Transformative Research and Robotics
Kazuhiro Kosuge Distinguished Professor Department of Robotics Tohoku University 2020 IEEE Vice President-elect for Technical Activities IEEE Fellow, JSME Fellow, SICE Fellow, RSJ Fellow, JSAE Fellow My brief history • March 1978 Bachelor of Engineering, Department of Control Engineering, Tokyo Institute of Technology • Marcy 1980 Master of Engineering, Department of Control Engineering, Tokyo Institute of Technology • April 1980 Research staff, Department of Production Engineering Nippondenso (Denso) Corporation • October 1982 Research Associate, Tokyo Institute of Technology • July 1988 Dr. of Engineering, Tokyo Institute of Technology • September 1989 - August 1990 Visiting Research Scientist, Department of Mechanical Engineering, Massachusetts Institute of Technology • September 1990 Associate Professor, Faculty of Engineering, Nagoya University • March 1995 Professor, School of Engineering, Tohoku University • April 1997 Professor, Graduate School of Engineering, Tohoku University • December 2018 Tohoku University Distinguished Professor 略 歴
• 1978年3月 東京工業大学工学部制御工学科卒業 • 1980年3月 東京工業大学大学院理工学研究科修士課程修了(制御工学専攻,工学修士) • 1980年4月 日本電装株式会社(現 株式会社デンソー) • 1982年10月 東京工業大学工学部制御工学科助手(工学部) • 1988年7月 東京工業大学大学院理工学研究科 工学博士(制御工学専攻) • 1989年9月-1990年8月 米国マサチューセッツ工科大学機械工学科客員研究員 (Visiting Research Scientist, Department of Mechanical Engineering, Massachusetts Institute of Technology) • 1990年 9月 名古屋大学 助教授(工学部) • 1995年 3月 東北大学 教授(工学部) • 1997年 4月 東北大学 教授(工学研究科)大学院重点化による配置換 • 2018年12月 東北大学 Distinguished Professor My another history
• Select Fellow, Center for Research and Development Strategy, Japan Science and Technology Agency, FY2005 - FY2011 • Review Board Member, PE7, ERC Advance Grant, 2008, 2010, 2012, 2014, 2019 • Senior Program Officer JSPA • Senior Program Office, Research Center for Science Systems, Japan Society of Promotion of Science, FY2007 - FY2009 • Science Officer, Research Promotion Bureau, Ministry of Education, Culture, Sports, Science and Technology, FY2010 - FY2013 • President, IEEE Robotics and Automation Society, FY2010 - FY2011 • Director & Delegate, Division X, IEEE Board of Directors, FY2015 - FY 2016 • 2020 IEEE Vice President for Technical Activities,FY2020 もう一つの略歴
• 科学技術振興機構, 研究開発戦略センター 特任フェロー,FY2005 - FY2011 • Review Board Member, PE7, FP7,ERC Advance Grant, 2008, 2010, 2012, 2014 • 日本学術振興会 学術システム研究センター 主任研究員, FY2007 - FY2009 • 文部科学省 研究振興局 科学官 FY2010 - FY2013 • President, IEEE Robotics and Automation Society, FY2010 - FY2011 • Director & Delegate, Division X, IEEE Board of Directors, FY2015 - FY 2016 – Member, IEEE Public Visibility Committee, FY2015 - FY2016 – Member, IEEE TAB Nominations and Appointments Committee, FY2015 - FY2016 – Member, IEEE Ad Hoc Committee on Strategic Planning, FY2015, FY2016 • 2020 IEEE Vice President for Technical Activities,FY2020 Outline
• Some of my research in robotics • Robot Systems Integration • Physical Human-Robot Interaction – Human robot collaboration through interaction – Co-worker robot • Universal Manipulation – Issues and visual servoing for program-free robot • Conclusions Impedance Controller Design Based on Virtual Internal Model Cooperation of Humans for Handling an Object
Coordination of dualCoordination arms of both arms Coordination of Manipulators
Single-Master Multi-Slaves System (1989) K. Kosuge, J. Ishikawa, K. Furuta, M. Sakai, “Control of Single-Master Multi-Slave Manipulator Using VIM,” Proceedings of the 1990 IEEE International Conference on Robotics and Automation, 1990, 1172-1177. Coordination of Manipulators
Single-Master Multi-Slaves System (1989) K. Kosuge, J. Ishikawa, K. Furuta, M. Sakai, “Control of Single-Master Multi-Slave Manipulator Using VIM,” Proceedings of the 1990 IEEE International Conference on Robotics and Automation, 1990, 1172-1177. Assembly of Two Parts (1994)
K. Kosuge, H. Yoshida, T. Fukuda, Masaru Sakai, K. Kanitani, K. Hariki, ”Unified Control for Dynamic Cooperative Manipulation”, Proceedings of the 1994 IEEE/RSJ International Workshop on Intelligent Robotics and Systems, 1994, 1042-1047. Assembly of Two Parts (1994)
