S-Curve Path Planning Method with Initial Velocity

For the problem of S-curve path planning with initial velocity, firstly, reverse velocity update is performed to obtain the maximum initial velocity allowed for displacement. According to the principle of optimal time, the binary Newton iteration method is used to calculate the periods of variable acceleration and variable deceleration, and the periods are revised based on dynamic constraints. Then the same method is used to calculate the periods of uniform acceleration and deceleration. For the situation that the initial velocity exceeds the maximum initial velocity allowed for displacement and the acceleration reaches acceleration constraint, equation reconstruction is performed to re-establish equations for uniform acceleration and variable deceleration periods to solve. Finally, the uniform velocity period is calculated by a linear equation. After solving the time of each planning segment, the expected velocity and position can be calculated, which achieves closed-loop control of the S-curve with initial velocity. This method can solve boundary situations, such as initial velocity being negative, initial velocity exceeding the maximum initial velocity allowed for displacement and acceleration reaching acceleration constraint. Simulation and experimental results show that this method is simple, efficient, and boundary full coverage, which can meet the control requirements of efficient and smooth in inertial navigation system.