Full-rotation singularity-safe workspace for kinematically redundant parallel robots

This paper introduces and computes a novel type of work-space for kinematically redundant parallel robots that defines the regionin which the end-effector can make full rotations without coming close tosingular configurations; it departs from the traditional full-rotation dex-terous workspace, which considers full rotations without encounteringsingularities but does not take into account the performance problemsresulting from closeness to these locations. Kinematically redundant ar-chitectures have the advantage of being able to be reconfigured withoutchanging the pose of the end-effector, thus being capable of avoidingsingularities and being suitable for applications where high dexterityis required. Knowing the workspace of these robots in which the end-effector is able to complete full, smooth rotations is a key design aspectto improve performance; however, since this singularity-safe workspaceis generally small, or even non-existent, in most parallel manipulators,its characterisation and calculation have not received attention in theliterature. The proposed workspace for kinematically redundant robotsis introduced using a planar parallel architecture as a case study; the for-mulation works by treating the manipulator as two halves, calculatingthe full-rotation workspace of the end-effector for each half whilst ensur-ing singularity conditions are not approached or met, and then findingthe intersection of both regions. The method is demonstrated ontwoexample robot instances, and a numerical analysis is also carried out asa comparison

Kinematically redundant parallel robots for high performance applications

This thesis addresses the development of kinematically redundant parallel robots for high performance applications and methods of kinematic analyses tailored towards them. Parallel robot manipulators are well known to hold various advantages over serial manipulators, including having better speeds, accuracies, and power-to-weight ratios. However, a major disadvantage they have is that they suffer from limited workspaces and rotational capabilities; indeed, it can be argued that this is the main reason serial robots are used more frequently in many industries. This thesis aims to address this major shortcoming of parallel robots, whilst maintaining all of their advantages, by concentrating on the solution of kinematic redundancy. Firstly, an introduction to the topic of kinematically redundant parallel robots for high performance applications is presented and a review of the relevant literature is given. In the second section, a novel kinematically redundant architecture of parallel robot is presented. The kinematic redundancy of the mechanism allows it to achieve full cycle rotations of the end-effector without encountering kinematic singularities, a feat that is not possible for non-redundant systems. The third section addresses the issue with current methods of singularity analyses of parallel robots when applied to kinematically redundant architectures. It is shown that conventional Jacobian-based methods of singularity analysis are unreliable when applied to kinematically redundant architectures. In the fourth section a novel, more robust, method of singularity analysis is presented, which is then used to develop a method of singularity avoidance. The fifth section presents a kinematically redundant architecture that is dynamically balanced, meaning that the shaking forces and moments imposed on the base by the manipulator are nullified. An issue for manipulators moving at high speeds is that shaking forces and moments generated can cause vibration and inhibit the performance of the system. By dynamically balancing the system, the manipulator is able to move at high speeds without experiencing these drawbacks. The aim of this PhD thesis is that the work presented here can provide some of the building blocks for developers of robot manipulators to create high performance parallel robots which exhibit high speed, strength, and dexterity, through the use of kinematic redundancy

Modeling, Control and Estimation of Reconfigurable Cable Driven Parallel Robots

The motivation for this thesis was to develop a cable-driven parallel robot (CDPR) as part of a two-part robotic device for concrete 3D printing. This research addresses specific research questions in this domain, chiefly, to present advantages offered by the addition of kinematic redundancies to CDPRs. Due to the natural actuation redundancy present in a fully constrained CDPR, the addition of internal mobility offers complex challenges in modeling and control that are not often encountered in literature. This work presents a systematic analysis of modeling such kinematic redundancies through the application of reciprocal screw theory (RST) and Lie algebra while further introducing specific challenges and drawbacks presented by cable driven actuators. It further re-contextualizes well-known performance indices such as manipulability, wrench closure quality, and the available wrench set for application with reconfigurable CDPRs. The existence of both internal redundancy and static redundancy in the joint space offers a large subspace of valid solutions that can be condensed through the selection of appropriate objective priorities, constraints or cost functions. Traditional approaches to such redundancy resolution necessitate computationally expensive numerical optimization. The control of both kinematic and actuation redundancies requires cascaded control frameworks that cannot easily be applied towards real-time control. The selected cost functions for numerical optimization of rCDPRs can be globally (and sometimes locally) non-convex. In this work we present two applied examples of redundancy resolution control that are unique to rCDPRs. In the first example, we maximize the directional wrench ability at the end-effector while minimizing the joint torque requirement by utilizing the fitness of the available wrench set as a constraint over wrench feasibility. The second example focuses on directional stiffness maximization at the end-effector through a variable stiffness module (VSM) that partially decouples the tension and stiffness. The VSM introduces an additional degrees of freedom to the system in order to manipulate both reconfigurability and cable stiffness independently. The controllers in the above examples were designed with kinematic models, but most CDPRs are highly dynamic systems which can require challenging feedback control frameworks. An approach to real-time dynamic control was implemented in this thesis by incorporating a learning-based frameworks through deep reinforcement learning. Three approaches to rCDPR training were attempted utilizing model-free TD3 networks. Robustness and safety are critical features for robot development. One of the main causes of robot failure in CDPRs is due to cable breakage. This not only causes dangerous dynamic oscillations in the workspace, but also leads to total robot failure if the controllability (due to lack of cables) is lost. Fortunately, rCDPRs can be utilized towards failure tolerant control for task recovery. The kinematically redundant joints can be utilized to help recover the lost degrees of freedom due to cable failure. This work applies a Multi-Model Adaptive Estimation (MMAE) framework to enable online and automatic objective reprioritization and actuator retasking. The likelihood of cable failure(s) from the estimator informs the mixing of the control inputs from a bank of feedforward controllers. In traditional rigid body robots, safety procedures generally involve a standard emergency stop procedure such as actuator locking. Due to the flexibility of cable links, the dynamic oscillations of the end-effector due to cable failure must be actively dampened. This work incorporates a Linear Quadratic Regulator (LQR) based feedback stabilizer into the failure tolerant control framework that works to stabilize the non-linear system and dampen out these oscillations. This research contributes to a growing, but hitherto niche body of work in reconfigurable cable driven parallel manipulators. Some outcomes of the multiple engineering design, control and estimation challenges addressed in this research warrant further exploration and study that are beyond the scope of this thesis. This thesis concludes with a thorough discussion of the advantages and limitations of the presented work and avenues for further research that may be of interest to continuing scholars in the community

