Trajectory representation in design and testing of a surgical robot

For kinetic sizing, the dynamic torque to be provided by a robotic system may be based off of, in part, a maximum acceleration. Rather than trying to extract maximum acceleration from many samples, a relationship of velocity to acceleration from repetitive user inputs relative to a non-surgical target in different situations (e.g., accurate, fast, or balance tracing of the target movement) is established. The velocity for any given situation may be used to estimate the acceleration from the relationship. Rather than using many trajectory samples from many users, a synthetic trajectory may be used. The synthetic trajectory may be fit to user data while maintaining high-coverage properties for direction of movement for any given pose of the robot. Alternatively, a virtual trajectory decoupled from time is used. The virtual trajectory samples the directions at any given pose in a global high-coverage manner, without specifically using a time-dependent sequence of poses.