Vijay Muralidharan

Bio: Vijay Muralidharan is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Nonholonomic system & Inverted pendulum. The author has an hindex of 6, co-authored 15 publications receiving 124 citations. Previous affiliations of Vijay Muralidharan include Luleå University of Technology.

Geometric Controllability and Stabilization of Spherical Robot Dynamics

Abstract: Geometric control of a spherical robot rolling on a horizontal plane with three independent inertia disc actuators is considered in this note. The dynamic model of the spherical robot in the geometric framework is used to establish the strong accessibility and small-time local controllability properties. Smooth stabilizability to an equilibrium fails for the nonholonomic spherical robot. A novel contribution of this note is a smooth, asymptotically stabilizing geometric control law for position and reduced attitude, which corresponds to an equilibrium submanifold of dimension one. From Brockett's condition, this is the best possible dimension of a smoothly stabilized equilibrium submanifold. We also present a novel smooth global tracking controller for tracking position trajectories.

Formation Control and Trajectory Tracking of Nonholonomic Mobile Robots

Abstract: In this brief, we design Lyapunov-based control laws to achieve two multi-objective tasks for a network of open-loop unstable, nonholonomic mobile inverted pendulum (MIP) robots, using a connected undirected graph for inter-agent communication. Using the first protocol, translationally invariant formations are achieved along with the synchronization of attitudes and heading velocities to desired values. Using the second protocol, the robots move into a formation and asymptotically track a trajectory. The control laws are based on the kinematic model of the mobile robot, and control torques for the MIPs are extracted using a two-loop control architecture. Both the protocols guarantee boundedness of the linear heading velocity, which is necessary for the stability of the two-loop control architecture. The proposed control laws are experimentally validated on indigenously built MIP robots.

Position Stabilization and Waypoint Tracking Control of Mobile Inverted Pendulum Robot

Abstract: The mobile inverted pendulum (MIP) is a mechanical system that presents multiple control challenges. In particular, two objectives, namely desired position control and stabilization of the unstable pendulum-like central body, need to be simultaneously met. In this brief, we propose a novel smooth time-invariant controller to achieve the twin objectives. A feature of the controller design is that it readily extends to achieve waypoint tracking, another interesting task for mobile platforms. To validate the theory developed, an MIP has been indigenously designed and fabricated. Extensive experiments on the MIP have been performed. It has been observed that the system accomplishes position stabilization as well as waypoint tracking with negligible error.

Extending interconnection and damping assignment passivity-based control (IDA-PBC) to underactuated mechanical systems with nonholonomic Pfaffian constraints: The mobile inverted pendulum robot

Abstract: In this paper, we extend the interconnection and damping assignment passivity-based control strategy to systems subjected to nonholonomic Pfaffian constraints. The results are applied to stabilize the pitch dynamics of an underactuated mobile inverted pendulum (MIP) robot subjected to nonholonomic constraints arising out of no-slip conditions. A novel feature of this paper is that we reduce the kinetic energy partial differential equations and potential energy partial differential equation to a set of ordinary differential equations, that are explicitly solved.

A Deterministic Attitude Estimation Using a Single Vector Information and Rate Gyros

Abstract: This paper proposes a deterministic estimator for the estimation of the attitude of a rigid body. A deterministic estimator uses a minimal set of information and does not try to minimize a cost function or fit the measurements into a stochastic process. The proposed estimator obtains the attitude estimation utilizing only the properties of the rotational group $SO(3)$ . The information set required by the proposed estimator is a single vector information and rate gyro readings. For systems in which one of the rotational freedom is constrained, the proposed estimator provides an accurate estimate of the reduced attitude. The performance of the algorithm is verified on different experimental testbeds.

Observer-Based Incremental Predictive Control of Networked Multi-Agent Systems With Random Delays and Packet Dropouts

Abstract: This brief addresses the cooperative output tracking control problem for a linear heterogeneous networked multi-agent system with random network-induced delays and packet dropouts in the feedback channel of each agent, which consists of one leader agent and multiple following agents. To compensate for adverse effects of those random communication constraints, an incremental networked predictive control scheme based on state observers is proposed. A necessary and sufficient condition is derived for the stability of the resulting closed-loop system, which is independent of random communication constraints. Experimental results on a networked multi-motor control test rig show the effectiveness and applicability of the proposed scheme, including a feature that zero steady-state output tracking errors can be achieved even for the case with plant-model mismatch.

Energy-Aware Adaptive Attitude Estimation Under External Acceleration for Pedestrian Navigation

Abstract: In this paper, we consider the problem of a rigid body attitude estimation under external acceleration using a small inertial/magnetic sensors module containing a triad of gyroscope, accelerometer, and magnetometer. This paper is focused on two main challenges. The first one concerns the attitude estimation during dynamic cases, in which external acceleration occurs. In order to compensate for such external acceleration, we design a quaternion-based adaptive Kalman filter q-AKF. Precisely, a smart detector is designed to decide whether the body is in static or dynamic case. Then, the covariance matrix of the external acceleration is estimated to tune the filter gain. The second challenge is related to the energy consumption issue of gyroscope. In order to ensure a longer battery life for the inertial measurement units, we study the way to reduce the gyro measurements acquisition by switching on/off the sensor while maintaining an acceptable attitude estimation. The switching policy is based on the designed detector. The efficiency of the proposed scheme is evaluated by means of numerical simulations and experimental tests.