades of computational multibody system (MBS) dynamics, current research is centered at the development of compact and user friendly yet computationally efficient formulations for the analysis of complex MBS. The key to this is a holistic geometric approach to the kinematics modeling observing that the general motion of rigid bodies a...

Series elastic actuators (SEA) were introduced for serial robotic arms. Their model-based trajectory tracking control requires the second time derivatives of the inverse dynamics solution, for which algorithms were proposed. Trajectory control of parallel kinematics manipulators (PKM) equipped with SEAs has not yet been pursued. Key element for thi...

In optical motion capture, camera placement strongly effects the dimensions of the measurable area and the accuracy of measured 3D marker positions calculated via triangulation. Aligning a given set of cameras by hand according to spatial conditions and measurement requirements relies on expertise and experience. This paper introduces an approach t...

In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization problem in terms of a path parameter. Thus, smooth trajectory generation while maintaining a low computational...

In this paper, an approach for gait assistance with a lower body exoskeleton is described. Two concepts, transparency and motion assistance, are combined. The transparent mode, where the system is following the user’s free motion with a minimum of perceived interaction forces, is realized by exploiting the gear backlash of the actuation units. Duri...

In the automotive industry new technology has to be tested thoroughly before a market launch. In addition, many regulations hinder a short time-to-market, as well as the manually operated proving grounds (PG). Therefore, a toolchain is introduced to be able to automate and to increase the efficiency of test scheduling. Three steps are proposed. In...

The synthesis and control of a closed–chain reconfigurable mechanism is considered, which finds direct applications in reconfigurable architecture. This term refers to building structures whose shape can be adjusted towards certain objectives including energy efficiency and improved occupants’ comfort. The structural concept for the building is pre...

Reconfigurable architecture refers to buildings whose shape can be adjusted. Such buildings exhibit potential advantages compared to traditional fixed–shape ones, including better energy efficiency and improved comfort for the occupants. A family of planar linkage mechanisms is presented to establish a framework for reconfigurable buildings. These...

A robotic system constructed as a wheeled inverted pendulum (WIP) serves as an impressive demonstrator, since this kind of system is inherently nonlinear, unstable, and nonminimum phase. These properties may pose several difficulties, when it comes to control and trajectory planning. This paper shows a method for deriving a highly dynamic trajector...

Modern geometric approaches to analytical mechanics rest on a bundle structure of the configuration space. The connection on this bundle allows for an intrinsic splitting of the reduced Euler-Lagrange equations. Hamel's equations, on the other hand, provide a universal approach to non-holonomic mechanics in local coordinates. The link between Hamel...

Modern geometric approaches to analytical mechanics rest on a bundle structure of the configuration space. The connection on this bundle allows for an intrinsic splitting of the reduced Euler–Lagrange equations. Hamel’s equations, on the other hand, provide a universal approach to non-holonomic mechanics in local coordinates. The link between Hamel...

Redundantly actuated parallel kinematic manipulators (RA‐PKM) are ideal candidates in robotic applications combining dynamic performance with high accuracy. Actuation redundancy further allows for modulation of the end‐effector (EE) stiffness. A recent trend in robotics is the use of inherently compliant and elastic components, eventually leading t...

The time-optimal path following (OPF) problem is to find a time evolution along a prescribed path in task space with shortest time duration. Numerical solution algorithms rely on an algorithm-specific (usually equidistant) sampling of the path parameter. This does not account for the dynamics in joint space, that is, the actual motion of the robot,...

Structures enabling transformability of buildings, components and materials at different levels gain significance in view of a sustainable built environment. Such structures are capable of obtaining different shapes in response to varying functional, environmental or loading conditions. Certain limitations of classic tensegrity and scissor-like str...

This paper deals with the kinematics of the orthogonal Bricard 6R mechanism. The paper presents the loop equations formulated in terms of dual-quaternions. The analysis reveals a symmetric relationship between the odd and even pairs of revolute joint angles. The kinematic model was used to compute the instantaneous screw axis of the coupler. Finall...