K. Kosuge, H. Yoshida, T. Fukuda, Masaru Sakai, K. Kanitani, K. Hariki, ”Unified Control for Dynamic Cooperative Manipulation”, Proceedings of the 1994 IEEE/RSJ International Workshop on Intelligent Robotics and Systems, 1994, 1042-1047. Bilateral Feedback of Master-slave Manipulator System
Ordinary bilateral feedback Passivity-based realization of bilateral feedback Segment Assembly System (1996)
Segment Assembly System for Tunnel Shield Machine
K. Kosuge, K. Takeo, D. Taguchi, T. Fukuda, H. Murakami, “Task-Oriented Force Control of Parallel Link Robot for the Assembly of Segments of a Shield Tunnel Excavation System,” IEEE/ASME Transactions on Mechatronics, 1 (3), (1996), 250-258. Parts-mating Theory (2001)
K. Kosuge, M. Shimizu, “Planar Parts-mating Using Structured Compliance,” Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, (2001), 1477-1482. M. Shimizu, K. Kosuge, “An Admittance Design Method for General Spatial Parts Mating,” Proceedings of the 2004 IEEE International Conference on Robotics and Automation, (2004), 3571-3576. Robot System for Dish Washing Machine (2009.3.)
K. Kosuge, Y. Hirata, J. Lee, A. Kawamura, K. Hashimoto, S. Kagami, Y. Hayashi, N. Yokoshima, H. Miyazawa, R. Teranaka, Y. Natsuizaka, K. Sakai, “Development of an Automatic Dishwashing Robot System,” Proceedings of the 2009 International Conference on Mechatronics and Automation, (2009), 43-48. Cooperation of Humans for Handling an Object
Coordination of multiple humans Multiple Mobile Manipulator Coordination (2001)
Y. Kume, Y. Hirata, Z. D. Wang, K. Kosuge, ”Decentralized Control of Multiple Mobile Manipulators Handling a Single Object in Coordination”, Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2002, 2758-2763. Y. Hirata, Y. Kume, Z. D. Wang, K. Kosuge, ”Decentralized Control of Multiple Mobile Manipulators Based on Virtual 3-D Caster Motion for Handling an Object in Cooperation with a Human”, Proceedings of the 2003 IEEE International Conference on Robotics and Automation, 2003, 938-943. Cooperation of Mobile Dual Manipulators (2003)
Y. Hirata, Y. Kume, T. Sawada, Z. D. Wang, K. Kosuge, ”Handling of an Object by Multiple Mobile Manipulators in Coordination based on Caster-like Dynamics”, Proceedings of the 2004 IEEE International Conference on Robotics and Automation, 2004, 807-812. Mechanical Parking Systems
Elevator Parking Systems Convey Parking Systems Shuttle Parking Systems Mechanical Parking Systems
Users are required to position their cars in a narrow space. Mechanical Parking Systems
• A parking system is required to have a caretaker. • Each driver is required to park his/her car in a narrow space precisely, which is not easy for a novice driver. iCART Concept
Intelligent Cooperative Autonomous Robot Transporters iCART (intelligent Cooperative Autonomous Robot Transporters)
M. Endo, K. Hirose, Y. Hirata, K. Kosuge, T. Kanbayashi, M. Oomoto, K. Akune, H. Arai, H. Shinoduka, K. Suzuki, “A Car Transportation System by Multiple Mobile Robots -iCART-”, Proceedings of 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2008, 2795-2801. Demonstration of iCARTII Concept
Koshi Kashiwazaki, Kazuhiro Kosuge, Yasuhisa Hirata, Yusuke Sugahara, Takashi Kanbayashi, Koki Suzuki, Kazunori Murakami and Kenichi Nakamura, “Cooperative Transportation Control in Consideration of not only Internal Force but also External Force Applied to “MRWheel,” Proceedings of the 2012 IEEE International Conference on Robotics and Biomimetics, (2012), 1867-1873. in Germany
https://www.youtube.com/watch?v=Gnypt72F20Q Outline
• Some of my research in robotics • Robot Systems Integration • Physical Human-Robot Interaction – Human robot collaboration through interaction – Co-worker robot • Universal Manipulation – Issues and visual servoing for program-free robot • Conclusions Robotics and Societal Values
• Societal Level Societal Values
• Service Level – Service enablers Services
• Fundamental Technologies Level Foundations
