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Survey Paper

Model predictive control of legged and humanoid robots: models and algorithms

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Pages 298-315 | Received 14 Jun 2022, Accepted 03 Jan 2023, Published online: 09 Feb 2023

References

  • Murphy MP, Saunders A, Moreira C, et al. The LittleDog robot. Int J Rob Res. 2011;30(2):145–149.
  • Semini C, Tsagarakis NG, Guglielmino E, et al. Design of HyQ – a hydraulically and electrically actuated quadruped robot. Proc Inst Mech Eng I J Syst Control Eng. 2011;225(6):831–849.
  • Hutter M, Gehring C, Jud D, et al. ANYmal – a highly mobile and dynamic quadrupedal robot. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). 2016. p. 38–44.
  • Bledt G, Powell MJ, Katz B, et al. MIT cheetah 3: design and control of a robust, dynamic quadruped robot. In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). 2018. p. 2245–2252.
  • Katz B, Carlo JD, Kim S. Mini Cheetah: a platform for pushing the limits of dynamic quadruped control. In: International Conference on Robotics and Automation. 2019. p. 6295–6301.
  • Hirukawa H, Kanehiro F, Kaneko K, et al. Humanoid robotics platforms developed in HRP. Rob Auton Syst. 2004;48(4):165–175. Humanoids 2003.
  • Kaneko K, Harada K, Kanehiro F, et al. Humanoid robot HRP-3. In: 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems. 2008. p. 2471–2478.
  • Kaneko K, Kanehiro F, Morisawa M, et al. Humanoid robot HRP-4 – humanoid robotics platform with lightweight and slim body. In: 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems. 2011. p. 4400–4407.
  • Englsberger J, Werner A, Ott C, et al. Overview of the torque-controlled humanoid robot TORO. In: 2014 IEEE-RAS International Conference on Humanoid Robots. 2014. p. 916–923.
  • Feng S, Whitman E, Xinjilefu X, et al. Optimization based full body control for the atlas robot. In: 2014 IEEE-RAS International Conference on Humanoid Robots. 2014. p. 120–127.
  • Stasse O, Flayols T, Budhiraja R, et al. TALOS: a new humanoid research platform targeted for industrial applications. In: 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids). 2017. p. 689–695.
  • Kanemoto Y, Yoshiike T, Muromachi M, et al. Compact and high performance torque-controlled actuators and its implementation to disaster response robot. In: 2018 IEEE International Conference on Robotics and Automation (ICRA). 2018. p. 4057–4063.
  • Gong Y, Hartley R, Da X, et al. Feedback control of a Cassie bipedal robot: walking, standing, and riding a segway. In: 2019 American Control Conference (ACC). 2019. p. 4559–4566.
  • 6th workshop on legged robots; 2022. Available from: https://leggedrobots.org/lrws_2022/index.html
  • Nishiwaki K, Kagami S, Kuniyoshi Y, et al. Online generation of humanoid walking motion based on a fast generation method of motion pattern that follows desired ZMP. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2002. p. 2684–2689.
  • Kajita S, Kanehiro F, Kaneko K, et al. Biped walking pattern generation by using preview control of zero-moment point. In: IEEE International Conference on Robotics and Automation. Vol. 2, 2003. p. 1620–1626.
  • Nishiwaki K, Kagami S. High frequency walking pattern generation based on preview control of ZMP. In: IEEE International Conference on Robotics and Automation. 2006. p. 2667–2672.
  • Urata J, Nshiwaki K, Nakanishi Y, et al. Online decision of foot placement using singular LQ preview regulation. In: IEEE-RAS International Conference on Humanoid Robots. 2011. p. 13–18.
  • Erez T, Lowrey K, Tassa Y, et al. An integrated system for real-time model predictive control of humanoid robots. In: IEEE-RAS International Conference on Humanoid Robots. 2013. p. 292–299.
  • Feng S, Xinjilefu X, Huang W, et al. 3D walking based on online optimization. In: IEEE-RAS International Conference on Humanoid Robots. 2013. p. 21–27.
  • Faraji S, Pouya S, Atkeson CG, et al. Versatile and robust 3D walking with a simulated humanoid robot (Atlas): a model predictive control approach. In: IEEE International Conference on Robotics and Automation. 2014. p. 1943–1950.