A Kinematic Analysis and Evaluation of Planar Robots Designed From Optimally Fault-Tolerant Jacobians Khaled M. Ben-Gharbia, Student Member, IEEE,

Abstract—It is common practice to design a robot’s kinematics from the desired properties that are locally specified by a manipulator Jacobian. In this work, the desired property is fault tolerance, defined as the postfailure Jacobian possessing the largest possible minimum singular value over all possible locked-joint failures. A mathematical analysis based on the Gram matrix that describes the number of possible planar robot designs for optimally fault-tolerant Jacobians is presented. It is shown that rearranging the columns of the Jacobian or multiplying one or more of the columns of the Jacobian by ±1 will not affect local fault tolerance; however, this will typically result in a very different manipulator. Two examples, one that is optimal to a single joint failure and the second that is optimal to two joint failures, are analyzed. This analysis shows that there is a large variability in the global kinematic properties of these designs, despite being generated from the same Jacobian. It is especially surprising that major differences in global behavior occurs for manipulators that are identical in the working area. Index Terms—Fault-tolerant robots, robot kinematics, redundant robots. I

A Cartesian Space Approach to Teleoperate a Slave Robot with a Kinematically Dissimilar Redundant Manipulator

Due to the inability of humans to interact with certain unstructured environments,telemanipulation of robots have gained immense importance. One of the primary tasks in telemanipulating robots remotely, is the effective manipulation of the slave robot using the master manipulator. Ideally a kinematic replica of the slave manipulator is used as the master to provide a joint-to-joint control to the slave. This research uses the 7-DOF Whole Arm Manipulator© (WAM) as the master manipulator and a 6-DOF Titan as the slave manipulator. Due to the kinematic dissimilarity between the two, a Cartesian space position mapping technique is adapted in which the slave is made to follow the same trajectory as the end effector of the master with respect to its reference frame. The main criterion in undertaking this mapping approach is to provide a convenient region of operation to the human operator. Various methods like pseudo inverse, Jacobian transpose and Damped least squares have been used to perform the inverse kinematics for the Titan. Joint limit avoidance and obstacle avoidance constraints were used to perform the inverse kinematics for the WAM and thereby remove the redundancy. Finally a joint volume limitation constraint (JVLC) was adopted which aims at providing the operator, a comfortable operational space in union with the master manipulator. Each inverse methodfor the Titan was experimentally tested and the best method identified from thesimulation results and the error analysis. Various experiments were also performed for the constrained inverse kinematics for the WAM and results were simulated. RoboWorks© was used for simulation purposes

Combined Admittance Control With Type II Singularity Evasion for Parallel Robots Using Dynamic Movement Primitives

[EN] This article addresses a new way of generating compliant trajectories for control using movement primitives to allow physical human-robot interaction where parallel robots (PRs) are involved. PRs are suitable for tasks requiring precision and performance because of their robust behavior. However, two fundamental issues must be resolved to ensure safe operation: first, the force exerted on the human must be controlled and limited, and second, Type II singularities should be avoided to keep complete control of the robot. We offer a unified solution under the dynamic movement primitives (DMP) framework to tackle both tasks simultaneously. DMPs are used to get an abstract representation for movement generation and are involved in broad areas, such as imitation learning and movement recognition. For force control, we design an admittance controller intrinsically defined within the DMP structure, and subsequently, the Type II singularity evasion layer is added to the system. Both the admittance controller and the evader exploit the dynamic behavior of the DMP and its properties related to invariance and temporal coupling, and the whole system is deployed in a real PR meant for knee rehabilitation. The results show the capability of the system to perform safe rehabilitation exercises.This work was supported in part by the Fondo Europeo de Desarrollo Regional under Grant PID2021-125694OB-I00, in part by the Vicerrectorado de Investigacion de la Universitat Politecnica de Valencia under Grant PAID-11-21, and in part by the Ministerio de Universidades, Gobierno de Espana under Grant FPU18/05105.Escarabajal-Sánchez, RJ.; Pulloquinga-Zapata, J.; Valera Fernández, Á.; Mata Amela, V.; Vallés Miquel, M.; Castillo-García, FJ. (2023). Combined Admittance Control With Type II Singularity Evasion for Parallel Robots Using Dynamic Movement Primitives. IEEE Transactions on Robotics. 39(3):2224-2239. https://doi.org/10.1109/TRO.2023.32381362224223939

