Due to the hands-free, non-invasive nature of electroencephalography (EEG) based control, research into brain-computer interface (BCI) systems has been a topic of interest in robotics applications. BCI systems have been studied in several applications including designing simple prosthesis, wheelchairs and virtual navigation, but its scope has often been constrained by several limiting factors. These factors include the need for lengthy training per each specific action desired, poor accuracy when dealing with multiple potential outputs and differences in brain signal behavior for each participant that make finding patterns that work for all individual test subjects a challenge. This research will focus on a method of controlling a robotic arm and dexterous hand system using a combination of BCI and machine learning to quickly train a model to recognize patterns from raw EEG data from a specific individual. This model will be tailored to that individual, allowing the subject to send a high-level input to initiate an adaptive command. The high-level adaptive command considers not only a broad intention of a desired action through EEG signals, but also sensor inputs and other user inputs to perform a desired action effectively. Research will be presented on a system wide implementation of a prototype of this design. The proposed brain-controlled robot is comprised of several major subsystems including the high level BCI input, a 4-degree of freedom (DOF) robot arm system with microcontroller, a 3-wheel omnidirectional mobile platform, a 9-DOF Brunel robot hand, and a MATLAB interface with an interactive GUI. The system receives inputs from an Xbox Kinect color and depth camera and respective microcontrollers that communicate with each other through serial ports, Bluetooth, and wired connections and with the environment through a force sensor, a Kinect depth sensor, and inputs from a MATLAB GUI and Xbox controller. This thesis research demonstrates the development of this multi degree of freedom integrated mobile robotic arm and gripper system that uses EEG data, Kinect image and depth inputs, and a force sensor to successfully control its operation after being trained using one machine learning session. A case study was performed where a subject was asked to record at least 25 sessions of each BCI command. 25% of the data from each test set was set aside for testing purposes. For a total of four different cases, an accuracy of 80% was reached whereas for five different cases, an accuracy of 76% was obtained. Motion of the robotic arm was simulated in MATLAB and successfully replicated in the robot prototype for grabbing different sized objects.