  • Henze B, Ott C, Roa MA. Posture and balance control for humanoid robots in multi-contact scenarios based on model predictive control. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2014. p. 3253–3258.
  • Koenemann J, Del Prete A, Tassa Y, et al. Whole-body model-predictive control applied to the HRP-2 humanoid. In: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). 2015. p. 3346–3351.
  • Feng S, Xinjilefu X, Atkeson CG, et al. Robust dynamic walking using online foot step optimization. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2016. p. 5373–5378.
  • Kuindersma S, Deits R, Fallon M, et al. Optimization based locomotion planning, estimation and control design for the atlas humanoid robot. Auton Robots. 2016;40(3):429–455.
  • Bledt G, Wensing PM, Kim S. Policy-regularized model predictive control to stabilize diverse quadrupedal gaits for the MIT cheetah. In: 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE; 2017. p. 4102–4109.
  • Naveau M, Kudruss M, Stasse O, et al. A reactive walking pattern generator based on nonlinear model predictive control. IEEE Robot Autom Lett. 2017;2(1):10–17.
  • Farshidian F, Jelavic E, Satapathy A, et al. Real-time motion planning of legged robots: a model predictive control approach. In: 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids). IEEE; 2017. p. 577–584.
  • Kamioka T, Kaneko H, Takenaka T, et al. Simultaneous optimization of ZMP and footsteps based on the analytical solution of divergent component of motion. In: IEEE International Conference on Robotics and Automation. 2018. p. 1763–1770.
  • Di Carlo J, Wensing PM, Katz B, et al. Dynamic locomotion in the MIT cheetah 3 through convex model-predictive control. In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). 2018. p. 1–9.
  • Neunert M, Stäuble M, Giftthaler M, et al. Whole-body nonlinear model predictive control through contacts for quadrupeds. IEEE Robot Autom Lett. 2018;3(3):1458–1465.
  • Bledt G, Kim S. Implementing regularized predictive control for simultaneous real-time footstep and ground reaction force optimization. In: 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE; 2019. p. 6316–6323.
  • Agravante DJ, Cherubini A, Sherikov A, et al. Human-humanoid collaborative carrying. IEEE Trans Robot. 2019;35(4):833–846.
  • Bledt G, Kim S. Extracting legged locomotion heuristics with regularized predictive control. In: IEEE International Conference on Robotics and Automation. 2020. p. 406–412.
  • Chignoli M, Wensing PM. Variational-based optimal control of underactuated balancing for dynamic quadrupeds. IEEE Access. 2020;8:49785–49797.
  • Ishihara K, Itoh TD, Morimoto J. Full-body optimal control toward versatile and agile behaviors in a humanoid robot. IEEE Robot Autom Lett. 2020;5(1):119–126.
  • Scianca N, De Simone D, Lanari L, et al. MPC for humanoid gait generation: stability and feasibility. IEEE Trans Robot. 2020;36(4):1171–1188.
  • Bjelonic M, Grandia R, Harley O, et al. Whole-body MPC and online gait sequence generation for wheeled-legged robots. In: 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE; 2021. p. 8388–8395.
  • Grandia R, Taylor AJ, Ames AD, et al. Multi-layered safety for legged robots via control barrier functions and model predictive control. In: 2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE; 2021. p. 8352–8358.
  • Sleiman JP, Farshidian F, Minniti MV, et al. A unified MPC framework for whole-body dynamic locomotion and manipulation. IEEE Robot Autom Lett. 2021;6(3):4688–4695.
  • Xin G, Xin S, Cebe O, et al. Robust footstep planning and LQR control for dynamic quadrupedal locomotion. IEEE Robot Autom Lett. 2021;6(3):4488–4495.
  • Xiong X, Reher J, Ames AD. Global position control on underactuated bipedal robots: step-to-step dynamics approximation for step planning. In: IEEE International Conference on Robotics and Automation. 2021. p. 2825–2831.
  • Ding J, Zhou C, Xin S, et al. Nonlinear model predictive control for robust bipedal locomotion: exploring angular momentum and com height changes. Adv Robot. 2021;35(18):1079–1097.
  • Dantec E, Budhiraja R, Roig A, et al. Whole body model predictive control with a memory of motion: experiments on a torque-controlled TALOS. In: 2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE; 2021. p. 8202–8208.
