Description du sujet de thèse

Robot design, motion planning and control require a good understanding and modeling of the kinematic and static behavior of robots. To achieve this, we need to identify the set of singular configurations of the robot under study. This set is generally defined by relations describing surfaces in the space of inputs (actuated joint coordinates) and/or outputs (end-effector pose coordinates). These singularity surfaces provide valuable information on the robot's overall performance. They generate boundaries in the workspace that the robot cannot always cross, particularly external boundaries. They also enable us to check whether the robot is cuspidal, i.e. whether it can change solution without passing through a singularity (Wenger and Chablat [2022]). However, it has recently been shown that a cuspidal robot, if not identified as such, can exhibit erratic behavior when executing certain trajectories (Salunkhe et al. [2024]), which can even be dangerous in the case of a collaborative robot (cobot) (Verheye [2021]). This analysis is all the more important as many of the cobots that have appeared on the market in recent years are cuspidal, even though neither the manufacturer nor the user is aware of it. While cuspidality analysis is now well mastered for robots with up to 3 degrees of freedom (dofs) (Wenger and Chablat [2022]), it remains difficult for robots with 6 dofs, such as commercial cobots (Salunkhe et al. [2024]). This difficulty is due to the dimension of the spaces in which the singularity surfaces are defined, which are of dimension greater than 3.
To make robots less dangerous when interacting with humans, a very promising solution is to use the tensegrity paradigm (Quennouelle and Gosselin [2008]), (Furet and Wenger [2019], Fasquelle et al. [2020, 2021], Muralidharan et al. [2023], Chevallereau et al. [2023], John et al. [2024], Munoz et al. [2024a], Muralidharan et al. [2024], Wenger and Chevallereau [2024], Munoz et al. [2024b]). A tensegrity robot is composed of rigid elements in compression and flexible elements in tension, such as cables and springs. Less complex and easier to control than a continuously deformable robot, a tensegrity robot can be actuated using motorized cables and reels attached to its base, thus reducing moving masses. Moreover, elements subject only to compression can be dimensioned with small cross-sections, contributing to the robot's light weight. Tensegrity robots raise new challenges by adding constraints linked to static equilibrium, which must be verified throughout the workspace. Balance stability must also be guaranteed. In addition, it is often useful to be able to modulate stiffness. For example, good stiffness is desired on precision points. Conversely, it is preferable for the robot to be more compliant when moving between these work points, to facilitate interaction with its environment. The workspace of a tensegrity robot must therefore be calculated by integrating all these constraints, which in turn generate new surfaces that need to be characterized and analyzed.
1/Cuspidal robots:
First, we will look at a family of 6R-type serial robots with an offset at the wrist. This offset is the only difference from the most common industrial robots, which have a spherical wrist. The presence of this offset drastically alters the robot's properties: it has 16 inverse solutions instead of 8, and the singularities are no longer decoupled. Several of these robots have been identified as cupsidal, but no general results have yet been established. The aim is to determine and analyze the singularity surfaces in joint space. This analysis will make it possible to determine the number of singularity-free components in this space. Then, it will be possible to count the number of solutions in each component and conclude on cuspidity. The next step will be to obtain cuspidality rules for other 6R robots with certain simplifications, such as parallel or intersecting axes.
2/Tensegrity robots
Secondly, the candidate will analyze two promising architectures for cobotic use of tensegrity robots studied at LS2N: the “prism” type joint and the “anti-gravity” type joint, for which solutions to the inverse and direct models have not been counted, and whose singularity surfaces have not been studied.