For the adaptation of a process in a flexible production environment, robotic systems are basically a suitable option to ensure the required agility. In case of a human-robot work system, however, the flexibility of a robot is currently severely limited due to safety reasons; therefore, new tasks for the robot can only be implemented with significa...

This paper presents the kinematics about the center of mass (CoM) for robotic mechanisms based on Lie Group theory because the movements of CoM is very important for mobile manipulating robots. Different from general kinematics, the CoM kinematics relates the position of the CoM to the joint angles and the pose of the robot. The concept of the homo...

Parallel kinematic manipulators (PKM) are characterized by closed kinematic loops, due to the parallel arrangement of limbs but also due to the existence of kinematic loops within the limbs. Moreover, many PKM are built with limbs constructed by serially combining kinematic loops. Such limbs are called hybrid, which form a particular class of compl...

Recent increase in space debris combined with the increase in the number of satellites launched has created an increased risk of collisions. The effects of the increased risk can be seen in the form of an increased number of near misses in recent years. The use of robotic manipulators has been suggested for Active Debris Removal (ADR) to reduce the...

Many industrial applications require the displacement of liquid-filled containers on planar paths (namely, paths on a horizontal plane), by means of linear transport systems or serial robots. The movement of the liquid inside the container, known as sloshing , is usually undesired, thus there is the necessity to keep under control the peaks that th...

Linkages able to change their finite degree of freedom due to geometric constraints are commonly known as kinematotropic linkages. Although a considerable number of examples of such linkages can be found in the literature, the amount of reported kinematotropic parallel manipulators remains small. Even more rare are publications presenting systemati...

Modeling closed loop mechanisms is a necessity for the control and simulation of various systems and poses a great challenge to rigid body dynamics algorithms. Solving the forward and inverse dynamics for such systems require resolution of loop closure constraints which are often solved via numerical procedures. This brings an additional burden to...

Slides of the talk to the paper 'On the Use of Ternary Products to Characterize the Dexterity of Spatial Kinematic Chains'

Two performance indices are introduced that characterize the singularities and the manipulability of a general spatial kinematic chain in a threefold, physically significant manner. The ternary volume and shape indices are obtained as characteristic scalars of two ternary product matrices that capture the geometry of the joint axes in a certain con...

Mechanisms may possess kinematic singularities that are smooth points of the configuration space (c-space). At such points, a mechanism becomes shaky as its instantaneous mobility changes, but in contrast to c-space singularities, like bifurcations or cusps, these kinematic singularities are not reflected in the c-space. They are therefore called h...

In this paper, a methodology to generate realistic gait patterns is presented. Human gait motion capture data is used along with a kinematic model of the human lower extremity to derive a parametric and time-continuous analytical description of the walking motion. This allows for reproduction of individual recorded gait cycles and for generating ne...

The constantly increasing usage of quadruped robots in science as well as in industry shows that the last decade has experienced an immense leap in this technology. Several commercial products are already available and have been deployed in various applications. One of them is Spot® from Boston Dynamics, a ready-to-use, highly agile, robust mobile...

Over the last decades, research on robotic devices for the replacement of lost limbs, such as actively actuated prostheses, has been intensified. In this paper we present the development of a low-cost robotic arm together with a sensor bracelet for electromyographic (EMG) control. With a total cost of about $300 the introduced system aims at contri...

A consistent method is presented for solving the so-called general waiter problem, which is to move a tray (mounted at the end-effector of a robot) with a number of loosely placed objects (e.g. cups) as fast as possible such that the objects do not slide at any time. The geometric path of the tray motion is prescribed while the attitude of the tray...

The finite degree of freedom (DOF) of a mechanism is determined by the number of independent loop constraints. In this paper a method to determine the maximal number of loop closure constraints (which is independent of a specific configuration) of multi-loop linkages is introduced and applied to calculate the finite DOF. It rests on an algebraic co...

