A practical optimal control approach for two-speed actuators

This paper addresses the closed-loop control of an actuator with both a continuous input variable (motor torque) and a discrete input variable (mode selection). In many applications, robots have to bear large loads while moving slowly and also have to move quickly through the air with almost no load, leading to conflicting requirements for their actuators. An actuator with multiple gear ratios, like in a powertrain, can address this issue by allowing an effective use of power over a wide range of output speed. However, having discrete modes of operation adds complexity to the high-level control and planning. Here a controller for two-speed actuators that automatically select both the best gear ratio and the motor torque is developed. The approach is to: first derive a low-dimensional model, then use dynamic programming to find the best actions for all possible situations, and last use regression analysis to extract simplified global feedback laws. This approach produces simple practical nearly-optimal feedback laws. A controller that globally minimizes a quadratic cost function is derived for a two-speed actuator prototype, global stability is proven and performance is demonstrated experimentally.

[1]  John T. Betts,et al.  Practical Methods for Optimal Control and Estimation Using Nonlinear Programming , 2009 .

[2]  Mohamed Benrejeb,et al.  Hybrid approach for optimal control problem of switched systems , 2010, 2010 IEEE International Conference on Systems, Man and Cybernetics.

[3]  Kyung-Soo Kim,et al.  Finger module design based on dual-mode twisting actuation for explosive ordnance disposal gripper , 2013, IEEE ISR 2013.

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

[5]  Iason Vittorias,et al.  A novel piezohydraulic actuator as artificial muscle in robotic applications , 2015, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[6]  Fumiya Iida,et al.  Linear multi-modal actuation through discrete coupling , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[7]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[8]  Alberto Bemporad,et al.  Dynamic programming for constrained optimal control of discrete-time linear hybrid systems , 2005, Autom..

[9]  M. Gerdts Solving mixed‐integer optimal control problems by branch&bound: a case study from automobile test‐driving with gear shift , 2005 .

[10]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[11]  Shigeo Hirose,et al.  A Study of Design and Control of a Quadruped Walking Vehicle , 1984 .

[12]  H. Harry Asada,et al.  A two-speed actuator for robotics with fast seamless gear shifting , 2015, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[13]  Panos J. Antsaklis,et al.  Optimal control of switched systems based on parameterization of the switching instants , 2004, IEEE Transactions on Automatic Control.