arXiv subjects

Abdul Basit Memon

Publications and source records attributed to Abdul Basit Memon.

4 recordsLinked to original sources

arXiv2026

Analyzing Uncertainty in the Spatial Representation of the Kinematic Bicycle Model

Locating a vehicle and determining its orientation in an uncertain environment is a critical challenge in autonomous vehicle navigation and path planning. To address these challenges, a vehicle estimates its pose while depending on sensor data that offer noisy measurements. These uncertainties in pose quantities are expressed mathematically as a covariance matrix. The real-time computation of the covariance matrix is critical because of the non-linearity involved in the kinematic model. The challenge is thus to evaluate the evolution of the covariance matrix of a vehicle's discretized stochastic kinematics. The purpose of this study is to obtain a near-accurate evolution of the covariance matrix of the rear-wheel bicycle kinematic model under uncertainties in wheel displacement and steering angle. We used Taylor's series to linearize the nonlinear trigonometric functions and provided closed-form expectations of random variables with the required accuracy. Our analytical findings are in good agreement with those obtained from Monte-Carlo simulations. Our contribution is probably the first detailed closed-form presentation of the covariance matrix constituents of the vehicle under evaluation, which were previously reported either incorrectly or incompletely. These findings aid in identifying the potential and constraints of the discretized kinematic model as well as its stochastic analysis. The techniques presented here are useful for the simultaneous localization and odometry self-calibration of certain mobile robots and autonomous vehicles.

cs.RO↗

arXiv2024

Context-aware Mamba-based Reinforcement Learning for social robot navigation

Social robot navigation (SRN) is a relevant problem that involves navigating a pedestrian-rich environment in a socially acceptable manner. It is an essential part of making social robots effective in pedestrian-rich settings. The use cases of such robots could vary from companion robots to warehouse robots to autonomous wheelchairs. In recent years, deep reinforcement learning has been increasingly used in research on social robot navigation. Our work introduces CAMRL (Context-Aware Mamba-based Reinforcement Learning). Mamba is a new deep learning-based State Space Model (SSM) that has achieved results comparable to transformers in sequencing tasks. CAMRL uses Mamba to determine the robot's next action, which maximizes the value of the next state predicted by the neural network, enabling the robot to navigate effectively based on the rewards assigned. We evaluate CAMRL alongside existing solutions (CADRL, LSTM-RL, SARL) using a rigorous testing dataset which involves a variety of densities and environment behaviors based on ORCA and SFM, thus, demonstrating that CAMRL achieves higher success rates, minimizes collisions, and maintains safer distances from pedestrians. This work introduces a new SRN planner, showcasing the potential for deep-state space models for robot navigation.

cs.RO↗

arXiv2014

Maximally persistent connections for the periodic type

This paper considers the optimal control problem of connecting two periodic trajectories with maximal persistence. A maximally persistent trajectory is close to the periodic type in the sense that the norm of the image of this trajectory under the operator defining the periodic type is minimal among all trajectories. A solution is obtained in this paper for the case when the two trajectories have the same period but it turns out to be only piecewise continuous and so an alternate norm is employed to obtain a continuous connection. The case when the two trajectories have different but rational periods is also solved. The problem of connecting periodic trajectories is of interest because of the observation that the operating points of many biological and artificial systems are limit cycles and so there is a need for a unified optimal framework of connections between different operating points. This paper is a first step towards that goal.

eess.SY↗

arXiv2013

Kernel representation approach to persistence of behavior

The optimal control problem of connecting any two trajectories in a behavior B with maximal persistence of that behavior is put forth and a compact solution is obtained for a general class of behaviors. The behavior B is understood in the context of Willems's behavioral theory and its representation is given by the kernel of some operator. In general the solution to the problem will not lie in the same behavior and so a maximally persistent solution is defined as one that will be as close as possible to the behavior. A vast number of behaviors can be treated in this framework such as stationary solutions, limit cycles etc. The problem is linked to the ideas of controllability presented by Willems. It draws its roots from quasi-static transitions in thermodynamics and bears connections to morphing theory. The problem has practical applications in finite time thermodynamics, deployment of tensigrity structures and legged locomotion.

math.OC↗