CRDS, JST, 2009, Modified by Kosuge, August, 2011 Societal Values
• For Individuals ★Quality of Life • For Communities ★Industrial Competitiveness – For Families – For Industries – For Local Government – For Nations • For the Globe ★Global Issues
CRDS, JST, 2009, Modified by Kosuge, August, 2011 Challenges and Opportunities in Robotics
Social Value Global Level Community Level Quality of Life
•Government orientedRobotics Service/Application •Environmental Monitoring •Utilities •Medicine •Security Service •Natural Resources Exploration •Retailer/Wholesaler •Therapy •Mobility •Agriculture •Transportation •Daily Life Assist •Shopping and Development •Forestry •Communication •Healthcare •Hobby •Space Exploration •Fishery Services •Service Industries •Rehabilitation •Entertainment •Mining •Deep Undersea and Underground •Medicine •Mental care •Sports •Manufacturing Exploration •Education •Learning •Comfort Life •Construction •Anti-terrorism ・Rescue Operation •Research and •Child care •Watch •Wastes Treatment/ Development •Housekeeping •Communication •Prevention of Infectious Diseases Management
•Cyborg (Cybernetic organism) •Software framework - •Stochasticity in Robotics •Social Concerns Emerging •Performance evaluation and Benchmarking •Functional Safety •Ambient intelligence •Nano-micro Robotics Technology •Autonomous Robots •Human Modeling Foundations Robotics •Teleoperation •Wearable Technology •Robotic Emotion (artificial emotion) •Service Contents Design
•Robot Systems Integration •Robot Kinematics and Dynamics •Human Robot Interaction •Manipulation Fundamental •Real-world Real-time Intelligence •Mobility •Spatio-temporal System Design •Actuation •Sensing and Machine Cognition •Physics-based Control
CRDS, JST, 2009, Modified by Kosuge, August, 2011 Robot Systems Integration Unit Technologies Technical Issues
Required Services
Domain ① Domain ② Domain ③ Applications/Services Elderly Care Agriculture Medicine orientedRobotics Service/Application New New ・・・ Services - Foundations Robotics
Robotics Foundations
Current Robot Function CRDS, JST, 2009, Modified by Kosuge, August, 2011 Design/IdentifyRobot Systems a service/services Integration Unit Technologies necessary for the application as a Technical Issues sustainable business. Required Services
Domain ① Domain ② Domain ③ Applications/Services Elderly Care Agriculture Medicine orientedRobotics Service/Application New New ・・・ Services - Foundations Robotics
Robotics Foundations
Current Robot Function CRDS, JST, 2009, Modified by Kosuge, August, 2011 Robot Systems Integration Design a robotUnit Technologies system architecture for the serviveTechnical/services Issues with necessary unit technologies Required Services
Domain ① Domain ② Domain ③ Applications/Services Elderly Care Agriculture Medicine orientedRobotics Service/Application New New ・・・ Services - Foundations Robotics
Robotics Foundations
Current Robot Function CRDS, JST, 2009, Modified by Kosuge, August, 2011 Robot Systems Integration Unit Technologies Technical Issues
Required Services
Domain ① Domain ② Domain ③ Applications/Services Elderly Care Agriculture Medicine orientedRobotics Service/Application
New New Enhance unit technologies to meet ・・・
Services the requirements for the service/services. - Foundations Robotics
Robotics Foundations
Current Robot Function CRDS, JST, 2009, Modified by Kosuge, August, 2011 Robot Systems Integration Unit Technologies Technical Issues
Required Services
Domain ① Domain ② Domain ③ Applications/Services Elderly Care Agriculture Medicine orientedRobotics Service/Application New New Develop new fundamentals ・・・ necessary forServices the service/services. - Foundations Robotics
Robotics Foundations
Current Robot Function CRDS, JST, 2009, Modified by Kosuge, August, 2011 Robot Systems Integration Unit Technologies Technical Issues
Required Services
Domain ① Domain ② Domain ③ Applications/Services Elderly Care Agriculture Medicine orientedRobotics Service/Application New New ・・・ Services -
Integrate the unit technologies and Foundations Robotics create the robot.