  • Rathod N, Bratta A, Focchi M, et al. Model predictive control with environment adaptation for legged locomotion. IEEE Access. 2021;9:145710–145727.
  • Romualdi G, Dafarra S, L'Erario G, et al. Online non-linear centroidal MPC for humanoid robot locomotion with step adjustment. In: IEEE International Conference on Robotics and Automation. 2022. p. 10412–10419.
  • Dantec E, Taix M, Mansard N. First order approximation of model predictive control solutions for high frequency feedback. IEEE Robot Autom Lett. 2022;7(2):4448–4455.
  • Jeon SH, Kim S, Kim D. Online optimal landing control of the MIT Mini Cheetah. In: IEEE International Conference on Robotics and Automation. 2022. p. 178–184.
  • Kajita S, Espiau B. Legged robots. Berlin, Heidelberg: Springer Handbook of Robotics; 2008.
  • Sugihara T, Morisawa M. A survey: dynamics of humanoid robots. Adv Robot. 2020;34(21-22):1338–1352.
  • Tazaki Y, Murooka M. A survey of motion planning techniques for humanoid robots. Adv Robot. 2020;34(21-22):1370–1379.
  • Carpentier J, Wieber PB. Recent progress in legged robots locomotion control. Curr Robot Rep. 2021;2:231–238.
  • Perrin N. Biped footstep planning. In: Humanoid robotics: a reference. Springer Netherlands; 2019. p. 1697–1717.
  • Wieber PB. Model predictive control. In: Humanoid robotics: a reference. Springer Netherlands; 2019. p. 1077–1097.
  • Bouyarmane K, Caron S, Escande A, et al. Multi-contact motion planning and control. In: Humanoid robotics: a reference. Springer Netherlands; 2019. p. 1763–1804.
  • Featherstone R. Rigid body dynamics algorithms. Berlin, Heidelberg: Springer; 2008.
  • Carpentier J, Mansard N. Multicontact locomotion of legged robots. IEEE Trans Robot. 2018;34(6):1441–1460.
  • Kurtz V, Li H, Wensing PM, et al. Mini Cheetah, the falling cat: a case study in machine learning and trajectory optimization for robot acrobatics. In: IEEE International Conference on Robotics and Automation. 2022. p. 4635–4641.
  • Stewart DE, Trinkle JC. An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and coulomb friction. Int J Numer Methods Eng. 1996;39(15):2673–2691.
  • Neunert M, Farshidian F, Winkler AW, et al. Trajectory optimization through contacts and automatic gait discovery for quadrupeds. IEEE Robot Autom Lett. 2017;2(3):1502–1509.
  • Todorov E. Convex and analytically-invertible dynamics with contacts and constraints: theory and implementation in mujoco. In: 2014 IEEE International Conference on Robotics and Automation (ICRA). IEEE; 2014. p. 6054–6061.
  • Todorov E, Erez T, Tassa Y. Mujoco: a physics engine for model-based control. In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE; 2012. p. 5026–5033.
  • Acosta B, Yang W, Posa M. Validating robotics simulators on real world impacts. IEEE Robot Autom Lett. 2022;7(3):6471–6478.
  • Kajita S, Tani K. Study of dynamic biped locomotion on rugged terrain – derivation and application of the linear inverted pendulum mode. In: IEEE International Conference on Robotics and Automation. 1991. p. 1405–1411.
  • Caron S, Pham QC, Nakamura Y. ZMP support areas for multicontact mobility under frictional constraints. IEEE Trans Robot. 2017;33(1):67–80.
  • Koolen T, de Boer T, Rebula J, et al. Capturability-based analysis and control of legged locomotion, part 1: theory and application to three simple gait models. Int J Robot Res. 2012;31(9):1094–1113.
  • Ferreau HJ, Kirches C, Potschka A, et al. qpOASES: a parametric active-set algorithm for quadratic programming. Math Program Comput. 2014;6(4):327–363.
  • Frasch JV, Sager S, Diehl M. A parallel quadratic programming method for dynamic optimization problems. Math Program Comput. 2015;7(3):289–329.
  • Mattingley J, Boyd S. CVXGEN: a code generator for embedded convex optimization. Optim Eng. 2012;13(1):1–27.
  • Frison G, Diehl M. Hpipm: a high-performance quadratic programming framework for model predictive control. IFAC-PapersOnLine. 2020;53(2):6563–6569.
