Multibody System Dynamics, Robotics and Control

Time-optimal motion planning along specified paths is a well-understood problem in robotics, for which well-established methods exist for some standard effects, such as actuator force limits, maximal path velocity, or sliding friction. This paper describes some extensions of the classical methods which consider, on the one hand side, additional non linear constraints such as sticking friction, acceleration limits at the end-effector, as well power limits for the overall system, and on the other, general paths featuring smooth interpolation of angular acceleration as well as arbitrary multibody systems comprising multiple loops. The methods are illustrated with two applications from robotics and the mining industry.

This paper presents a fast computation method for time-optimal robot state trajectories along specified geometric paths. A main feature of this new algorithm is that joint positions can be generated in realtime. Hence, not only joint velocities and accelerations limits but also constraints on joint jerks and motor torques can be considered. Jerk limits are essential to avoid vibrations due to (not-modeled) gear or structure flexibilities. For the limitation of motor torques a complete dynamic robot model including Coulomb and viscous friction is used. The underlying optimal control problem is found by projecting the problem onto the geometric path. The resulting state vector contains path position, speed and acceleration while path jerk is used as input. From optimal control theory it follows that the path jerk has to be chosen at its boundaries, which can be computed for each state in each step. Continuous state progress is assured via so called test trajectories which are additionally computed in each step. As an example the algorithm is applied to a six-axis industrial robot moving along a straight line in Cartesian space.

The models used in the conceptual phase of the mechatronic design should not be too complicated, yet they should capture the dominant system behaviour. Firstly, the awareness and possibly the avoidance of an overconstrained condition is important. Secondly, the models should reveal the system’s natural frequencies and mode shapes in a relevant frequency range. For the control system synthesis the low frequent behaviour up to the cross-over frequency needs to be known. Furthermore, the closed-loop system can be unstable due to parasitic modes at somewhat higher frequencies.

In this chapter the applicability of a multibody modelling approach based on non-linear finite elements is demonstrated for the mechatronic design of a compliant six DOF manipulator. A kinematic analysis is applied to investigate the exact constrained design of the system. From dynamic models the natural frequencies and mode shapes are predicted and a state-space model is derived that describes the system’s input-output relations. The models have been verified with experimental identification and closed-loop motion experiments. The predicted lowest natural frequencies and closed-loop performance agree sufficiently well with the experimental data.

This contribution deals with the problem of sensors and sensor data fusion for mobile robots localization and position control. For this, the robot internal odometry is first corrected and used for position control. Then, an extended Kalman filter based on the corrected odometry and a novel North Star navigation system is designed in a distributed manner. The estimated information from the extended Kalman filter is feed back to the desired poses for further accelerating and precising the position control process. Finally, after the analysis of data flows and uncertainties, the whole developed scheme is verified by experiments on an omnidirectional mobile robot.

We consider a port-Hamiltonian representation for infinite-dimensional systems described by partial differential equations. Then the control by interconnection method is applied, by using a finite-dimensional controller system interacting via an energy port at the boundary of the infinite-dimensional system. This will be demonstrated by means of a heavy chain system, modelled as a partial differential equation. Furthermore, we sketch the stability proof in the infinite-dimensional setting. To motivate for the presented ideas we recapitulate the well-known concepts for finite-dimensional systems as well, but mainly as a starting point for the discussion of the infinite setting.

Iterative learning control is a popular method for accurate trajectory tracking of systems that repeat the same motion many times. This paper presents a norm-optimal iterative learning control scheme for a fast two-degree-of-freedom parallel robot driven by two pairs of pneumatic muscle actuators. The robot consists of a light-weight closed-chain structure with four moving links connected by revolute joints. The two base joints are active and driven by pairs of pneumatic muscles by means of toothed belt and pulley. The proposed control has a cascade structure. The internal pressure of each pneumatic muscle is controlled by a fast underlying control loop. Hence, the control design for the outer control loop can be simplified by considering these controlled muscle pressures as ideal control inputs. The angles of the active joints as well as the corresponding angular velocities represent the controlled variables of the outer loop. The implemented ILC algorithm takes advantage of actual state information as well as of data from previous trials. Experimental results from an implementation on a test rig show an excellent control performance.

This work presents an overview of a new approach for balance and posture control by regulating simultaneously the center of mass position and trunk orientation of a biped robot. After an unknown external perturbation deviates the robot from a desired posture, the controller computes a wrench (force and torque) required to recover the desired position and orientation, according to a compliance control law. This wrench is distributed to predefined supporting contact points at the feet. The forces at these points are computed via a constrained optimization problem, adopted from the grasping literature, which minimizes the contact forces while including friction restrictions and torque limits at each joint.

Instabilities of artificial joints are prevalent complications in total joint arthroplasty. In order to investigate failure mechanisms like dislocation of total hip replacements or instability of total knee replacements, a novel test approach is introduced by means of a hardware-in-the-loop (HiL) simulation combining the advantages of an experimental with a numerical approach. The HiL simulation is based on a six-axes industrial robot and a musculoskeletal multibody model. Within the multibody model, the anatomical environment of the correspondent joint is represented such that the soft tissue response is considered during an instability event. Hence, the robot loads and moves the real implant components according to the data provided by the multibody model while transferring back the relative displacement of the implant components and the resisting moments recorded. HiL simulations provide a new biomechanical testing tool which enables comparable and reproducible investigations of various joint replacement systems with respect to their instability behaviour under realistic movements and physiological load conditions.

