Research projects

By leveraging optimal control techniques and addressing the unique challenges posed by each system, this research aims to theoretically contribute to the field of robotics and control. Along these lines, to deal with these constraints, our research objectives are focussed on optimal control strategies for three distinct robotic systems: an Autonomous Underwater Vehicle (AUV), a WheeledInverted Pendulum (WIP), and a Spherical Mobile Robot (SMR).

Objective 1: 

• The first system analyzed in this research is the AUV due to its unique constraints and the presence of external dissipative forces.

•  In this research, we examined both three-DoF and six-DoF AUV slender shaped AUV model depicted in Figure 2 to account for kinematic constraints, underactuation, and the effects of external disturbances. 

Objective 2:

• To overcome the Euler angle singularity associated with attitude representation in the coordinate setting formulated in objective 1, a Lie group optimal control problem formulation for a stabilization objective is addressed for a 6 DoF AUV named Hybrid Propulsion Underwater Remote Vehicle (HPURV).

• The necessary optimality conditions and Hamiltonian equations for a trade-off control objective are derived for a 6 DoF HPURV system using a PMP approach based on left-trivialization of Hamiltonian approach.

Objective 3:

• The third objective is centered around a WIP (Wheeled Inverted Pendulum) system, which represents a mixed-constraint system featuring both nonholonomic and holonomic constraints arising due to pure rolling motion and yaw moments respectively. Furthermore, it is an underactuated system since there are noactuators directly attached to the pendulum body.

• An optimal motion planning problem with static obstacle avoidance  is addressed using PMP. In this setting, an optimal motion planning problem algorithm incorporating obstacle constraints into the Hamiltonian is developed, ensuring collision-free paths through adaptive obstacle parameter tuning.

•  Furthermore, we also attempted a tracking control objective using PMP principles for the WIP system aimed at minimum pitch angle deviation of intermediate pendulum body and reduced control effort.

Objective 4:

• In this objective, we dealt with a rolling robot, SMR (Spherical Mobile Robot) with internal actuation having mechanical (nonholonomic) constraint. This system is particularly significant because it is nonlinear and has nonholonomic constraints. 

• It has inherent rolling constraints, that is, rolling without slipping and it translates solely due to rotation. This puts constraints at both velocity and position levels. 

• Mathematically, its configuration space exhibits a non-Lie group structure. Unlike many conventional robotic systems whose configuration spaces forms Lie group structures, the SMR, where the sphere is restricted to roll on a horizontal plane, has its configuration space which is not a Lie group.

• This poses challenges in exploiting the algebraic and geometric properties of the Lie groups.

•  The procedure of left trivialization cannot be directly employed here and hence we solved this  optimal control problem using variational approach.

Systems and Tools: Hiwonder Raspberry Pi 5 Robot Car MentorPi M1 Mecanum-wheel Chassis RO, MATLAB, Python, Gazebo-ROS.

• Designed a finite-time feedback control law for stabilization, trajectory tracking, and navigation in humped obstacle scenarios. 

• The control strategy was implemented in Gazebo-ROS and integrated with a hardware-in-the-loop simulation framework. 

Systems and Tools : Fields2Cover project, MATLAB, Python, Motion planning.

• Developing path planning algorithms for Agrobot parallel swath tracking. 

• Several control case studies considering the field-specific requirements are accommodated. 

Tools used: MATLAB, Gazebo-ROS, Python

• Developing vision-based precise servo tracking control strategy to make a quadrotor land on a dynamic target like a moving ship.

• Adaptive learning mechanism to deal with parametric uncertainties internal and external to the system.

• Comprehensive stability proof showing asymptotic stability of system states and parameter convergence.

• Designed generalized predictor strategy in a cascade control architecture and implemented it for a Continuous-stirred tank reactor control application.

• Considered a nonlinear jacketed CSTR model with the objective of maintaining the temperature and concentration of the reactor within constrained limits.

• Experimental validation of the proposed generalized control strategy on a mechanical system: Unstable Inverted pendulum.

Tools used: MATLAB, Classifier, machine learning algorithms

• A two-class BCI manipulated through imagination of left hand, right hand movements is implemented, inducing different spatial patterns of Event-Related Desynchronization (ERD) on mu rhythms over the sensory-motor cortex. 

• We made use of various machine learning techniques to implement the algorithm. 

• The optimized parameters and classifiers can be utilized for online control. 

• This paradigm facilitated two directional movement controls which could be easily applied to help the motion-disabled to operate a wheelchair which may be extended as a future scope of this work.