Abstract Multibody dynamics comprises methodologies for the design and analysis of mechanical systems, with Kalman filters being the principal state estimation methods. The Kalman filters are generally formulated for unconstrained systems, the dynamics of which are described by ordinary differential equations in state-space models. However, multibody systems are constrained systems, and the commonly used method to describe their dynamics involves using differential algebraic equations (DAEs) comprising differential and algebraic equations. The differential equations also include the Lagrange multipliers. Hence, incorporating multibody systems, described by DAEs into the scheme of Kalman filters, cannot be achieved straightforwardly, which facilitates different strategies being addressed. This study develops a novel method for converting DAEs into a state-space model. A transition model of the time derivatives of Lagrange multipliers and a Lagrange multiplier constraint vector are devised and used in the state and output equations, respectively. The continuous- and discrete-time extended Kalman filters (CEKF and DEKF) are constructed using the proposed state-space model, and state estimations are simulated on the benchmark planar four- and five-bar linkages. Further, a demonstration of system observability is conducted, and sensitivity to the initial state estimates is studied. These tests demonstrate that the proposed state-space model achieves observable systems and that both the CEKF and DEKF, constructed using the proposed state-space model, can estimate the states with a wide range of initial conditions.

Shoulder muscle forces estimated via modelling are typically indirectly validated against measurements of glenohumeral joint reaction forces (GHJ-RF). This validation study benchmarks the outcomes of several muscle recruitment strategies against public GHJ-RF measurements. Public kinematics, electromyography, and GHJ-RF data from a selected male participant executing a 2.4 kg weight shoulder abduction task up to 92° GHJ elevation were obtained. The Delft Shoulder and Elbow Model was scaled to the participant. Muscle recruitment was solved by 1) minimising muscle activations squared (SO), 2) accounting for dynamic muscle properties (CMC) and 3) constraining muscle excitations to corresponding surface electromyography measurements (CEINMS). Moreover, the spectrum of admissible GHJ-RF in the model was determined via Markov-chain Monte Carlo stochastic sampling. The experimental GHJ-RF was compared to the resultant GHJ-RF of the different muscle recruitment strategies as well as the admissible stochastic range. From 21 to 40 degrees of humeral elevation, the experimental measurement of the GHJ-RF was outside the admissible range of the model (21 to 659% of body weight (%BW)). Joint force RMSE was between 21 (SO) and 24%BW (CEINMS). At high elevation angles, CMC (11%BW) and CEINMS (14%BW) performed better than SO (25%BW). A guide has been proposed to best select muscle recruitment strategies. At high elevation angles, CMC and CEINMS were the two most accurate methods in terms of predicted GHJ-RF. SO performed best at low elevation angles. In addition, stochastic muscle sampling highlighted the lack of consistency between the model and experimental data at low elevation angles.

In this paper, a new high-performance and memory-efficient contact and road model is developed. Specifically, the road is modeled as a rectangular structured grid of deformable springs in the vertical direction, thus enabling fast execution. The new road model stands out due to its ability to handle large road scenarios by allocating computer memory dynamically for each spring, resulting in efficient memory utilization. Furthermore, each spring represents a small road patch that entails various information, such as the soil elevation, the soil properties, and the soil compaction, allowing for complicated simulations incorporating spatially varying soil properties and phenomena related to the multi-pass effect. In addition, using the new contact model, complex terrain geometries are handled in a computationally efficient way by approximating locally the irregular road profile with a suitable equivalent plane. For this, two different strategies are proposed, namely the radial basis function (RBF) interpolation method and the 3D enveloping contact model. Finally, the proposed techniques are implemented in Altair MotionSolve, a comprehensive multi-body simulation software for complex mechanical systems. In particular, a single-wheel test bed is initially examined followed by a four-wheeled rover model and the next-generation NATO reference mobility model (NG-NRMM). In all cases, the proposed model is validated by using available experimental data. Lastly, a case involving both wheeled and tracked vehicles is also examined by using a shared road model.

Abstract In this work, a detailed multibody model of an electric kickscooter is presented. The model includes toroidal wheels as well as rear and front suspensions. The equations of motion are derived and linearized along the steady forward motion of the vehicle. Using an efficient linearization approach, suitable for complex multibody systems with holonomic and nonholonomic constraints, allows for obtaining the reduced linearized equations of motion as a function of the geometric, dynamic, wheels’, and suspensions’ parameters. The proposed electric kickscooter multibody model is validated with the stability results of a previously presented electric kickscooter benchmark. Since the resulting eigenvalues are parameterized regarding the design parameters, a detailed linear stability analysis of the system is performed. In particular, the influence on the stability of the toroidal geometry of the wheels, the elliptic cross-section of the toroidal wheels, the rider model, the steering axis inclination angle, the inertia tensor of the front frame, and the rear and front suspensions is analyzed. The model presented, together with the linearized equations of motion obtained in this work, enables a systematic analysis of the stability of these vehicles, which helps design new electric kickscooters with improved vehicle safety conditions and oriented to a wider range of potential users.

Cable-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.

The 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.