References
*Christine Chevallereau, Philippe Wenger, and Anick Abourachid. A new bio-inspired joint with variable stiffness. In International Workshop on Medical and Service Robots, pages 220–227. Springer, 2023.
*B. Fasquelle, M. Furet, P. Khanna, D. Chablat, C. Chevallereau, and P. Wenger. A bioinspired 3-DOF lightweight manipulator with tensegrity x-joints. In 2020 IEEE International Conference on Robotics and Automation (ICRA), pages 5054–5060. IEEE, 2020.
*B. Fasquelle, P. Khanna, C. Chevallereau, D. Chablat, D. Creusot, S. Jolivet, P. Lemoine, and P. Wenger. Identification and control of a 3-x cable-driven manipulator inspired by the bird neck. Journal of Mechanisms and Robotics, 13(5):1–25, 2021.
*M. Furet and P. Wenger. Kinetostatic analysis and actuation strategy of a planar tensegrity 2-x manipulator. ASME Journal of Mechanisms and Robotics, 11(6):060904, 2019.
*I. John, S. Mohan, and P.Wenger. Kinetostatic analysis of a spatial cable-actuated variable stiffness joint. ASME. J. Mechanisms Robotics, 16(9):091003, September 2024. doi: 10.1115/1.4064254. URL https://doi.org/10.1115/1.4064254.
*V. Muralidharan, P. Wenger, and C. Chevallereau. Design considerations and workspace computationof 2-x and 2-r planar cable-driven tensegrity-inspired manipulators. Mechanism and Machine Theory, 195:104189, 2024.
*Vimalesh Muralidharan, Nicolas Testard, Christine Chevallereau, Anick Abourachid, and Philippe Wenger. Variable stiffness and antagonist actuation for cable-driven manipulators inspired by the bird neck. Journal of Mechanisms and Robotics, 15(3):035002, 2023.
*K. Mu˜noz, M. Porez, and P. Wenger. Kinematic and static analyses of a 3-DOF spatial tensegrity mechanism. In J. Lenarˇciˇc and M. Husty, editors, Advances in Robot Kinematics 2024, volume 31 of Springer Proceedings in Advanced Robotics, page 36. Springer, 2024a.
*K. Mu˜noz, M. Porez, and P. Wenger. Modeling and analysis of a four-leg tensegrity mechanism. Mechanism and Machine Theory, 2025.
C. Quennouelle and C. Gosselin. Stiffness matrix of compliant parallel mechanisms. Advances in Robot Kinematics: Analysis and Design, pages 331–341, 2008.
*Durgesh Haribhau Salunkhe, Tobias Marauli, Andreas Muller, Damien Chablat, and Philippe Wenger. Kinematic issues in 6R cuspidal robots, guidelines for path planning and deciding cuspidality. The International Journal of Robotics Research, September 2024. doi: 10.1177/ ToBeAssigned. URL https://hal.science/hal-04712576.
*Achille Verheye. Why hasn't anyone heard of cuspidal robots?, 2021. URL https://achille0.medium.com/why-has-no-one-heard-of-cuspidal-robots-fa2fa60ffe9b.
*Philippe Wenger and Damien Chablat. A review of cuspidal serial and parallel manipulators. Journal of Mechanisms and Robotics, pages 1–37, September 2022. doi: 10.1115/1.4055677. URL https://hal.science/hal-03809104.
*Philippe Wenger and Christine Chevallereau. A simple revolute joint with coactivation principle. In European Conference on Mechanism Science, pages 174–182. Springer, 2024.

Contexte de travail

The thesis will be carried out at the Laboratoire des Sciences du Numérique de Nantes (LS2N), in the robotics, process and computing department. It is part of the ANR StratMesh collaborative project (ANR-24-CE48-1899). This project, which brings together LS2N and the INRIA centers of Nancy, Paris and Sophia-Antipolis, aims to provide efficient tools for calculating and modeling surfaces in high dimensions using triangulation. The thesis will be supervised by Damien Chablat, Mathieu Porez and Philippe Wenger from LS2N, in collaboration with Guillaume Moroz from INRIA Nancy-Lorraine, a specialist in surface layering

Informations complémentaires

Prerequisites:
- Master's degree in robotics or graduate of an engineering school with a specialization in robotics.
- Good knowledge of geometric modeling and robot kinematics.
- Fluency in solving algebraic equations using computer algebra tools will be appreciated.
- Ability to communicate and promote work
- Autonomy, organizational and reporting skills