Real-time trajectory generation for three-times continuous trajectories

A method for generating Cⁿ, n = {1, 2, 3} close to time optimal trajectories, is presented. Therby constraints within the first n+1 derivatives are considered. The trajectory generator is able to perform within a real-time environment. The algorithm makes use of the recursive structure of the problem. The method can be used in the interpretation of hand lever input signals, to generate smooth transition trajectories between the current reference values and the desired target velocity, which then can be used to generate feed forward control inputs.