محاﺳﺒﻪ ﻇﺮﻓﯿﺖ ﺣﻤﻞ ﺑﺎر رﺑﺎت ﻣﺘﺤﺮك ﮐﺸﻨﺪه-ﭘﯿﺮو ﺑﺎ در ﻧﻈﺮ ﮔﺮﻓﺘﻦ روش ﮐﻨﺘﺮل ﺑﻬﯿﻨﻪ ﻏﯿﺮﺧﻄﯽ

Load carrying capacity of tractor-trailer mobile robots considering the nonlinear optimal control

رﺑﺎت ﮐﺸﻨﺪه-ﭘﯿﺮو ﺑﻪ ﻋﻨﻮان ﻣﺠﻤﻮﻋﻪ رﺑﺎت ﻣﺘﺤﺮك ﺑﺮاي ﺣﻤﻞ ﺑﺎر ﻣﻮرد ﮐﺎرﺑﺮد ﻗﺮار ﻣﯽﮔﯿﺮد. ﻟﺬا ﻇﺮﻓﯿﺖ ﺣﻤﻞ ﺑﺎر آن از اﻫﻤﯿﺖ وﯾﮋهاي ﺑﺮﺧﻮردار ﺑﻮده و ﺗﺎﮐﻨﻮن ﻣﻮرد ﺗﻮﺟﻪ ﻗﺮار ﻧﮕﺮﻓﺘﻪاﺳﺖ. در اﯾﻦ ﻣﻘﺎﻟﻪ، ﻣﺤﺎﺳﺒﻪ ﻇﺮﻓﯿﺖ ﺣﻤﻞ ﺑﺎر رﺑﺎت ﻣﺘﺤﺮك ﮐﺸﻨﺪه-ﭘﯿﺮو ﺑﺎ اﺳﺘﻔﺎده از روش ﮐﻨﺘﺮل ﺑﻬﯿﻨﻪ ﻏﯿﺮﺧﻄﯽ ﻣﻮرد ﺑﺮرﺳﯽ ﻗﺮار ﻣﯽﮔﯿﺮد. درﺣﺮﮐﺖ ﻧﻘﻄﻪ ﺑﻪ ﻧﻘﻄﻪ رﺑﺎت ﮐﺸﻨﺪه- ﭘﯿﺮو، ﯾﮏ اﻟﮕﻮرﯾﺘﻢ ﭘﯿﺸﺮﻓﺘﻪ ﺑﺮ ﻣﺒﻨﺎي ﺣﻞ ﻏﯿﺮﻣﺴﺘﻘﯿﻢ ﻣﺴﺌﻠﻪ ﮐﻨﺘﺮل ﺑﻬﯿﻨﻪ ﻏﯿﺮﺧﻄﯽ و ﺑﻪ ﻣﻨﻈﻮر ﻣﺤﺎﺳﺒﻪ ﻇﺮﻓﯿﺖ ﺣﻤﻞ ﺑﺎر رﺑﺎت ﻣﺘﺤﺮك ﮐﺸﻨﺪه-ﭘﯿﺮو اراﺋﻪ ﻣﯽﮔﺮدد. ﻓﺮﻣﻮل ﺑﻨﺪي ﮐﻨﺘﺮل ﺑﻬﯿﻨﻪ ﺑﺎ در ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﻣﻌﺎدﻻت دﯾﻨﺎﻣﯿﮏ ﻏﯿﺮﺧﻄﯽ رﺑﺎت ﻣﺘﺤﺮك ﮐﺸﻨﺪه-ﭘﯿﺮو و ﺑﺎ در ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﻗﯿﻮد ﻏﯿﺮﻫﻮﻟﻮﻧﻮﻣﯿﮏ ﺑﻪﻋﻨﻮان ﻗﯿﻮد ﻣﺴﺌﻠﻪ اﻧﺠﺎم ﻣﯽﺷﻮد. ﺳﭙﺲ ﺑﺎ ﺑﯿﺎن ﯾﮏ اﻟﮕﻮرﯾﺘﻢ ﺗﮑﺮاري ﭘﯿﺸﺮﻓﺘﻪ، ﺑﺎر ﻗﺎﺑﻞﺣﻤﻞ رﺑﺎت ﭘﯿﺮو ﺑﻪ ﺗﺪرﯾﺞ اﻓﺰاﯾﺶ ﯾﺎﻓﺘﻪ و در ﻫﺮ ﻣﺮﺣﻠﻪ ﺷﺮاﯾﻂ ﺑﻬﯿﻨﮕﯽ ﻣﺴﯿﺮ ﺑﻪ ﻋﻨﻮان ﻣﺠﻤﻮﻋﻪ ﻣﻌﺎدﻻت دﯾﻔﺮاﻧﺴﯿﻞ ﮐﻮﭘﻠﻪ ﻏﯿﺮﺧﻄﯽ در ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪه و ﺣﻞ ﻣﻌﺎدﻻت اﻧﺠﺎم ﻣﯽﺷﻮد. ﻇﺮﻓﯿﺖ ﺣﻤﻞ ﺑﺎر ﻣﺠﻤﻮﻋﻪ رﺑﺎت ﮐﺸﻨﺪه-ﭘﯿﺮو در ﭘﺎﯾﺎن اﻟﮕﻮرﯾﺘﻢ ﺑﺎ در ﻧﻈﺮ ﮔﺮﻓﺘﻦ اﺷﺒﺎع ﮔﺸﺘﺎور ﻣﺤﺮك ﻫﺎي ﮐﺸﻨﺪه در ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﻣﯽﺷﻮد. ﻟﺬا ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ روش ﭘﯿﺸﻨﻬﺎدي، ﺷﺒﯿﻪ ﺳﺎزي ﺣﺮﮐﺖ ﻧﻘﻄﻪ ﺑﻪ ﻧﻘﻄﻪ رﺑﺎت ﻣﺘﺤﺮك ﮐﺸﻨﺪه-ﭘﯿﺮو اﻧﺠﺎم ﺷﺪه و ﻇﺮﻓﯿﺖ ﺣﻤﻞ ﺑﺎر ﻣﺤﺎﺳﺒﻪ ﻣﯽﺷﻮد. ﻧﺘﺎﯾﺞ ﻧﺸﺎﻧﻪ ﮐﺎراﯾﯽ اﻟﮕﻮرﯾﺘﻢ ﭘﯿﺸﻨﻬﺎدي ﺑﻪ ﻣﻨﻈﻮر ﻣﺤﺎﺳﺒﻪ ﻇﺮﻓﯿﺖ ﺣﻤﻞ ﺑﺎر رﺑﺎت ﮐﺸﻨﺪه-ﭘﯿﺮو را ﺑﻮده و ﻗﺎﺑﻞ ﮐﺎرﺑﺮد در ﻣﺄﻣﻮرﯾﺖﻫﺎي ﻣﺨﺘﻠﻒ اﯾﻦ رﺑﺎت اﺳﺖ.

Tractor-trailer robot is a kind of mobile robots used to carrey heavy loads. So, load carrying capacity of such robots is an appealing subject which has not been considered up to now. In this article, load carrying capacity of the tractor-trailer mobile robots is investigated using the nonlinear optimal control theory. In point-to-point motion of the tractor-trailer robot, an advanced algorithm based on the indirect solution of the nonlinear optimal control is presented to calculate load carrying capacity of the tractor-trailer robot. Formulation of the optimal control is performed by considering the nonlinear dynamic and nonholonomic equations of the robot as constraints of the problem. Then, by presentation of an advanced iterative algorithm, load of the robot is gradually increased and in each step, optimal conditions are considered as a set of coupled nonlinear differential equation and solved. Load carrying capacity of the tractor-trailer robot is calculated at the final step of the algorithm with consideration of saturation of actuators. Then, the simulation of the tractor-trailer point-to-point motion is performed and the load carrying capacity obtained. The results demonstrate the capability of the proposed algorithm to calculate the load carrying capacity of the tractor-trailer robots and can be applicable for various missions.