Cuspidal robots are robots with at least two inverse kinematic solutions that can be connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been studied in the past, but extending the study to six-degree-of-freedom robots can be a challenging problem. Many robots can be modeled as a polynomial map together with a real algebraic set so that the notion of cuspidality can be extended to these data. In this paper we design an algorithm that, on input a polynomial map in n indeterminates, and s polynomials in the same indeterminates describing a real algebraic set of dimension d, decides the cuspidality of the restriction of the map to the real algebraic set under consideration. Moreover, if D and τ are, respectively the maximum degree and the bound on the bit size of the coefficients of the input polynomials, this algorithm runs in time log-linear in τ and polynomial in ((s+d)D)O(n2). It relies on many high-level algorithms in computer algebra which use advanced methods on real algebraic sets and critical loci of polynomial maps. As far as we know, this is the first algorithm that tackles the cuspidality problem from a general point of view.

Cuspidal robots can travel from one inverse kinematic solution (IKS) to another without meeting a singularity. This property can be analyzed by understanding the inverse kinematic model (IKM) as well as the singularities in the joint space and in the workspace. In this article, we revisit the geometrical interpretation of the IKM with conics. The conditions of getting different conics and their implication on singularities are discussed and the observations regarding the nature of the conics are presented. Further, a sufficient condition for a 3R robot to be binary (i.e. with up to 2 IKS) as well as quaternary (i.e. with up to 4 IKS) is put forth by analyzing the geometrical interpretation of the IKM. The possibility to derive a necessary and sufficient condition is presented too.

Cuspidal robots can travel from one inverse kinematic solution to another without meeting a singularity. The name cuspidal was coined based on the existence of a cusp point in the workspace of 3R serial robots. The existence of a cusp point was proved to be a necessary and sufficient condition for orthogonal robots to be cuspidal, but it was not possible to extend this condition to non-orthogonal robots. The goal of this paper is to prove that this condition stands for any generic 3R serial robot. This result would give the designer more flexibility. In the presented work, the geometrical interpretation of the inverse kinematics of 3R robots is revisited and important observations on the nonsingular change of posture are noted. The paper presents a theorem regarding the existence of reduced aspects in any generic 3R serial robot. Based on these observations and on this theorem, we prove that the existence of a cusp point is a necessary and sufficient condition for any 3R generic robot to be cuspidal.

The optimization of parallel kinematic manipulators (PKM) involve several constraints that are difficult to formalize, thus making optimal synthesis problem highly challenging. The presence of passive joint limits as well as the singularities and self-collisions lead to a complicated relation between the input and output parameters. In this article, a novel optimization methodology is proposed by combining a local search, Nelder–Mead algorithm, with global search methodologies such as low discrepancy distribution for faster and more efficient exploration of the optimization space. The effect of the dimension of the optimization problem and the different constraints are discussed to highlight the complexities of closed-loop kinematic chain optimization. The work also presents the approaches used to consider constraints for passive joint boundaries as well as singularities to avoid internal collisions in such mechanisms. The proposed algorithm can also optimize the length of the prismatic actuators and the constraints can be added in modular fashion, allowing to understand the impact of given criteria on the final result. The application of the presented approach is used to optimize two PKMs of different degrees of freedom.

In otolaryngologic surgery, more and more robots are being studied to meet the clinical needs of operating rooms. However, to help design and optimize these robots, the workspace must be precisely defined taking into account patient variability. The aim of this work is to define a geometric atlas of the middle ear and paranasal sinuses for endoscopic robotic applications. Scans of several patients of different ages and sexes were used to determine the average size of these workspaces, which are linked by the similar use of endoscopes in surgery.

The use of an endoscope in otological surgery as compared to using a microscope provides many benefits in terms of visibility and access to the operating region. The disadvantage of using an endoscope is that it has to be handled by the surgeon during the surgery. A novel parallel kinematic mechanism has been proposed recently for manipulating the endoscope during surgery. This paper details the design requirements considered for the optimization of the process, after consulting surgeons with various expertise. The paper further presents the different evaluation strategies that can be used to optimize the design parameters as per the needs of the application. The contribution of the presented work is the implementation of the surgeons’ requirements into an objective function and the optimization of a proposed architecture of a parallel kinematic mechanism suitable for otological surgery.

In otolaryngologic surgery, endoscopy is increasingly used to provide a better view of hard-to-reach areas and to promote minimally invasive surgery. However, the need to manipulate the endoscope limits the surgeon's ability to operate with only one instrument at a time. Currently, several robotic systems are being developed, demonstrating the value of robotic assistance in microsurgery. The aim of this literature review is to present and classify current robotic systems that are used for otological and endonasal applications. For these solutions, an analysis of the functionalities in relation to the surgeon's needs will be carried out to produce a set of specifications for the creation of new robots.

In this paper, a kinematic motion planning algorithm for cooperative spatial payload manipulation is presented. A hierarchical approach is introduced to compute realtime collision-free motion plans for a formation of mobile manipulator robots. Initially, collision-free configurations of a deformable 2-D virtual bounding box are identified, over a planning horizon, to determine a convex workspace for the entire system. Then, 3-D payload configurations whose projections lie within the convex workspace are computed. Finally, a convex decentralized model-predictive controller is formulated to plan collision-free trajectories for the formation of mobile manipulators. Our work facilitates real-time motion planning for the system and is scalable in the number of robots. The algorithm is validated in simulated dynamic environments.

Parallel manipulators are being used extensively to cater to the needs of a multitude of industrial automation applications. Due to its kinematic accuracy and structural stiffness, parallel manipulators have proven considerable advantage over their serial counterparts. In modern applications, humans train, collaborate and interact with the manipulators in order to maximize the productivity and the quality of the final product. The critical factor in this human-robot interaction is safety and the ability of the mechanism to comply with human intentions. It thus becomes a necessity for the manipulator to detect external disturbances and interactions, and be able to react accordingly. In this research, a methodology for sensor-less full body active compliance is proposed on a 6-DOF RSS (Rotary-Spherical-Spherical) parallel manipulator. By using the proposed approach, the manipulator can detect and comply with the external forces on any part of its body without using any explicit force/torque sensor at the joint or the end-effector. This is done by utilizing the estimated joint torque based on the actuator current feedback only. A three-layer cascaded impedance controller for active compliance and reaction to various human interactions are reported. The proposed design and unique methodology for compliance exhibits an effective and inexpensive yet reliable alternative to be used in safe human-robot interactions and force controlled manufacturing applications.

Parallel manipulators are widely used in the industries for several applications. Due to its precision in motion as well as its robustness, parallel manipulators have proved its advantage over serial manipulators. In this paper, a 3DOF parallel manipulator is presented and force control of the manipulator is demonstrated. The proposed manipulator uses a direct drive voice coil arc actuators to achieve compliance required for human-robot interaction or soft mechanical manipulations. Its implementation in the proposed delta manipulator is discussed in the paper. The paper has discussed a unique method of controlling position as well as the force at the end-effector of the delta manipulator. The method used in making the manipulator compliant does not need an explicit force sensor and is convenient to implement. The method is inexpensive and works satisfactorily in a human interactive environment which is demonstrated through experiments discussed in the paper. The proposed design finds its application in robot-assisted assembly, surface finishing, cooperative manipulation, haptics etc.