Synthèse cinématique d'un octopode parallèle sans surcontrainte avec conditions de singularité simples

Ce mémoire présente l'étude du lieu des singularités de type II pour un mécanisme parallèle cinématiquement redondant à (6+2) degrés de liberté dont l'architecture est préalablement donnée. Cette étude se concentre sur les conditions mathématiques telles que le déterminant de la matrice jacobienne s'annule pour toutes configurations dues à la mobilité interne du mécanisme permise par la redondance cinématique. Pour ce faire, la construction d'une matrice partageant les mêmes conditions de singularité que la matrice jacobienne du mécanisme est présentée. La réécriture du déterminant de cette matrice par une sommation de quatre sous-déterminants pondérée par les paramètres de mobilité interne du mécanisme mène à un système d'équations non linéaires à résoudre pour obtenir le lieu des singularités. Une méthode d'élimination de variables, le résultant des polynômes, est ensuite appliquée de manière récursive à ce système d'équations afin d'en extraire les conditions pouvant le résoudre. Les lieux de singularité sont ensuite analysés suivant deux cas de figure. Le premier se penche sur les configurations spécifiques du mécanisme où l'angle de torsion de la plateforme est nul, et le second se concentre sur le cas général, où cet angle de torsion n'est pas nécessairement nul. Dans le premier cas d'analyse, il est montré que les lieux de singularité se situent à l'extérieur de l'espace atteignable du mécanisme cinématiquement redondant. Dans le second cas d'analyse, il est montré que l'espace en orientation demeure quelque peu affecté par la présence de singularités, bien que leur localisation par des équations mathématiques analytiques simples soit possible. Finalement, une comparaison graphique des espaces atteignables en orientation entre le mécanisme cinématiquement redondant et le mécanisme non redondant standard est effectuée afin de visualiser l'impact de l'ajout de la redondance cinématique sur l'agrandissement de l'espace en orientation.This thesis presents the study of the type II singularity locus of a kinematically redundant(6+2) degree-of-freedom parallel mechanism whose architecture is prescribed. This studyfocuses on the mathematical conditions for which the determinant of the Jacobian matrixvanishes for all configurations of the internal mobility in the mechanism due to its kinematicredundancy. To do so, a matrix that captures the same conditions of singularity as the Jacobian matrix is presented. The expansion of the determinant of the aforementioned matrixinto a weighted sum of four sub-determinants whose weighting factors correspond to theinternal mobility parameters leads to a nonlinear system of equations whose solution yieldsthe locus of singularity. A method of elimination theory, the resultant of polynomials, isapplied afterwards on the system of equations in a recursive manner to extract the mathematical conditions corresponding to the solution. The loci of singularity are then analyzedfollowing two cases. The first case focuses on the specific configurations of the mechanismwhere the torsion angle of the platform is zero, whereas the second case takes into accountthe general configurations, i.e. the configurations in which the torsion angle is not necessarily zero. In the former case of analysis, it is shown that the loci of singularity lie outsideof the reachable orientational workspace of the kinematically redundant mechanism. In thelatter case of analysis, it is presented that the orientational workspace is still somewhat restrained by singularities, yet their localization by simple analytical mathematical equationsis possible. Finally, a graphical comparison of the orientational reachable workspace of thekinematically redundant mechanism and that of the standard non-redundant mechanism isperformed to visualize the impact of the kinematic redundancy on the enhancement of theorientational workspace

Dynamic Active Constraints for Surgical Robots using Vector Field Inequalities

Robotic assistance allows surgeons to perform dexterous and tremor-free procedures, but robotic aid is still underrepresented in procedures with constrained workspaces, such as deep brain neurosurgery and endonasal surgery. In these procedures, surgeons have restricted vision to areas near the surgical tooltips, which increases the risk of unexpected collisions between the shafts of the instruments and their surroundings. In this work, our vector-field-inequalities method is extended to provide dynamic active-constraints to any number of robots and moving objects sharing the same workspace. The method is evaluated with experiments and simulations in which robot tools have to avoid collisions autonomously and in real-time, in a constrained endonasal surgical environment. Simulations show that with our method the combined trajectory error of two robotic systems is optimal. Experiments using a real robotic system show that the method can autonomously prevent collisions between the moving robots themselves and between the robots and the environment. Moreover, the framework is also successfully verified under teleoperation with tool-tissue interactions.Comment: Accepted on T-RO 2019, 19 Page