A Fuel-Optimal Landing Guidance and Inverse Kinematics Coupled PID Control Solution for Power-Descent Vertical Landing in Simulation

Yongfeng Lu, Zejian Chen


This article presents a guidance path planning and real-time control solution for power-descent landing of an ovoid-shape vehicle in simulation. Given a vehicle initially in free-fall state at a location in mid-air site, the proposed solution will guide and control it by the thrusters to land it at a target location on the ground. The solution consists of an offline guidance path planning step and a real-time control step. It uses the result of a convexified guidance path planning to tune an Inverse Kinematics coupled PID controller with feedforward routes. In a Bullet Physics [1] based simulation environment, experiments were conducted to show good alignment with guidance, i.e. averaged Root Mean Square Error of position, velocity and attitude-in-quaternion are within,  and  respectively during a divert up to 120 m horizontally and 100 m vertically, against several disturbances including reducing mass, fluctuating center of mass, scheduling uncertainty and simulated wind, while the simulation frame rate is kept at around 60 fps for convenient real-time interaction.


Convex optimization; Inverse kinematics; Path planning; PID; SOCP.

Article Metrics

Abstract view : 237 times
PDF - 51 times

Full Text:



E. Coumans, Bullet physics simulation, ACM SIGGRAPH 2015 Courses, New York, USA, 2015.

B. Acikmese and S. R. Ploen, Convex programming approach to powered descent guidance for mars landing, Journal of Guidance, Control, and Dynamics, 30(5), 2007, 1353-1366.

B. Acıkmese, J. M. Carson and L. Blackmore, Lossless convexification of nonconvex control bound and pointing constraints of the soft landing optimal control problem, IEEE Transactions on Control Systems Technology, 21(6), 2013, 2104-2113.

B. Acikmese, J. Casoliva, J. Carson and L. Blackmore, G-fold: A real-time implementable fuel optimal large divert guidance algorithm for planetary pinpoint landing, Concepts and Approaches for Mars Exploration, 1679, 2012, 4193.

J. Wang, N. Cui and C. Wei, Optimal rocket landing guidance using convex optimization and model predictive control, Journal of Guidance, Control, and Dynamics, 42(5), 2019, 1078-1092.

A. Botelho, M. Martinez, C. Recupero, A. Fabrizi and G. De Zaiacomo, Design of the landing guidance for the retro-propulsive vertical landing of a reusable rocket stage, CEAS Space Journal, 2022, 1-14.

S. Kim, N. Das and R. Bhattacharya, Modeling and optimal control of hybrid UAVs with wind disturbance, 2020, arXiv:2006.11192.

S. -J. Jo, C. -O. Min, D. -W. Lee and K. -R. Cho, Control of powered descent phase for a lunar lander using PID controller, Journal of the Korean Society for Aeronautical & Space Sciences, 39(5), 2011, 408-415.

Z. Hilmi, H. S. Enol and F. G. Uner, Lunar excursion module landing control system design with P, PI and PID controllers, Karadeniz Fen Bilimleri Dergisi, 9(2), 2019, 390-405.

H. J. Ferreau, Model predictive control algorithms for applications with millisecond timescales, PhD Thesis, Department of Electrical Engineering, KU Leuven University, Belgium, 2011.

M. Schwenzer, M. Ay, T. Bergs and D. Abel, Review on model predictive control: an engineering perspective, The International Journal of Advanced Manufacturing Technology, 117(5), 2021, 1327-1349.

I. Sarras, A. Venkatraman, R. Ortega and A. van der Schaft, Partial linearization of mechanical systems with application to observer design, Citeseer, 2008.

S. Skogestad and C. Grimholt, The SIMC method for smooth PID controller tuning, PID Control in the Third Millennium, Springer, 2012, 147-175.

C. Grimholt and S. Skogestad, Optimal PID control of double integrating processes, IFAC-PapersOnLine, 49(7), 2016, 127-132.

D. L. D. Ruscio and C. Dalen, Tuning PD and PID controllers for double integrating plus time delay systems, Modeling, Identification and Control, 38(2), 2017, 95-110.

F. Alizadeh and D. Goldfarb, Second-order cone programming, Mathematical Programming, 95(1), 2003, 3-51.

A. Domahidi, E. Chu and S. Boyd, ECOS: An SOCP solver for embedded systems, 2013 European Control Conference (ECC), Zurich, Switzerland, 2013, 3071-3076.

A. Visioli, A new design for a PID plus feedforward controller, Journal of Process Control, 14(4), 2004, 457-463.

S. Maneewongvatana and D. M. Mount, Analysis of approximate nearest neighbor searching with clustered point sets, 1999, arXiv preprint cs/9901013.

D. Kraft, Algorithm 733: Tomp–fortran modules for optimal control calculations, ACM Transactions on Mathematical Software (TOMS), 20(3), 1994, 262-281.

Student, Probable error of a correlation coefficient, Biometrika, 1908, 302-310.

M. J. Casiano, J. R. Hulka and V. Yang, Liquid-propellant rocket engine throttling: A comprehensive review, Journal of Propulsion and Power, 26(5), 2010, 897-923.

E. Betts and R. Frederick, A historical systems study of liquid rocket engine throttling capabilities, 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Nashville, USA, 2010, 6541.


  • There are currently no refbacks.