The numerical simulation of robot dynamics is widely diffused in research, industrial and education contexts. It can support the design of new devices from the very beginning, as well as the validation and comparison of different actuation and control systems. Simulations can also be employed to efficiently generate data for learning-based approaches. A comprehensive review of the available simulators for robotic systems has been recently presented in (Collins et al., 2021). As underlined by Tselegkaridis and Sapounidis (2021), simulators constitute also useful and accessible resources for teachers and educators. Eminent examples of software tools for simulating robots include the Robotics Toolbox available in MATLAB and Python (Corke, 2017; Corke and Haviland, 2021), Gazebo (Koenig and Howard, 2004; Qian et al., 2014), that is integrated in the ROS framework, and SOFA (Allard et al., 2007), designed for soft robots.

When it comes to the particular problem of simulating robotic grasping and manipulation, an effective software simulation environment should allow to model the used gripper, the grasped object, the environment, and their interactions. GraspIt! (Miller and Allen, 2004), OpenGRASP (Ulbrich et al., 2011), and SynGrasp (Malvezzi et al., 2015), are some of the few available simulators expressly designed for simulating grasping systems. All of them allow to define simulation environments including different hand and object models, but only SynGrasp has been explicitly designed for analysing underactuated and compliant grasps and is implemented in MATLAB. In robotic systems, the structural and mechanical behaviour is strictly related to actuation, sensing and control aspects, therefore a holistic approach is needed to properly design and analyse them. MATLAB has the advantage of being a widely used and powerful environment that allows managing all these aspects in an effective way, without requiring extremely advanced programming and modeling skills.

This paper introduces a method to conduct the multibody simulation of grasping systems in a rather intuitive and user-friendly manner, exploiting widespread software tools like MATLAB™ and Simulink™. Building upon the SynGrasp Toolbox, in which hand and object models can easily be defined, we implemented a new toolbox of functions which connect SynGrasp to Simscape™ Multibody™ (MathWorks, Inc., Natick, Massachusetts, United States) through the programmatic creation of Simulink models. In this way, SynGrasp is enriched with the possibility of performing dynamic simulations, and the Simscape simulation outcomes can be seamlessly processed with the SynGrasp functions for grasp analysis. The proposed approach is illustrated in Figure 1.

The multibody simulation of mechanical systems is widely used in mechanical engineering for solving the mechanism’s kinematic and dynamic problems. Applications range from mechanical components (Logozzo and Valigi, 2019), to mechanisms (Valigi et al., 2020a) and robots (Achilli et al., 2021a; Zhu et al., 2022). The multibody model of a mechanical system is composed of rigid and deformable bodies, interconnected by means of kinematic pairs. Each body can undergo large translational and rotational displacements. The nonlinear analysis of mechanical systems can be performed by simulations considering dynamic loading conditions. Multibody simulators can also model the flexibility of bodies either by considering rigid bodies with lumped constraints, stiffness and damping to reproduce the deformability, or by means of models resulting from FEM (Finite Element Method) analyses (Shabana, 2003). These features can be particularly useful to simulate soft grippers and manipulators (Malvezzi et al., 2018, 2019; Pozzi et al., 2018; Achilli et al., 2020, 2021b; Valigi et al., 2020b).

Multibody simulation tools often offer the possibility of parametric modelling and the influence of the defined parameters on system dynamics can be investigated. This feature is particularly important in the first stages of product design, in which different solutions are investigated until the required performance is reached. In the successive phases of the development, parametric analysis is also important to study the effects of uncertainties and tolerances. Adams from MSC ¹ is one of the first and probably most famous commercial multibody dynamics simulation softwares, widely used in the study of the dynamics of mechanisms. Among open tools adopted in research contexts, Open Dynamics Engine ² is a very powerful and useful tool that allows creating, testing, and executing high-performance rigid body dynamics. OpenSim ³ , instead, is a free software that is widely used in research and rehabilitation centers for modeling and simulating human movement. MBDyn ⁴ is another free simulation software for multibody dynamics, originally developed for aerospace applications. Another free multibody dynamics simulation software that is used both in research and industrial contexts is FreeDyn ⁵ . It is also worth to observe that multibody simulation is a specific package of more general CAE (Computer Aided Engineering) software, as for instance Ansys ⁶ and Comsol ⁷ , or CAD systems like SolidWorks ⁸ .

In this paper, we adopted Simscape Multibody as it is fully integrated within the MATLAB framework and is thus easy to use in conjunction with the SynGrasp Toolbox. Simscape is also rather versatile, allowing the creation of models both in a programmatic way, and by manually assembling blocks. Notwithstanding Simscape Multibody is still less exploited than other simulation environments, also due to its more recent development, examples of robot modeling with Simscape have already been presented, including parallel (Olaya et al., 2017; Noskievič and Walica, 2020), industrial (Udai et al., 2011; Ahn, 2014; Le Ngoc and Nguyen, 2020), aerial (De Simone et al., 2017), legged (Eldirdiry and Zaier, 2018; Aldair et al., 2020), mobile (Khnissi et al., 2019; Siwek et al., 2019), and surgical (Taghizadegan et al., 2016) robots.

