A Set-Theoretic Approach to Multi-Task Execution and Prioritization

Executing multiple tasks concurrently is important in many robotic applications. Moreover, the prioritization of tasks is essential in applications where safety-critical tasks need to precede application-related objectives, in order to protect both the robot from its surroundings and vice versa. Furthermore, the possibility of switching the priority of tasks during their execution gives the robotic system the flexibility of changing its objectives over time. In this paper, we present an optimization-based task execution and prioritization framework that lends itself to the case of time-varying priorities as well as variable number of tasks. We introduce the concept of extended set-based tasks, encode them using control barrier functions, and execute them by means of a constrained-optimization problem, which can be efficiently solved in an online fashion. Finally, we show the application of the proposed approach to the case of a redundant robotic manipulator.

[1]  J. Corriou.  Chapter 12 – Nonlinear Control , 2017 .

[2]  Paulo Tabuada,et al.  Control Barrier Functions: Theory and Applications , 2019, 2019 18th European Control Conference (ECC).

[3]  Aaron D. Ames,et al.  Sufficient conditions for the Lipschitz continuity of QP-based multi-objective control of humanoid robots , 2013, 52nd IEEE Conference on Decision and Control.

[4]  Magnus Egerstedt,et al.  Boolean Composability of Constraints and Control Synthesis for Multi-Robot Systems via Nonsmooth Control Barrier Functions , 2018, 2018 IEEE Conference on Control Technology and Applications (CCTA).

[5]  Kristin Ytterstad Pettersen,et al.  Set-Based Tasks within the Singularity-Robust Multiple Task-Priority Inverse Kinematics Framework: General Formulation, Stability Analysis, and Experimental Results , 2016, Front. Robot. AI.

[6]  Oussama Khatib,et al.  A unified approach for motion and force control of robot manipulators: The operational space formulation , 1987, IEEE J. Robotics Autom..

[7]  Gianluca Antonelli,et al.  Experiments of Formation Control With Multirobot Systems Using the Null-Space-Based Behavioral Control , 2009, IEEE Transactions on Control Systems Technology.

[8]  Paulo Tabuada,et al.  Control barrier function based quadratic programs with application to adaptive cruise control , 2014, 53rd IEEE Conference on Decision and Control.

[9]  Li Wang,et al.  Multi-objective compositions for collision-free connectivity maintenance in teams of mobile robots , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[10]  Dimos V. Dimarogonas,et al.  Control Barrier Functions for Multi-Agent Systems Under Conflicting Local Signal Temporal Logic Tasks , 2019, IEEE Control Systems Letters.

[11]  Vijay Kumar,et al.  Realization of $r$ -Robust Formations in the Plane Using Control Barrier Functions , 2020, IEEE Control Systems Letters.

[12]  Paolo Robuffo Giordano,et al.  Passive Task-Prioritized Shared-Control Teleoperation with Haptic Guidance , 2019, 2019 International Conference on Robotics and Automation (ICRA).

[13]  Magnus Egerstedt,et al.  Persistification of Robotic Tasks , 2019, IEEE Transactions on Control Systems Technology.

[14]  W. Marsden.  I and J , 2012 .

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

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

[17]  Pierre-Brice Wieber,et al.  Analysis of the Discontinuities in Prioritized Tasks-Space Control Under Discrete Task Scheduling Operations , 2020 .

[18]  Vincent Padois,et al.  Generalized projector for task priority transitions during hierarchical control , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[19]  Aaron D. Ames,et al.  Towards the Unification of Locomotion and Manipulation through Control Lyapunov Functions and Quadratic Programs , 2013, CPSW@CISS.

[20]  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.

[21]  Magnus Egerstedt,et al.  Persistification of Robotic Tasks Using Control Barrier Functions , 2018, IEEE Robotics and Automation Letters.

[22]  Sanghyun Kim,et al.  Continuous Task Transition Approach for Robot Controller Based on Hierarchical Quadratic Programming , 2019, IEEE Robotics and Automation Letters.

[23]  Cristian Secchi,et al.  Safety Barrier Functions for Human-Robot Interaction with Industrial Manipulators , 2019, 2019 18th European Control Conference (ECC).

[24]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

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

[26]  Jochen J. Steil,et al.  Dynamically-consistent Generalized Hierarchical Control , 2019, 2019 International Conference on Robotics and Automation (ICRA).

[27]  Magnus Egerstedt,et al.  Constraint-Driven Coordinated Control of Multi-Robot Systems , 2018, 2019 American Control Conference (ACC).

[28]  Nguyen Dong Yen,et al.  Continuity of the Solution Map in Quadratic Programs under Linear Perturbations , 2006 .

[29]  Gianluca Antonelli,et al.  Safety-Related Tasks Within the Set-Based Task-Priority Inverse Kinematics Framework , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[30]  Eiichi Yoshida,et al.  Real-time smooth task transitions for hierarchical inverse kinematics , 2013, 2013 13th IEEE-RAS International Conference on Humanoid Robots (Humanoids).

[31]  Pierre-Brice Wieber,et al.  Analysis of the discontinuities in prioritized tasks-space control under discreet task scheduling operations , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[32]  Nicolas Mansard,et al.  Intermediate Desired Value Approach for Task Transition of Robots in Kinematic Control , 2012, IEEE Transactions on Robotics.

[33]  Aaron D. Ames,et al.  Safety Barrier Certificates for Collisions-Free Multirobot Systems , 2017, IEEE Transactions on Robotics.

[34]  Siddharth Mayya,et al.  An Optimal Task Allocation Strategy for Heterogeneous Multi-Robot Systems , 2019, 2019 18th European Control Conference (ECC).

[35]  G. Oriolo,et al.  Robotics: Modelling, Planning and Control , 2008 .

[36]  Paulo Tabuada,et al.  Robustness of Control Barrier Functions for Safety Critical Control , 2016, ADHS.

[37]  Nicolas Mansard,et al.  Continuity of Varying-Feature-Set Control Laws , 2009, IEEE Transactions on Automatic Control.

[38]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[39]  Surya P. N. Singh,et al.  V-REP: A versatile and scalable robot simulation framework , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[40]  Jochen J. Steil,et al.  Continuously Shaping Projections and Operational Space Tasks , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[41]  Gianluca Antonelli,et al.  Stability analysis for prioritized closed-loop inverse kinematic algorithms for redundant robotic systems , 2008, 2008 IEEE International Conference on Robotics and Automation.