A robotic system constructed as a wheeled inverted pendulum (WIP) serves as an impressive demonstrator, since this kind of system is inherently non-linear, unstable and non-minimum-phase. But the same properties which make it impressive also introduce serveral difficulties, when it comes to control and trajectory planning. Therefore this paper show...

The inverse kinematics problem is ill-posed near kinematic singularities leading to extremely large joint velocities. This classical problem is addressed from a different perspective; instead of prescribing the end-effector (EE) motion in terms of a path parameter, the motion is parameterized in terms of the arc length in joint space. This allows t...

Elastic joints and/or links greatly influence the position and orientation accuracy of robots. Hence, standard geometric calibration might be insufficient for elastic robots and stiffness identification is also required for improved accuracy. This paper describes the simultaneous identification of geometric as well elasticity parameters of a 3-DoF...

Robotic surface treatment is already broadly used in the manufacturing industry because it guarantees repeatable high-quality surfaces at short production time. Such a robotic solution, with an accurate control of the applied force on a surface, requires a robot that is either equipped with a force/torque sensor or, alternatively, with a force comp...

Reconfigurable architecture is a disruptive concept with unique opportunities for creativity in design towards more usable buildings, better energy efficiency and improved comfort for the occupants. From an engineering perspective, implementations involve mechanism design and control, while analytical approaches from robotics become relevant. A str...

This paper presents a method of optimizing the design of robotic manipulators using a novel kinematic model pruning technique. The optimization departs from an predefined candidate linkage consisting of a initial topology and geometry. It allows simultaneously optimizing the degree of freedom, the link lengths and other kinematic or dynamic perform...

Identifying dynamic parameters of an elastic robotic system can be a quite challenging task. This is because elastic robotic systems are often highly underactuated and sensor data may only be available for the driven states. To overcome this shortcoming, the identification process can be addressed by different experiments based on different reduced...

Parallel manipulators, also called parallel kinematics machines (PKM), enable robotic solutions for highly dynamic handling and machining applications. The safe and accurate design and control necessitates high-fidelity dynamics models. Such modeling approaches have already been presented for PKM with simple limbs (i.e. each limb is a serial kinema...

The characterization of the workspace for general spatial 3R chains with skew joint axes is refined by describing the variety of singular displacements as the union of the singular configuration manifolds of orientation type, position type, and attitude type. The surface of attitude singularities is revealed by transferring the singularity sets of...

Handling of parts that are loosely placed at the end-effector (EE) of a robot is a task with high practical relevance, which is synonymously known as the waiter motion problem, and the time optimal motion planning is an important task for factory automation. In the past, this problem was often relaxed to a time-optimal path following problem by ass...

A classical approach to the MBS modeling is to use absolute coordinates, i.e. a set of (possibly redundant) coordinates that describe the absolute position and orientation of the individual bodies w.r.t. to an inertial frame (IFR). A well-known problem for the time integration of the equations of motion (EOM) is the lack of a singularity-free param...

Derivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but als...

Corrections to the published article

The characterization of the workspace for general spatial 3R chains with skew joint axes is refined by describing the variety of singular displacements as the union of the singular configuration manifolds of orientation type, position type, and attitude type. The surface of attitude singularities is revealed by transferring the singularity sets of...

The characterization of the workspace for general spatial 3R chains with skew joint axes is refined by describing the variety of singular displacements as the union of the singular configuration manifolds of orientation type, position type, and attitude type. The surface of attitude singularities is revealed by transferring the singularity sets of...

The exponential and Cayley maps on SE(3) are the prevailing coordinate maps used in Lie group integration schemes for rigid body and flexible body systems. Such geometric integrators are the Munthe–Kaas and generalized- α schemes, which involve the differential and its directional derivative of the respective coordinate map. Relevant closed form ex...

The inquest of spatial motions of rigid bodies is a classic topic in mechanism science and an ongoing activity that is relevant, amongst others, for planning and real-time control of robotic systems. This document describes the concept for a poster contribution to the RSS workshop Geometry and Topology in Robotics: Learning, Optimization, Planning,...

