AbstractCable-driven parallel robots are parallel robots where light-weight cables replace rigid bodies to move an end-effector. Their peculiar design allows obtaining large workspaces, high-dynamic handlings, ease of reconfigurability and, in general, low-cost architecture. Knowing the full state variables of a cable robot may be essential to implement advanced control and monitoring strategies and imposes the development of state observers. In this work a general approach to develop nonlinear state observers based on an extended Kalman filter (EKF) is proposed and validated both numerically and experimentally by referring to a cable-suspended parallel robot. The state observer is based on a system model obtained by converting a set of differential algebraic equations into ordinary differential equations through different formulations: the penalty formulation, the Udwadia–Kalaba formulation, and the Udwadia–Kalaba–Phohomsiri formulation, which have been chosen since they can handle the presence of redundant constraints as often happens in cable-driven parallel robots. In the numerical investigation, the EKF is validated simulating encoders heavily affected by quantization errors to demonstrate the filtering capabilities of EKF. In the experimental investigation, a very challenging validation is proposed: only two sensors measuring the rotations of two motors are used to estimate the actual position and velocity of the end-effector. This result cannot be achieved by sole forward kinematics and clearly proves the effectiveness of the proposed observer.

AbstractThe present contribution introduces the design, methods, functionalities, and capabilities of the open-source multibody dynamics code Exudyn, which has been developed since 2019. The code has been designed for rigid and flexible multibody systems, with a focus on performance for multicore desktop processors. It includes script-language-based modeling and it is intended to be used in science and education, but also in industry. The open-source code is available on GitHub and consists of a main C++ core, a rich Python interface including pre- and postprocessing modules in Python, and a collection of rigid and flexible bodies with appropriate joint, load, and sensor functionality. Integrated solvers allow explicit and implicit time integration, static solution, eigenvalue analysis, and optimization. In the paper, the code design, structure, computational core, computational objects, and multibody formulations are addressed. In addition, the computational performance is evaluated with examples of rigid and flexible multibody systems. The results show the significant impact of multithreading especially for small systems, but also for larger models.

AbstractElectrically assisted bicycles lead to a change in the driving characteristics compared to conventional bicycles because of the additionally attached masses of motor and battery. In order to describe the resulting interaction of the electric drive components on the driving characteristics, this paper examines simulations of the driving behavior of bicycles with different positions of battery and motor in open- and closed-loop tests. The integration of human driving behavior by control loops allows the evaluation of driving characteristic under more realistic driving conditions compared to the existing studies of the eigenbehavior. The results are analyzed using characteristic values that describe the system behavior in a suitable way. Furthermore, a design of experiments is performed to classify the influence of the presented research results in relation to other system parameters, such as different types of bicycles and different rider postures.

AbstractDirect methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal solution. While the benefits of structure preserving or geometric methods have been known for decades, their exploration in the context of optimal control problems is a relatively recent field of research. In this work, the discrete adjoint method is derived for variational integrators yielding structure preserving approximations of the dynamics firstly in the ODE case and secondly for the case in which the dynamics is subject to holonomic constraints. The convergence rates are illustrated by numerical examples. Thirdly, the discrete adjoint method is applied to geometrically exact beam dynamics, represented by a holonomically constrained PDE.

AbstractMinimum-lap-time planning (MLTP) problems, which entail finding optimal trajectories for race cars on racetracks, have received significant attention in the recent literature. They are commonly addressed as optimal control problems (OCPs) and are numerically discretized using direct collocation methods. Subsequently, they are solved as nonlinear programs (NLPs). The conventional approach to solving MLTP problems is serial, whereby the resulting NLP is solved all at once. However, for problems characterized by a large number of variables, distributed optimization algorithms, such as the alternating direction method of multipliers (ADMM), may represent a viable option, especially when multicore CPU architectures are available.This study presents a consensus-based ADMM approach tailored to solving MLTP problems through a distributed optimization algorithm. The algorithm partitions the problem into smaller subproblems based on different sectors of a track, distributing them among multiple processors. ADMM is then used to ensure consensus among the distributed computational processes. In particular, here the term “consensus” denotes the requirement for each subproblem to achieve mutual agreement across the junction areas. The paper also outlines specific strategies leveraging domain knowledge to improve the convergence of the distributed algorithm. The ADMM approach is validated against the serial approach, and numerical results are presented for both single-lap and multilap scenarios. In both cases, the ADMM approach proves superior for problem dimensions of 70k+ variables compared to serial methods. In planning scenarios with complex vehicle models on long track horizons, i.e., for problems with 1M+ variables, the efficiency gain of the ADMM approach is substantial, and it becomes the only viable option to maintain computational times within acceptable limits.

AbstractOptical motion capture is an essential tool for the study and analysis of human movement. Currently, most manufacturers of motion-capture systems provide software applications for reconstructing the movement in real time, thus allowing for on-the-fly visualization. The captured kinematics can be later used as input data for a further musculoskeletal analysis. However, in advanced biofeedback applications, the results of said analysis, such as joint torques, ground-reaction forces, muscle efforts, and joint-reaction forces, are also required in real time.In this work, an extended Kalman filter (EKF) previously developed by the authors for real-time, whole-body motion capture and reconstruction is augmented with inverse dynamics and muscle-efforts optimization, enabling the calculation and visualization of the latter, along with joint-reaction forces, while capturing the motion.A modified version of the existing motion-capture algorithm provides the positions, velocities, and accelerations at every time step. Then, the joint torques are calculated by solving the inverse-dynamics problem, using force-plate measurements along with previously estimated body-segment parameters. Once the joint torques are obtained, an optimization problem is solved, in order to obtain the muscle forces that provide said torques while minimizing an objective function. This is achieved by a very efficient quadratic programming algorithm, thoroughly tuned for this specific problem.With this procedure, it is possible to capture and label the optical markers, reconstruct the motion of the model, solve the inverse dynamics, and estimate the individual muscle forces, all while providing real-time visualization of the results.

AbstractThe rapid ageing of the worldwide population raises pressing concerns related to ensuring proper healthcare and quality of life for older adults. A human-like mobile domestic robot, named CHARMIE, is being produced to aid in these situations by performing household chores, thus increasing the autonomy of persons with mobility limitations. The present work provides a valuable contribution to the development of CHARMIE by building a simulation environment that computes the system’s main dynamics. The obtained environment is used to evaluate the quality of the robot’s control system, to perform its structural optimization and to allow a proper selection of actuators. The system is tackled as a kinematic tree that starts on the robot’s base and then splits into three branches at the torso: the left arm, the right arm, and the head. The multibody model solves the forward kinematics and inverse dynamics of the main mechanisms by employing two recursive algorithms centred around the Newton–Euler formulation. A novel, modular, and efficient seven-step methodology was created to implement these two algorithms and program a simulator from start to finish. These seven steps include studying the system’s configuration, converting its properties into software inputs, and computing the phenomena that cannot be automatically addressed by the two recursive formulations. The presented methodology was fully validated by comparing its results to those obtained from a commercial software; the two models produced identical results.