Three-Dimensional Path Planning of a Climbing Robot Using Mixed Integer Linear Programming

The City-Climber robot is a novel wall-climbing robot developed at The City College of New York that has the capability to move on floors, climb walls, walk on ceilings and transit between them. In this paper, we first develop the dynamic model of the City-Climber robot when it travel on different surfaces, i.e., floors, walls and ceilings, respectively. Then, we present a path planning method for the City-Climber robot using mixed integer linear programming (MILP) in three-dimensional (3-D) building environments that consist of objects with primitive geometrical shapes. MILP provides an optimization framework that can directly incorporate dynamic constraints with logical constraints such as obstacle avoidance and waypoint selection. In order to use MILP to solve the obstacle avoidance problem, we simplify and decouple the robot dynamic model into a linear system by introducing a restricting admissible controller. The decoupled model and obstacle can be rewritten as a linear program with mixed-integer linear constraints that account for the collision avoidance. A key benefit of this approach is that the path optimization can be readily solved using the AMPL and CPLEX optimization software with a MATLAB interface. Simulation results show that the framework of MILP is well suited for path planning and obstacle avoidance problems for the wall-climbing robot in 3-D environments.

[1]  Antonio Bicchi,et al.  Conflict resolution problems for air traffic management systems solved with mixed integer programming , 2002, IEEE Trans. Intell. Transp. Syst..

[2]  Aybars Uur,et al.  Path planning on a cuboid using genetic algorithms , 2008, Inf. Sci..

[3]  Eric Feron,et al.  Multivehicle path planning for nonline‐of‐sight communication , 2006, J. Field Robotics.

[4]  N. Tennant.  On ε and , 1980 .

[5]  R. D'Andrea,et al.  Modeling and control of a multi-agent system using mixed integer linear programming , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[6]  Aybars Ugur.  Path planning on a cuboid using genetic algorithms , 2008, Inf. Sci..

[7]  Y. Kuwata,et al.  Stable trajectory design for highly constrained environments using receding horizon control , 2004, Proceedings of the 2004 American Control Conference.

[8]  Jonathan P. How,et al.  Aircraft trajectory planning with collision avoidance using mixed integer linear programming , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[9]  Katsuhiko Ogata,et al.  Discrete-time control systems , 1987 .

[10]  Jonathan P. How,et al.  Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming , 2002 .

[11]  Raffaello D'Andrea,et al.  Multi-Vehicle Cooperative Control Using Mixed Integer Linear Programming , 2005, ArXiv.

[12]  R. D'Andrea,et al.  Low observability path planning for an unmanned air vehicle using mixed integer linear programming , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[13]  Jizhong Xiao,et al.  City-Climber: A New Generation Wall-Climbing Robots , 2007 .

[14]  Yoshiaki Kuwata,et al.  Three Dimensional Receding Horizon Control for UAVs , 2004 .

[15]  Raffaello D'Andrea,et al.  Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle , 2004, Robotics Auton. Syst..

[16]  B. Moor,et al.  Mixed integer programming for multi-vehicle path planning , 2001, 2001 European Control Conference (ECC).

[17]  Seth Hutchinson,et al.  Coordinating the motions of multiple robots with specified trajectories , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[18]  Lining Sun,et al.  Dynamic Load Effect on Tracked Robot Obstacle Performance , 2007, 2007 IEEE International Conference on Mechatronics.

[19]  Raffaello D'Andrea,et al.  Iterative MILP methods for vehicle-control problems , 2005, IEEE Transactions on Robotics.

[20]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[21]  Jonathan P. How,et al.  Cooperative path planning for multiple UAVs in dynamic and uncertain environments , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[22]  Srinivas Akella,et al.  Coordinating the motions of multiple robots with kinodynamic constraints , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[23]  John N. Tsitsiklis,et al.  Introduction to linear optimization , 1997, Athena scientific optimization and computation series.

[24]  Jizhong Xiao,et al.  Design of Mobile Robots with Wall Climbing Capability , 2005, AIM 2005.