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Nonlinear Model Predictive Control for Real-Time Optimal Path Tracking & Obstacle Avoidance of Redundant Robotic Manipulators

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Robotic manipulators are increasingly used in many tasks such as industry, medicine and space. In particular, these robots are needed to track a predefined path in such a way that no collision with obstacles in the environment occurs. High degrees of freedom for redundant manipulators lead to an infinity of possible joint positions for the same pose of the end-effector. Hence, for a given end-effector path in the Cartesian space, the robot can track it in many different configurations, among these, the collision free and singular free tracking must be selected. Finding feasible path for joints of redundant manipulators for a given end-effector path is called redundancy resolution .

   

This research presents a Nonlinear Model Predictive Control (NMPC) for redundant robotic manipulators. Using NMPC, the end-effector of robotic manipulator tracks a predefined geometry path in the Cartesian space in such a way that no collision with obstacles in the workspace and no singular configurations for robot occurs.

 

Unlike classical control schemes, in which the control actions are taken based on the past output of the system, the MPC is a model-based optimal controller, which uses predictions of the systems output to calculate the control law. At every sampling time k, based on measurements obtained at time k, the controller predicts the output of the system over prediction horizon NP in future using model of the system and determines the input over the control horizon NC  NP, such that a predefined cost function is minimized.



In this project, using NMPC, the input voltages of DC servomotors of joints are obtained in such a way that the end-effector of a redundant manipulator tracks a given path in the Cartesian space considering obstacles and singularity avoidance.

 

The advantages of proposed method are as follow. The proposed approach:

 

·    is optimal since a cost function is defined in order to fulfil control goals;

·    is online since defined cost function is finite horizon;

·    is efficient for dynamic environments because cost function is optimized in each sampling  

    time so that, changes in environment can be considered;

·    could consider nonlinear dynamic and constraints of robot in optimization process;

·    could implement online system identification for model prediction, yielding adaptive control  

    strategy.




Fuzzy NMPC:


One of the challenges in Nonlinear Model Predictive Control (NMPC) is tuning. NMPC has a set of tuning parameters such as weights in cost function, which can be used for good performance. These parameters are adjusted via a trial and error procedure. In this research, the on-line tuning of the weights in NMPC is performed using the fuzzy logic. The proposed method automatically adjusts the weights in cost function in order to obtain good performance.

 

The NMPC is implemented for path tracking and obstacle avoidance of redundant robotic manipulators. In this case, the proposed fuzzy system uses minimum distance between the manipulator and the obstacle and the rate of change of this distance as the inputs. The outputs of the fuzzy system are the weights Q and in cost function which are responsible for path tracking term and obstacle avoidance term in cost function, respectively.

To design the fuzzy system, a boundary around each obstacle is considered in such a way that the control algorithm does not care about obstacles unless the end-effector or any links of the manipulator enter this boundary region. Parameters of fuzzy systems are tuned in such a way that when the manipulator is outside the obstacle regions, R is equal to zero and when the manipulator is inside this region, R is increased and Q is decreased adaptively.





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