Numerical approach of collision avoidance and optimal control on robotic manipulators

Collision-free optimal motion and trajectory planning for robotic manipulators are solved by a method of sequential gradient restoration algorithm. Numerical examples of a two degree-of-freedom (DOF) robotic manipulator are demonstrated to show the excellence of the optimization technique and obstacle avoidance scheme. The obstacle is put on the midway, or even further inward on purpose, of the previous no-obstacle optimal trajectory. For the minimum-time purpose, the trajectory grazes by the obstacle and the minimum-time motion successfully avoids the obstacle. The minimum-time is longer for the obstacle avoidance cases than the one without obstacle. The obstacle avoidance scheme can deal with multiple obstacles in any ellipsoid forms by using artificial potential fields as penalty functions via distance functions. The method is promising in solving collision-free optimal control problems for robotics and can be applied to any DOF robotic manipulators with any performance indices and mobile robots as well. Since this method generates optimum solution based on Pontryagin Extremum Principle, rather than based on assumptions, the results provide a benchmark against which any optimization techniques can be measured

Optimal Reconfiguration of a Parallel Robot for Forward Singularities Avoidance in Rehabilitation Therapies. A Comparison via Different Optimization Methods

[EN] This paper presents an efficient algorithm for the reconfiguration of a parallel kinematic manipulator with four degrees of freedom. The reconfiguration of the parallel manipulator is posed as a nonlinear optimization problem where the design variables correspond to the anchoring points of the limbs of the robot on the fixed platform. The penalty function minimizes the forces applied by the actuators during a specific trajectory. Some constraints are imposed to avoid forward singularities and guarantee the feasibility of the active generalized coordinates for a certain trajectory. The results are compared with different optimization approaches with the aim of avoiding getting trapped into a local minimum and undergoing forward singularities. The comparison covers evolutionary algorithms, heuristics optimizers, multistrategy algorithms, and gradient-based optimizers. The proposed methodology has been successfully tested on an actual parallel robot for different trajectories.This research was funded by the Spanish Ministry of Education, Culture and Sports, grant number DPI2017-84201-R.Llopis-Albert, C.; Valero Chuliá, FJ.; Mata Amela, V.; Pulloquinga-Zapata, J.; Zamora-Ortiz, P.; Escarabajal-Sánchez, RJ. (2020). Optimal Reconfiguration of a Parallel Robot for Forward Singularities Avoidance in Rehabilitation Therapies. A Comparison via Different Optimization Methods. Sustainability. 12(14):1-18. https://doi.org/10.3390/su12145803S1181214Rubio, F., Valero, F., & Llopis-Albert, C. (2019). A review of mobile robots: Concepts, methods, theoretical framework, and applications. International Journal of Advanced Robotic Systems, 16(2), 172988141983959. doi:10.1177/1729881419839596Jamwal, P. K., Xie, S. Q., Hussain, S., & Parsons, J. G. (2014). An Adaptive Wearable Parallel Robot for the Treatment of Ankle Injuries. 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(2019). Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles. Robotics, 8(3), 68. doi:10.3390/robotics8030068Chen, Z., Xu, L., Zhang, W., & Li, Q. (2019). Closed-form dynamic modeling and performance analysis of an over-constrained 2PUR-PSR parallel manipulator with parasitic motions. Nonlinear Dynamics, 96(1), 517-534. doi:10.1007/s11071-019-04803-2Zhang, D., & Wei, B. (2017). Interactions and Optimizations Analysis between Stiffness and Workspace of 3-UPU Robotic Mechanism. Measurement Science Review, 17(2), 83-92. doi:10.1515/msr-2017-0011Wu, G., & Zou, P. (2016). Comparison of 3-DOF asymmetrical spherical parallel manipulators with respect to motion/force transmission and stiffness. Mechanism and Machine Theory, 105, 369-387. doi:10.1016/j.mechmachtheory.2016.07.017Meng, W., Xie, S. Q., Liu, Q., Lu, C. Z., & Ai, Q. (2017). Robust Iterative Feedback Tuning Control of a Compliant Rehabilitation Robot for Repetitive Ankle Training. 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Manipulability in trajectory tracking for constrained redundant manipulators via sequential quadratic programming

Trajectory tracking methods for constrained redundant manipulators are presented in this thesis, where the end-effector of a redundant serial manipulator has to track a desired trajectory while some points on its kinematic chain satisfy one or more constraints. In addition, two manipulability indexes are taken into account in order to optimize the trajectory. The first index is defined in terms of the geometric Jacobian of the manipulator in the constrained configuration. The second index is based on the constrained Jacobian, which maps velocities from joint space to task space, taking into account the holonomic constraints. Three methods for solving the trajectory tracking problem are discussed. The first two, kinematic control (KC) and quadratic programming (QP), are widely discussed in literature. The third, sequential quadratic programming (SQP), is a new approach, unlike KC or QP, has as advantages (despite some shortcomings) not explicitly depend on pseudoinverse Jacobian, derivative from the desired trajectory and linearization of indexes or constraints. A discussion of these three methods is presented in terms of tracking error, constraint violation, singularity distance, among others through experiments performed on a Baxter collaborative robot.Métodos de rastreamento de trajetória para manipuladores redundantes restritos são apresentados nesta tese, onde o efetuador de um manipulador serial redundante tem que rastrear uma trajetória desejada enquanto alguns pontos em sua cadeia cinemática satisfazem uma ou mais restrições. Além disso, dois índices de manipulabilidade são levados em consideração a fim de otimizar a trajetória para evitar singularidades. O primeiro índice é definido em função do jacobiano geométrico do manipulador na configuração restrita. O segundo índice é baseado no Jacobiano restrito, o qual mapeia velocidades no espaço das juntas para a espaço da tarefa, levando em conta as restrições holonômicas. Três métodos para resolver o problema de rastreamento de trajetória são discutidos. Os dois primeiros, controle cinemático e programação quadrática (QP), são amplamente discutidos na literatura. O terceiro, programação quadrática sequencial (SQP), é uma nova abordagem, diferentemente do controle cinemático ou QP, tem como vantagens (apesar de algumas deficiências) não depender explicitamente da pseudo-inversa de jacobianos, derivadas da trajetória desejada e linearização de índices ou restrições. Uma discussão desses três métodos é apresentada em termos de erro de rastreamento, violação da restrição, distância de singularidades, entre outros através de experimentos realizados em um robô colaborativo Baxter

A Motion Planner For Robot Manipulators Based on Support Vector Machines

ABSTRACT Moving a robot between two configurations without making a collision is of high importance in planning problems. Sampling-based planners have gained popularity due to their acceptable performance in practical situations. This body of work introduces the notion of a risk function that is provided using the Support Vector Machine (SVM) algorithm to find safe configurations in a sampled configuration space. A configuration is called safe if it is placed at maximum dis­tance from surrounding obstacle samples. Compared to previous solutions, this function is less sensitive to a selected sampling method and resolution. The proposed function is first used as a repulsive potential field in a local SVM-based planner. Afterwards, a global planner using the notion of the risk function is suggested to address some of the shortcomings of the suggested local planner. The proposed global planner is able to solve a problem with fewer number of milestones and less number of referrals to the collision detection module in comparison to the classical Probabilistic Roadmap Planner (PRM). The two proposed methods are evaluated in both simulated and experimental environments and the results are reported