  • Pandala AG, Ding Y, Park HW. qpSWIFT: a real-time sparse quadratic program solver for robotic applications. IEEE Robot Autom Lett. 2019;4(4):3355–3362.
  • Stellato B, Banjac G, Goulart P, et al. OSQP: an operator splitting solver for quadratic programs. Math Program Comput. 2020;12(4):637–672.
  • Kouzoupis D, Frison G, Zanelli A, et al. Recent advances in quadratic programming algorithms for nonlinear model predictive control. Vietnam J Math. 2018;46(4):863–882.
  • Ohtsuka T. A continuation/GMRES method for fast computation of nonlinear receding horizon control. Automatica. 2004;40(4):563–574.
  • Diehl M, Bock H, Schlöder JP. A real-time iteration scheme for nonlinear optimization in optimal feedback control. SIAM J Control Optim. 2005;43(5):1714–1736.
  • Zavala VM, Biegler LT. The advanced-step NMPC controller: optimality, stability and robustness. Automatica. 2009;45(1):86–93.
  • Zanelli A, Quirynen R, Jerez J, et al. A homotopy-based nonlinear interior-point method for NMPC. IFAC-PapersOnLine. 2017;50(1):13188–13193.
  • Nocedal J, Wright SJ. Numerical optimization. 2nd ed. New York: Springer; 2006.
  • Gill PE, Murray W, Saunders MA. SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev. 2005;47(1):99–131.
  • Wächter A, Biegler L. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program. 2006;106(1):25–57.
  • Bock H, Plitt K. A multiple shooting algorithm for direct solution of optimal control problems. In: 9th IFAC World Congress. 1984. p. 1603–1608.
  • Rawlings K, Mayne DQ, Diehl M. Model predictive control: theory, computation, and design. Madison, Wisconsin: Nob Hill; 2017.
  • Rao C, Wright SJ, Rawlings JB. Application of interior-point methods to model predictive control. J Optim Theory Appl. 1998;99(3):723–757.
  • Wang Y, Boyd S. Fast model predictive control using online optimization. IEEE Trans Control Syst Technol. 2010;18(2):267–278.
  • Zanelli A, Domahidi A, Jerez J, et al. FORCES NLP: an efficient implementation of interior-point methods for multistage nonlinear nonconvex programs. Int J Control. 2020;93(1):13–29.
  • Deng H, Ohtsuka T. A parallel Newton-type method for nonlinear model predictive control. Automatica. 2019;109:108560.
  • Verschueren R, Frison G, Kouzoupis D, et al. Acados – a modular open-source framework for fast embedded optimal control. Math Program Comput. 2021;14:147–183.
  • Howell TA, Jackson BE, Manchester Z. ALTRO: A fast solver for constrained trajectory optimization. In: 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). 2019. p. 7674–7679.
  • Sideris A, Rodriguez LA. A Riccati approach for constrained linear quadratic optimal control. Int J Control. 2011;84(2):370–380.
  • Giftthaler M, Buchli J. A projection approach to equality constrained iterative linear quadratic optimal control. In: 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids). 2017. p. 61–66.
  • Katayama S, Ohtsuka T. Efficient Riccati recursion for optimal control problems with pure-state equality constraints. In: American Control Conference (ACC) 2022 (to appear). 2022. p. 3579–3586.
  • Jacobson DH, Mayne DQ. Differential dynamic programming. New York: Elsevier; 1970.
  • Todorov E, Li W. A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems. In: Proceedings of the 2005, American Control Conference. 2005. p. 300–306.
  • Mastalli C, Budhiraja R, Merkt W, et al. Crocoddyl: an efficient and versatile framework for multi-contact optimal control. In: 2020 IEEE International Conference on Robotics and Automation (ICRA). 2020. p. 2536–2542.
  • Grandia R, Farshidian F, Ranftl R, et al. Feedback MPC for torque-controlled legged robots. In: 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE; 2019. p. 4730–4737.
  • Sleiman JP, Farshidian F, Hutter M. Constraint handling in continuous-time DDP-based model predictive control. In: 2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE; 2021. p. 8209–8215.
  • Goebel R, Sanfelice RG, Teel AR. Hybrid dynamical systems. Princeton, New Jersey: Princeton University Press; 2012.
