Viability and Feasibility of Constrained Kinematic Control of Manipulators

Recent advances in planning and control of robot manipulators make an increasing use of optimization-based techniques, such as model predictive control. In this framework, ensuring the feasibility of the online optimal control problem is a key issue. In the case of manipulators with bounded joint positions, velocities, and accelerations, feasibility can be guaranteed by limiting the set of admissible velocities and positions to a viable set. However, this results in the imposition of nonlinear optimization constraints. In this paper, we analyze the feasibility of the optimal control problem and we propose a method to construct a viable convex polyhedral that ensures feasibility of the optimal control problem by means of a given number of linear constraints. Experimental and numerical results on an industrial manipulator show the validity of the proposed approach.

[1]  Andrea Del Prete,et al.  Joint Position and Velocity Bounds in Discrete-Time Acceleration/Torque Control of Robot Manipulators , 2018, IEEE Robotics and Automation Letters.

[2]  Andrea Maria Zanchettin,et al.  Reactive Constrained Model Predictive Control for Redundant Mobile Manipulators , 2014, IAS.

[3]  Bengt Lennartson,et al.  Energy and peak-power optimization of time-bounded robot trajectories , 2017, 2017 13th IEEE Conference on Automation Science and Engineering (CASE).

[4]  Zhaoyu Wang,et al.  Global versus Local Optimization in Redundancy Resolution of Robotic Manipulators , 1988, Int. J. Robotics Res..

[5]  François Keith,et al.  Dynamic Whole-Body Motion Generation Under Rigid Contacts and Other Unilateral Constraints , 2013, IEEE Transactions on Robotics.

[6]  Jan Swevers,et al.  Time-Optimal Path Tracking for Robots: A Convex Optimization Approach , 2009, IEEE Transactions on Automatic Control.

[7]  Andrea Maria Zanchettin,et al.  Motion planning for robotic manipulators using robust constrained control , 2017 .

[8]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[9]  Pyung Hun Chang,et al.  Redundancy resolution for dual-arm robots inspired by human asymmetric bimanual action: Formulation and experiments , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[10]  Pierre-Brice Wieber,et al.  Hierarchical quadratic programming: Fast online humanoid-robot motion generation , 2014, Int. J. Robotics Res..

[11]  Antonio Visioli,et al.  Predictive Inverse Kinematics for Redundant Manipulators With Task Scaling and Kinematic Constraints , 2019, IEEE Transactions on Robotics.

[12]  Nikolaos G. Tsagarakis,et al.  OpenSoT: A whole-body control library for the compliant humanoid robot COMAN , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[13]  A. Liegeois,et al.  Automatic supervisory control of the configuration and behavior of multi-body mechanisms , 1977 .

[14]  Fan-Tien Cheng,et al.  Resolving manipulator redundancy under inequality constraints , 1994, IEEE Trans. Robotics Autom..

[15]  Jean-Jacques E. Slotine,et al.  A general framework for managing multiple tasks in highly redundant robotic systems , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[16]  Eiichi Yoshida,et al.  Integrating geometric constraints into reactive leg motion generation , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[17]  Corrado Guarino Lo Bianco,et al.  Nonlinear Variable Structure Filter for the Online Trajectory Scaling , 2009, IEEE Transactions on Industrial Electronics.

[18]  Antonio Visioli,et al.  Predictive Inverse Kinematics for Redundant Manipulators: Evaluation in Re-Planning Scenarios , 2018 .

[19]  Antonella Ferrara,et al.  A robust MPC/ISM hierarchical multi-loop control scheme for robot manipulators , 2013, 52nd IEEE Conference on Decision and Control.

[20]  David E. Orin,et al.  Generation of dynamic humanoid behaviors through task-space control with conic optimization , 2013, 2013 IEEE International Conference on Robotics and Automation.

[21]  Pierre-Brice Wieber,et al.  Kinematic Control of Redundant Manipulators: Generalizing the Task-Priority Framework to Inequality Task , 2011, IEEE Transactions on Robotics.

[22]  Alessandro De Luca,et al.  Discrete-time redundancy resolution at the velocity level with acceleration/torque optimization properties , 2015, Robotics Auton. Syst..

[23]  Anders Robertsson,et al.  Real-time trajectory generation using model predictive control , 2015, 2015 IEEE International Conference on Automation Science and Engineering (CASE).

[24]  M. Buss,et al.  Invariance control in robotic applications: Trajectory supervision and haptic rendering , 2008, 2008 American Control Conference.

[25]  Oussama Khatib,et al.  Control of Redundant Robots Under Hard Joint Constraints: Saturation in the Null Space , 2015, IEEE Transactions on Robotics.

[26]  Vincent Padois,et al.  Generalized hierarchical control , 2015, Autonomous Robots.

[27]  Antonio Visioli,et al.  A Predictive Approach to Redundancy Resolution for Robot Manipulators , 2017 .

[28]  Corrado Guarino Lo Bianco,et al.  Online Trajectory Scaling for Manipulators Subject to High-Order Kinematic and Dynamic Constraints , 2011, IEEE Transactions on Robotics.

[29]  Antonio Visioli,et al.  A global approach to manipulability optimisation for a dual-arm manipulator , 2016, 2016 IEEE 21st International Conference on Emerging Technologies and Factory Automation (ETFA).

[30]  Pyung Hun Chang,et al.  The enhanced compact QP method for redundant manipulators using practical inequality constraints , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).