This paper gives an overview of the dynamics and control of the humanoid walking robot Lola. A brief analysis of the robot’s multibody dynamics motivates our approach to biped walking control. After a brief description of the robot Lola we outline the architecture of its hierarchical walking control system. We also present the real-time planning method for center of gravity trajectories and the model-based hybrid position/force control module that acts as a basis for the stabilizing walking controller.

Control schemes for wheeled mobile robots typically assume a specific mobility capability of a drive and implicitly use the drive’s kinematics within its control procedures. This makes it difficult to deal with faults in the drive and to handle drives with diverse geometry and functionality that might even change during operation of a robot. As a consequence, we propose a model-based control scheme that builds upon an automated analysis of a robotic drive and on an on-line deduction of the drive’s kinematics. We achieve this functionality through (1) the introduction of steering-angle independent, generalized variants of the rolling and sliding constraints for wheeled mobile robots and (2) the corresponding reformulation of kinematic analysis. This leads to a computationally efficient algorithm that deduces the (inverse) kinematics of a drive for its mode of operation or failure. Fault tolerant and robust behavior, however, is only one aspect of our control architecture. On-line kinematics analysis enables us to easily handle robots that change in geometry or functionality such as self-configuring modular robot systems and teams of cooperative robots.

Simulations of the behaviour of complex mechatronic systems require optimal simulation parameters for obtaining realistic results. For highly accurate mechatronic simulations, an algorithm for searching the optimal parameters is required. In the field of robotics the identification based on minimization of the residuum with least square methods is state of the art. This chapter describes a special algorithm for automatic parameter identification for mechatronic systems, based on the theory of genetic optimization, which works also in case of multiple local minima of the simulation error distribution. Nominal parameters of a simulated belt drive are identified in time and frequency domain highly accurate. Special treatment of the simulation error in frequency domain leads to reduced identification effort. Finally, the algorithm for automatic parameter identification searches real robot parameters up to high accuracy. The automatic parameter identification algorithm leads to accurate simulation results, even though the measurement contains noise and also time delays.

This paper introduces a real-time multibody simulation approach. Two main sections have been described in depth and include a description of flexible bodies and modeling of a hydraulic system. In flexible bodies, the bodies are modelled using the floating frame of reference formulation. The equation of motion for the body is developed using the principle of virtual work. Penalty method is used when there are constraints in the mechanical system. The hydraulic system is modelled using lumped fluid theory. Two types of components, valves and hydraulic cylinders, are introduced for modelling. A numerical example is developed using two Craig-Bampton modes deformation modes modelled as flexible bodies.

The present contribution intends to promote an alternative form of Lagrange ’ s Equations, which rests upon the notion of momentum. We first present a short derivation of the proposed momentum based version of Lagrange’s Equations. From this derivation it becomes apparent that the derivatives of the kinetic energy with respect to the generalized coordinates must cancel out in the original kinetic energy based version of Lagrange’s Equations, and thus need not to be computed. The presented momentum based formulation of Lagrange’s Equations is valid for deformable bodies, modeled in the framework of the Ritz approximation technique, where rigid-body degrees-of-freedom may be present. After having stated this momentum based version of Lagrange’s Equations, we restrict to plane motions of rigid bodies, and demonstrate our proposed formulation for the case of a rotational degree of freedom, where we present an additional connection to the notion of momentum of the rigid body, particularly to angular momentum. Finally, we present the exemplary application to systems consisting of two rigid bodies, namely the pendulum with a point mass and movable support, and the Sarazin pendulum consisting of a rigid rotating disc and an attached point mass.

In this paper, the application of piezoelectric vibration control in flexible multibody systems is studied and verified. Exemplarily, beam-type structures are considered that are subject to inertial and external forces. The equations of motion for three-dimensional flexible and torsional vibrations are presented considering the influence of piezoelectric actuation strains. In the framework of Bernoulli-Euler beam theory the shape control solution is derived, i.e. the distribution of actuation strains such that the flexible displacements are completely compensated. For the experimental verification, a laboratory model has been developed, in which the theoretical distribution of actuation strains is discretized by piezoelectric patches. A suitable control algorithm is implemented within a dSpace environment. Finally, the results are validated by numerical computations utilizing ABAQUS and HOTINT, and verified by experimental evaluation.

Applications of multibody dynamics or control to human mobility, impact biomechanics, ergonomics or health and medical cases require that reliable models of human body, including all relevant anatomical segments and a representation of the musculoskeletal system, are developed. The system state variables are available either to a control algorithm or to appraise the internal forces or even to evaluate performance indexes associated to the particular task. Here, a biomechanical model of the human body is presented and applied to demonstrate the basic modeling requirements. A strategy for the control of the biomechanical model motion, based on a distributed hierarchical control, is proposed. The biomechanical model is used to study zero momentum maneuvers, such as those of an astronaut in space or of a high-platform diver. Recognizing that the internal driving forces in the human body result from the musculoskeletal system and not from torque actuators, a procedure to evaluate the muscle forces is presented. Muscle activation dynamics models and optimization techniques are part of the proposed methodology. A human locomotion task demonstrate the procedure and to show the relation between muscle forces and the joint torques used in the control model.

Wire Robots have become both a wide research field as well as a promising subject to application projects. The Chair of Mechatronics at the University Duisburg-Essen has been successful in the setup of prototypes in several application fields. Within this paper, two projects taking advantage from the special properties of wire robots are presented: The first project aims at the development of a wind tunnel suspension system. The second project focuses on the realization of a revolutionary storage and retrieval machine for high racks. Using the mechatronic approach of simulation-based development, major aspects of modeling, simulation, design, trajectory planning and practical realization are discussed.