  • Belotti P, Kirches C, Leyffer S, et al. Mixed-integer nonlinear optimization. Acta Numer. 2013;22:1–131.
  • Sager S, Jung M, Kirches C. Combinatorial integral approximation. Math Methods Oper Res. 2011;73(3):363–380.
  • Bürger A, Zeile C, Hahn M, et al. pycombina: an open-source tool for solving combinatorial approximation problems arising in mixed-integer optimal control. IFAC-PapersOnLine. 2020;53(2):6502–6508.
  • Hespanhol P, Quirynen R, Di Cairano S. A structure exploiting branch-and-bound algorithm for mixed-integer model predictive control. In: 2019 18th European Control Conference (ECC). IEEE; 2019. p. 2763–2768.
  • Marcucci T, Tedrake R. Warm start of mixed-integer programs for model predictive control of hybrid systems. IEEE Trans Automat Contr. 2020;66(6):2433–2448.
  • Yunt K, Glocker C. Trajectory optimization of mechanical hybrid systems using SUMT. In: 9th IEEE International Workshop on Advanced Motion Control. IEEE; 2006. p. 665–671.
  • Scheel H, Scholtes S. Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Math Oper Res. 2000;25(1):1–22.
  • Posa M, Cantu C, Tedrake R. A direct method for trajectory optimization of rigid bodies through contact. Int J Rob Res. 2014;33(1):69–81.
  • Hoheisel T, Kanzow C, Schwartz A. Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints. Math Program. 2013;137(1-2):257–288.
  • Nurkanovic A, Albrecht S, Diehl M. Limits of MPCC formulations in direct optimal control with nonsmooth differential equations. In: 2020 European Control Conference (ECC). 2020. p. 2015–2020.
  • Carius J, Ranftl R, Koltun V, et al. Trajectory optimization with implicit hard contacts. IEEE Robot Autom Lett. 2018;3(4):3316–3323.
  • Carius J, Ranftl R, Koltun V, et al. Trajectory optimization for legged robots with slipping motions. IEEE Robot Autom Lett. 2019;4(3):3013–3020.
  • Alp Aydinoglu MP. Real-time multi-contact model predictive control via ADMM. In: 2021 IEEE International Conference on Robotics and Automation (ICRA). 2022. p. 3414–3421.
  • Dempe S, Dutta J. Is bilevel programming a special case of a mathematical program with complementarity constraints?. Math Program. 2012;131(1-2):37–48.
  • Colson B, Marcotte P, Savard G. An overview of bilevel optimization. Ann Oper Res. 2007;153(1):235–256.
  • Xu X, Antsaklis PJ. Optimal control of switched systems based on parameterization of the switching instants. IEEE Trans Automat Contr. 2004;49(1):2–16.
  • Patterson MA, Rao AV. GPOPS-II: a MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans Math Softw. 2014;41(1).1–37.
  • Xu X, Antsaklis PJ. Optimal control of switched systems via non-linear optimization based on direct differentiations of value functions. Int J Control. 2002;75(16-17):1406–1426.
  • Farshidian F, Neunert M, Winkler AW, et al. An efficient optimal planning and control framework for quadrupedal locomotion. In: 2017 IEEE International Conference on Robotics and Automation (ICRA). 2017. p. 93–100.
  • Li H, Wensing PM. Hybrid systems differential dynamic programming for whole-body motion planning of legged robots. IEEE Robot Autom Lett. 2020;5(4):5448–5455.
  • Tedrake R, Kuindersma S, Deits R, et al. A closed-form solution for real-time ZMP gait generation and feedback stabilization. In: IEEE-RAS International Conference on Humanoid Robots. 2015. p. 936–940.
  • Katayama T, Ohki T, Inoue T, et al. Design of an optimal controller for a discrete-time system subject to previewable demand. Int J Control. 1985;41(3):677–699.
  • Likhachev M, Ferguson D, Gordon G, et al. Anytime dynamic A*: an anytime, replanning algorithm. In: International Conference on Automated Planning and Scheduling. 2005.
  • Chestnutt J, Kuffner J, Nishiwaki K, et al. Planning biped navigation strategies in complex environments. In: IEEE-RAS International Conference on Humanoid Robots. 2003.
