This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The generated bitstream is applied to the problem of chaotic path planning, for an autonomous robot or generally an unmanned aerial vehicle (UAV) exploring a given 3D area. The aim is to ensure efficient area coverage, while also maintaining an unpredictable motion. Numerical simulations were performed to evaluate the performance of the path planning strategy, and it is shown that the coverage percentage converges exponentially to 100% as the number of iterations increases. The discrete motion is also adapted to a smooth one through the use of B-Spline curves.
SUMMARYA mobile manipulator system (MMS) consists of a robotic arm mounted on a mobile platform that is used in rescue and relief, space exploration, warehouse automation, etc. As the total system has 14 Degrees of Freedom (DOF), it does not have a closed-form inverse kinematics (IK) solution. A learning-based method is proposed, which uses the forward kinematics data to learn the IK relation for motion of an MMS on a rough terrain, using a one-class support vector machine (SVM) framework. Once trained, the model estimates the joint probability distribution of the MMS configuration and end-effector position. This distribution is used to find the MMS configuration for a given desired end-effector path. Past research using a Kohonen Self organizing map (KSOM) neural network-based open-loop control method has shown that the MMS deviates from its desired path while moving on an uneven terrain due to unknown disturbances such as wheel slip, slide, and terrain deformation. Therefore, a new sequential two-stage SVM-based end-effector path-tracking control scheme is proposed to control the end-effector path. In this scheme, the error in the end-effector path is continuously tracked with the help of a Microsoft Kinect 2.0 (Microsoft Regional Sales, Singapore 119968) and is sent as a feedback to the controller. Once the error reaches a threshold value, the error correction step of the controller gets activated to correct the error until the desired accuracy is reached. The effectiveness of the proposed approach is proved through extensive simulations and experiments conducted on 3D terrain in which it is shown that the end effector can follow the desired path with an average experimental error of around 2 cm between the desired and final corrected path.
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