Hippotherapy, riding a horse in the context of rehabilitation, is a medical treatment that successfully has been employed in various fields, e.g. for improving locomotion performance of patients with movement disorders. Robotic systems enable the application of hippotherapy in clinical environments with additional benefits, like adjustable speed an...

Nowadays, automatized surface treatment via robots is already common in the manufacturing industry and such robotic solutions require accurate and reliable force control for high-quality surfaces. However, no standardized test for the quality assessment of robot force control exists yet. By comparison, the ISO 9283 test is used for the evaluation o...

Robotic manipulators physically interacting with their environment must be able to measure contact forces/torques. The standard approach to this end is attaching force/torque sensors directly at the end-effector (EE). This provides accurate measurements, but at a significant cost. Indirect measurement of the EE-loads by means of torque sensors at t...

The Boltzmann–Hamel (BH) equations are central in the dynamics and control of nonholonomic systems described in terms of quasi-velocities. The rigid body is a classical example of such systems, and it is well-known that the BH-equations are the Newton–Euler (NE) equations when described in terms of rigid body twists as quasi-velocities. It is furth...

Pseudo-omnidirectional vehicles (POV) are equipped with several center steered and driven standard wheels, and exhibit high maneuverability and positioning accuracy. Yet this class of mobile systems is rarely considered. Despite their simple setup, the mathematical modeling is challenging. Moreover all models presented so far suffer from artificial...

Derivatives of equations of motion describing the rigid body dynamics are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time deriva...

The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between mot...

Kinematic redundancy of manipulators is a well-understood topic, and various methods were developed for the redundancy resolution in order to solve the inverse kinematics problem, at least for serial manipulators. An important question, with high practical relevance, is whether the inverse kinematics solution is cyclic, i.e., whether the redundancy...

This paper revisits a three-loop spatial linkage that was proposed in an ARK 2004 paper by Karl Wohlhart (as extension of a two-loop linkage proposed by Eddie Baker in 1980) and later analyzed in an ARK 2006 paper by Diez-Martínez et al. A local analysis shows that this linkage has a finite degree of freedom (DOF) 3 (and is thus overconstrained) wh...

Based on the idea of variable stiffness mechanisms, a variety of such mechanisms is shown in this work. Specifically, 2-DOF parallel kinematic machines equipped with redundant actuators and non-linear springs in the actuated joints are presented and a comparative overview is drawn. Accordingly, a general stiffness formulation in task space of all m...

Dynamic balance eliminates the fluctuating reaction forces and moments induced by high-speed robots that would otherwise cause undesired base vibrations, noise and accuracy loss. Many balancing procedures, such as the addition of counter-rotating inertia wheels, increase the complexity and motor torques. There exist, however, a small set of closed-...

Optimal control in general, and flatness-based control in particular, of robotic arms necessitate to compute the first and second time derivatives of the joint torques/forces required to achieve a desired motion. In view of the required computational efficiency, recursive $O(n)$ -algorithms were proposed to this end. Aiming at compact yet efficie...

The modeling of parallel kinematic machines (PKM) has been a topic of ongoing research since PKM started to gain popularity more than twenty years ago. Due to the modular setup of most PKM, research has been conducted towards modular modeling paradigms. This applies in particular to so-called fully parallel PKM. Recently, a general modeling approac...

The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between mot...

The analysis of human movements rests on a realistic human body model. Deducing model parameters from anthropomorphic data is challenging since these are inherently imprecise. An approach to improve model accuracy is the parameter adaptation based on motion data. 3D motion capture data are already being used for generating the trajectories of a hum...

This paper presents several point-to-point optimization tasks of humanoid arm motions. The focus lies on optimization of elementary arm motions. Several cost functions for optimization tasks are defined. Tasks in respect of time optimal control, minimizing joint loads and maximizing the vertical torque of the torso are presented. The dynamic optima...