Robotics Foundations
Current Robot Function CRDS, JST, 2009, Modified by Kosuge, August, 2011 Robot Systems Integration Unit Technologies Technical Issues
Required Services
Domain ① Domain ② Domain ③ Applications/Services Elderly Care Agriculture Medicine orientedRobotics Service/Application New New ・・・ Services - Foundations Robotics
Robotics FoundationsEnrich robotics foundations through application-oriented research Current Robot Function CRDS, JST, 2009, Modified by Kosuge, August, 2011 System robotics is a new field of robotics dealing with robot-related issues in real environments. Systems Robotics Several prototypes of real world robots have been designed and developed based on robot technologies developed in our laboratory.
Walking Helper Power Assisted Chair Cycle
Assistive Robotics
Intention Recognition/Transfer
Intelligent Car Transportation Robot iCARTiCARTand ConceptiCART II Intelligent Car Autonomous-Robot- Transporters
Universal Robot Hand uGRIPP with Two-degrees of Freedom Robot Co-worker “PaDY” (in-time Parts/tools Delivery robot) Assembly and Manipulauion by Dual Manipulators
Stable Power Human Robot Integration of Visual and Impedance Servo Augmentation Coordination Mobile Manipulators Human-Robot Interaction Universal Manipulation Multiple Robots Coordination Outline
• Some of my research in robotics • Robot Systems Integration • Physical Human-Robot Interaction – Human robot collaboration through interaction – Co-worker robot • Universal Manipulation – Issues and visual servoing for program-free robot • Conclusions Human Power Augmentation(1993)
Human Power Augmentation [1] K. Kosuge, Y. Fujisawa, T. Fukuda, ”Mechanical System Control with Man-Machine-Environment Interactions”, Proceedings of the 1993 IEEE International Conference on Robotics and Automation, 1993, 239-244. [2] 小菅一弘, 藤沢佳生, 福田敏男, ”環境との相互作用が生じるマン ・ マシン系の制御”, 日本機械学会論文集(C編), 59 (562), 1993, 1751-1756. Human Power Augmentation
Fh
Q 1
M v Fe Dv Kv
Operator Tool Environment
Use of a Tool [1] K. Kosuge, Y. Fujisawa, T. Fukuda, ”Mechanical System Control with Man-Machine-Environment Interactions”, Proceedings of the 1993 IEEE International Conference on Robotics and Automation, 1993, 239-244. [2] 小菅一弘, 藤沢佳生, 福田敏男, ”環境との相互作用が生じるマン ・ マシン系の制御”, 日本機械学会論文集(C編), 59 (562), 1993, 1751-1756. Human Power Augmentation
Fh
Q 1
M v Fe Dv Kv
Mv !x!+ Dv x! + Kv x = QFh - Fe Virtual Tool Dynamics
[1] K. Kosuge, Y. Fujisawa, T. Fukuda, ”Mechanical System Control with Man-Machine-Environment Interactions”, Proceedings of the 1993 IEEE International Conference on Robotics and Automation, 1993, 239-244. [2] 小菅一弘, 藤沢佳生, 福田敏男, ”環境との相互作用が生じるマン ・ マシン系の制御”, 日本機械学会論文集(C編), 59 (562), 1993, 1751-1756. Human Power Augmentation(1993)
Human Power Augmentation [1] K. Kosuge, Y. Fujisawa, T. Fukuda, ”Mechanical System Control with Man-Machine-Environment Interactions”, Proceedings of the 1993 IEEE International Conference on Robotics and Automation, 1993, 239-244. [2] 小菅一弘, 藤沢佳生, 福田敏男, ”環境との相互作用が生じるマン ・ マシン系の制御”, 日本機械学会論文集(C編), 59 (562), 1993, 1751-1756. Robot Helpers
Human-Robot Cooperation (Kosuge, 1993~) Robot Helpers
Robot j
Robot i
Object Human l
Human m Robot k
Passive Dynamics
Stability Issues Robot Helpers
MR Helper (Mobile Robot Helper, 1997~) DR Helpers (Distributed Robot Helpers, 2000)