The paper is organized as follows. The main components and features of the proposed simulation framework are presented in Section 2. Results of grasp simulations conducted with the newly developed functions are reported in Section 3 and discussed in Section 4. Lastly, the current limitations and envisaged future developments of the toolbox are summarized in Section 5.

The basic elements of the presented framework are the SynGrasp toolbox (Malvezzi et al., 2015), Simscape Multibody, and the MATLAB Programmatic Model Editing functions. The latter allow to seamlessly connect the quasi-static model of a grasp defined in SynGrasp to its corresponding multibody dynamic model in Simscape. The presented framework is depicted in Figure 1 and described in the following, starting from its fundamental components.

The presented framework was tested in two sets of simulations: 1) grasps of objects with different shapes, and 2) grasps of objects made of different materials.

In all the simulated grasps, the hand was closed over the object using the actuation system detailed in Section 2.2.3.2, and contacts were detected with the strategy described in Section 2.2.3.1. Objects with primitive shapes (sphere, cylinder, cuboid), as well as object models from the YCB Dataset (Calli et al., 2015) were considered. The effect of gravity was deactivated, to show the working principles of the proposed contact detection and actuation strategies without external loads.

For the simulations, an explicit continuous fixed-step solver was chosen. Different solvers of this type are available in Simulink, according to the used numerical integration technique. As the order of the integration technique increases, also the computational complexity grows. We adopted the Ode3 solver, which computes the model state using the Bogacki-Shampine formula integration technique to evaluate state derivatives (Hosea and Shampine, 1994). Among the integration algorithms available in Simulink, we selected a fixed-step one also to simplify the post-processing phase and the analysis of the results (e.g. analysis in the frequency domain). The simulations described in this section were conducted with MATLAB R2021b version on a Laptop with Windows 10, Intel^R Core™ i7-10750H CPU @2.60GHz, and 16 GB RAM.

To increase the accuracy of the simulation, the model requires to use a step size that is as low as possible. The balance between solver order and step size can only be obtained through iterative trials, to achieve accurate results with a low computational burden. Furthermore, to simulate the grasp with generic objects, the contact model requires a high number of steps to avoid conditions in which the solution diverges. Through numerous tests, the value 10⁻⁵ s was identified as a suitable step size, that gives accurate solutions in a reasonable amount of time, and with several different objects.

In the next sections the results obtained with a four fingered gripper having the structure shown in Figure 5 are described. However, the conducted simulations can be easily performed with other types of hands.

In this paper, we introduced a numerical tool for the simulation of robotic grasping using Simulink and Simscape Multibody. The tool is based on SynGrasp, a previously developed MATLAB toolbox allowing purely kinematics or quasi-static analyses. The library of functions and blocks developed in this work adds a fundamental module enabling dynamics simulations. The Simscape Multibody model of a robotic hand can be defined in a straightforward way from SynGrasp models thanks to a series of functions based on programmatic model editing. In this way, even users with limited experience with the Simscape Multibody environment can build robotic hand models and run dynamics simulations. More expert users can improve hand models, for example importing realistic CAD representations of links and structural components, or introducing specific mechanical transmission systems, or completing the model with advanced hand control systems. Grasped objects can be selected among a series of primitive geometric shapes, or can be defined by means of their 3D CAD representation. Contact detection and contact force evaluation are defined by means of a specific block.

The developed library is presented and its features are demonstrated through a set of simulations performed using a multifingered gripper interacting with different objects. In the presented simulations, to better highlight the basic system characteristics, the effect of gravity was not considered. In particular, contact point detection was analysed, since it represents the most challenging part of the simulation, in terms of numerical complexity and in terms of result stability and reliability. In the first set of simulations, grasps with different objects were simulated, whereas in the second set we investigated grasping of objects with the same shapes but different inertial properties. The obtained results were coherent with the expected system behaviour in all the simulated cases.

Future developments of this work are manifold. To make the simulation more realistic, we will introduce the gravity, and the contact detection between the links of the hand themselves. In addition, we will study how to simulate the simultaneous grasping of multiple objects, and we will introduce the environment in the simulations. In this way, grasping strategies exploiting environmental constraints (Bimbo et al., 2019; Pozzi et al., 2020) could be tested. A deeper investigation on contact modeling and detection will also be conducted. As it is implemented now, the contact detection only allows retrieving the phalanx in which the contact was detected, and not the exact contact point on the phalanx surface. For this, it would be necessary to explicitly build and use a contact mesh. In addition, other contact models will be considered and possibly compared, depending on the type of simulated interactions and tasks (Skrinjar et al., 2018).

We will also consider the inclusion of blocks evaluating, during the simulation, specific grasp properties (e.g., grasp robustness, manipulability indices, grasp quality measures, etc.). Since the toolbox is capable of performing numerical dynamic simulations, it is particularly suitable to model and simulate soft robotic hands (Pozzi et al., 2018). The dynamic equations governing the motion of soft bodies are highly nonlinear and in most cases cannot be solved analytically in a closed form. For this reason, one must resort to the numerical solution of the resulting dynamic equations. We also plan to implement the complete simulation of the hand-arm system in grasping and manipulation tasks, possibly introducing dual-arm systems capable of executing complex bimanual tasks.