Abstract: A method for determining a torque for an operation of a robot that includes multiple components, using a model of the robot. Two components of the robot being movable using an actuator relative to one another at a connection point. The model maps parameters for the connection points onto a torque for the respective actuator. The method includes: providing values for the parameters including: a position or an angle a velocity, and an acceleration of the respective actuator; determining a value for the rigid body partial torque, the friction partial torque, and the machine learning partial torque, based on the values of the parameters and the model; determining a value of the torque of the respective actuator based on the values of the partial torques, and providing the value of the torque for the respective actuator for use during the operation, control or regulating of the robot.

Abstract: Methods, apparatus, and computer program products for transactions are provided. In one implementation, a transaction system is provided. The transaction system includes a share allocation engine that allocates for each eligible transaction a portion of a share fee in the form of shares to one or more levels of shareholders. The transaction system also includes a dividend distribution engine that is operable to accumulate dividends on shares and a qualifying event detector. The qualifying event detector is operable to determine if a qualifying event has occurred and if a qualifying event has occurred, allow the redemption of shares in a subsequent transaction.