K. Kosuge, M. Sato, ”Mobile Robot Helper”, [Proceedings of the 2000 IEEE International Y. Hirata, K. Kosuge, ”Distributed Robot Helpers Handling a Single Object in Cooperation with a Human”, Conference on Robotics and Automation (2000) 583-588]. [Proceedings of the 2000 IEEE International Conference on Robotics and Automations (2000) 458-463]. 小菅一弘, 須田理央, 風村典秀, 佐藤学, 角谷啓, ”人と双腕型移動ロボット“MR Helper”による物 平田泰久, 初雁卓郎, 小菅一弘, 淺間一, 嘉悦早人, 川端邦明, ”人間と複数の分散型ロボットヘル 体の協調搬送”, [日本機械学会論文集(C編) 69 (685) (2003) 84-90]. パ-との協調による単一物体の搬送”, [日本機械学会論文集(C編) 68 (668) (2002) 181-188]. Robot Helpers
DR Helpers (Distributed Robot Helpers)
Y. Hirata, Y. Kume, Z. D. Wang, K. Kosuge, ”Decentralized Control of Multiple Mobile Manipulators Based on Virtual 3-D Caster Motion for Handling an Object in Cooperation with a Human”, [Proceedings of the 2003 IEEE International Conference on Robotics and Automation (2003) 938-943]. Lessons Learned
DR Helper
MR Helper Lessons Learned from Robot Helpers
• Some simple tasks, which could not be done by a human/humans, could be done with a robot helper(s).
• General tasks could not be done easily even with the assistive robot system(s), because the robot does not know how to collaborate with the human. Lessons Learned from Robot Helpers
• In order to collaborate with the user, the robot has to know – the task, – its user’s intention, – how the user wants to be assisted – … Dance Partner Robot
To develop a mechanism for closer human-robot coordination/interaction Dance Partner Robot “PBDR”
PBDR as a Research Platform for Human-robot interaction (2005) Sensory Data Used for Estimation
Reference Data Transition
Dance Figure “A” Dance Figure “B”
Teffective Force/Moment
Time Time series data include uncertainty such as time-lag and variation because a dancer cannot always apply the same force/moment for each figure transition.
T. Takeda, K. Kosuge, Y. Hirata, ”HMM-based Dance Step Estimation for Dance Partner Robot -MS DanceR-”, [Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (2005) 1602-1607]. Sensory Data Used for Estimation
HMM-based “Figure Estimator”
Reference Data Transition
Dance Figure “A” Dance Figure “B”
Teffective Force/Moment
Time
T. Takeda, K. Kosuge, Y. Hirata, ”HMM-based Dance Step Estimation for Dance Partner Robot -MS DanceR-”, [Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (2005) 1602-1607]. Dance Partner Robot “PBDR”
PBDR as a Research Platform for Human-robot interaction(2005) Aichi Expo (March 24 ~ September 25, 2005)
PBDR as a Research Platform for Physical Human-Robot Interaction (2005) Outline
• Some of my research in robotics • Robot Systems Integration • Physical Human-Robot Interaction – Human robot collaboration through interaction – Co-worker robot • Universal Manipulation – Issues and visual servoing for program-free robot • Conclusions Automobile Assembly Line
• A sequence of the tasks, necessary parts/tools for each task, and when and where each task is performed are scheduled a priori for each type of the car produced. • During the work, the worker needs to return to a work bench with parts and tools several times to pick up necessary parts/tools. Automobile Assembly Line
• If a robot could provide the worker with necessary parts and tools when he/she needs them, the worker could concentrate on the assembly tasks.
