A system according to at least one embodiment of the present disclosure includes a processor; and at least one inertial sensor having a known physical relationship with a tracked object in a first pose, the at least one inertial sensor providing a measurement indicative of a movement of the tracked object from the first pose to a second pose, wherein the processor determines the second pose of the tracked object based, at least in part, on the measurement provided by the at least one inertial sensor.

A processor-implemented method based on an acceleration sensor and a geomagnetic sensor for determining an angular velocity of an object includes: deriving a state variable and a variance of the state variable based on an error quaternion and converting a quaternion-based rotation matrix into an error quaternion-based rotation matrix; calculating an observation matrix and an output matrix of the Kalman filter based on the error quaternion-based rotation matrix; calculating a gain of the Kalman filter based on the transferred variance of the state variable and the observation matrix of the Kalman filter after transferring the state variable and the variance of the state variable through a discretized transfer matrix; calculating a quaternion-based on a calibrated state variable and an estimated quaternion after calibrating the state variable and the variance of the state variable through the gain of the Kalman filter; and calculating angular velocity based on the quaternion.

A processor-implemented method based on an acceleration sensor and a geomagnetic sensor for determining an angular velocity of an object includes: deriving a state variable and a variance of the state variable based on an error quaternion and converting a quaternion-based rotation matrix into an error quaternion-based rotation matrix; calculating an observation matrix and an output matrix of the Kalman filter based on the error quaternion-based rotation matrix; calculating a gain of the Kalman filter based on the transferred variance of the state variable and the observation matrix of the Kalman filter after transferring the state variable and the variance of the state variable through a discretized transfer matrix; calculating a quaternion-based on a calibrated state variable and an estimated quaternion after calibrating the state variable and the variance of the state variable through the gain of the Kalman filter; and calculating angular velocity based on the quaternion.

A mobile robot and a safety control system therefor. The safety control system includes a first monitoring circuit to movement data of the mobile robot; a second monitoring circuit to monitor whether the mobile robot collides with an obstacle; a third monitoring circuit to monitor whether an obstacle exists within a preset range of the mobile robot; a safety control circuit to generate a first safety instruction based on the movement data, a second safety instruction based on the collision signal, a third safety instruction based on the alarm signal, and a fourth safety instruction based on state information of the safety input device; a servo circuit to receive and execute a corresponding safety instruction; and a main control board to output a drive control signal to the servo circuit, for causing the servo circuit to control a motor of the mobile robot based on the drive control signal.