[1] 衣川潤,川合雄太,菅原雄介,小菅一弘,“組立作業支援パートナロボットPaDY(第1報,コンセプトモデルの開発とその制御)”,日本機械学会論文集,C 編, 77(783), (2011), 4204-4217 [2] J. Kinugawa, Y. Kawaai, Y. Sugahara and K. Kosuge, “PaDY : Human-Friendly/Cooperative Working Support Robot for Production Site”, The 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems Proceedings, (2010), 5472-5479. Co-worker Robot “PaDY”
• PaDY is a robot which delivers necessary parts and tools to a worker when he/she needs them. – to reduce the worker’s load – to improve efficiency of the work PaDY – to prevent mistakes of the work – etc.
[1] 衣川潤,川合雄太,菅原雄介,小菅一弘,“組立作業支援パートナロボットPaDY (第1報,コンセプトモデルの開発とその制御)”,[日本機械学会論文集,C 編,77(783),(2011),4204-4217]
[2] J. Kinugawa, Y. Kawaai, Y. Sugahara and K. Kosuge, “PaDY : Human- Friendly/Cooperative Working Support Robot for Production Site”, [2010 IEEE/RSJ International Conference on Intelligent Robots and Systems Proceedings,(2010),5472- 5479]. “in-time Parts/tools Delivery to You” robot Co-worker Robot “PaDY”
• In order to deliver parts/tools to a place, where the worker needs them, when the worker needs them without disturbing the worker’s work, the robot needs to know
– the task, – its user’s intention, and – how the user want to be assisted “in-time Parts/tools Delivery to You” robot The First Prototype of PaDY (P1)
Size:(W)1370×(D)590×(H)1035[mm] Link Mechanism :Horizontal Articulated Robot Maximum Reach:2.0 [m](1st Link Length:1168[mm], 2nd Link Length:982[mm]) Weight of Working Parts:11.5[kg] Maximum Load:3 [kg] Range of Movement: 1st Joint: 200[deg], 2nd Joint: 360[deg] Actuator:1st Joint & 2nd Joint:DC Servo Motor 80[W], 3rd Joint: DC Servo Motor 15[W] Evaluation Experiment
+:LRF1 ×:LRF2
Measured data
Effect of PaDY The worker’s motion necessary for picking parts/tools has been reduced. The worker could finish his tasks earlier than the work schedule. Estimated result Architecture of the Adaptive Motion Planner Support
Desired trajectory Online Trajectory Generator Sensor Target position Robot
Target position Offset position Process determiner sheet
Initial model
Estimated Update current task Worker Motion Predictor Worker’s position Predicted moving • Estimates working trajectory position • Predicts moving trajectory Worker Motion Predictor[6] ü Worker’s movement is modeled by Gaussian mixture distribution using incremental learning algorithm. ü Worker motion predictor estimates worker’s current task and predicts worker’s motion trajectory.
Order Task ② ② Generate 1 Task1 ③ Initialization ③ 2 Task2 ① 3 Task3 ④ ④ ① 4 Task4 Process Chart Initial Worker Model
Sample Data
Prediction&Update Worker
Motion Prediction Model Update
[6] J. Kinugawa, A. Kanazawa, S. Arai, and K. Kosuge, “Adaptive task scheduling for an assembly task coworker robot based on incremental learning of human motion patterns,” IEEE Robot. Autom. Lett., vol. 2, no. 2, pp. 856–863, Apr. 2017. Online Trajectory Generator
Target position Target time 1st Term: Minimizing delivery time delay Predicted The endpoint of the manipulator arrives at the scheduled worker trajectory target position at the target time. Robot trajectory Time scale 2nd Term: Collision avoidance The manipulator avoids colliding with the predicted worker position at each time step. Worker Robot 3rd Term: Velocity / Acceleration limitation The manipulator moves under the preset velocity and acceleration limitations.
The trajectory that satisfies the above three requirements is calculated by minimizing the following cost function. �: Current time Target time ( ) ( ) ( ) ( ) � : � = � � + � � + � � , � �: Robot state 1st Term 2nd Term 3rd Term Cost Function for Uncertainty-based Collision Avoidance
Mean of The variance of the predicted trajectory tends Trajectory to Increase during irregular movement. Variance of Worker Trajectory We consider predicted variance (uncertainty) in the cost function of the collision avoidance.
Mahalanobis distance Predicted trajectory in a regular case Predicted trajectory in an irregular case � �, �, � = � − � � (� − �)