  • Hornung A, Dornbush A, Likhachev M, et al. Anytime search-based footstep planning with suboptimality bounds. In: IEEE-RAS International Conference on Humanoid Robots. 2012. p. 674–679.
  • Deits R, Tedrake R. Footstep planning on uneven terrain with mixed-integer convex optimization. In: IEEE-RAS International Conference on Humanoid Robots. 2014. p. 279–286.
  • Tonneau S, Song D, Fernbach P, et al. SL1M: Sparse L1-norm minimization for contact planning on uneven terrain. In: IEEE International Conference on Robotics and Automation. 2020. p. 6604–6610.
  • Park J, Youm Y. General ZMP preview control for bipedal walking. In: IEEE International Conference on Robotics and Automation. 2007. p. 2682–2687.
  • Wieber P. Trajectory free linear model predictive control for stable walking in the presence of strong perturbations. In: IEEE-RAS International Conference on Humanoid Robots. 2006. p. 137–142.
  • Herdt A, Perrin N, Wieber PB. LMPC based online generation of more efficient walking motions. In: IEEE-RAS International Conference on Humanoid Robots. 2012. p. 390–395.
  • Goto K, Tazaki Y, Suzuki T. Bipedal locomotion control based on simultaneous trajectory and foot step planning. J Robot Mechatron. 2016;28(4):533–542.
  • Xin S, Orsolino R, Tsagarakis N. Online relative footstep optimization for legged robots dynamic walking using discrete-time model predictive control. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2019. p. 513–520.
  • Herdt A, Diedam H, Wieber PB, et al. Online walking motion generation with automatic footstep placement. Adv Robot. 2010;24(5-6):719–737.
  • Dimitrov D, Paolillo A, Wieber PB. Walking motion generation with online foot position adaptation based on l1- and l∞-norm penalty formulations. In: IEEE International Conference on Robotics and Automation. 2011. p. 3523–3529.
  • Griffin RJ, Leonessa A. Model predictive control for dynamic footstep adjustment using the divergent component of motion. In: IEEE International Conference on Robotics and Automation. 2016. p. 1763–1768.
  • Shafiee-Ashtiani M, Yousefi-Koma A, Shariat-Panahi M. Robust bipedal locomotion control based on model predictive control and divergent component of motion. In: IEEE International Conference on Robotics and Automation. 2017. p. 3505–3510.
  • Jeong H, Sim O, Bae H, et al. Biped walking stabilization based on foot placement control using capture point feedback. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2017. p. 5263–5269.
  • Kojio Y, Ishiguro Y, Nguyen KNK, et al. Unified balance control for biped robots including modification of footsteps with angular momentum and falling detection based on capturability. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2019. p. 497–504.
  • Stephens BJ, Atkeson CG. Push recovery by stepping for humanoid robots with force controlled joints. In: IEEE-RAS International Conference on Humanoid Robots. 2010. p. 52–59.
  • Murooka M, Chappellet K, Tanguy A, et al. Humanoid loco-manipulations pattern generation and stabilization control. IEEE Robot Autom Lett. 2021;6(3):5597–5604.
  • Mason S, Rotella N, Schaal S, et al. An MPC walking framework with external contact forces. In: IEEE International Conference on Robotics and Automation. 2018. p. 1785–1790.
  • Morisawa M, Cisneros R, Benallegue M, et al. Sequential trajectory generation for dynamic multi-contact locomotion synchronizing contact. Int J HR. 2020;17(1):2050003.
  • Feng S, Whitman E, Xinjilefu X, et al. Optimization-based full body control for the darpa robotics challenge. J Field Robot. 2015;32(2):293–312.
  • Van Heerden K. Real-time variable center of mass height trajectory planning for humanoids robots. IEEE Robot Autom Lett. 2017;2(1):135–142.
  • Brasseur C, Sherikov A, Collette C, et al. A robust linear MPC approach to online generation of 3D biped walking motion. In: IEEE-RAS International Conference on Humanoid Robots. 2015. p. 595–601.
  • Takenaka T, Matsumoto T, Yoshiike T. Real time motion generation and control for biped robot - 1st report: walking gait pattern generation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2009. p. 1084–1091.
  • Englsberger J, Ott C, Albu-Schäffer A. Three-dimensional bipedal walking control based on divergent component of motion. IEEE Trans Robot. 2015;31(2):355–368.
  • Sugihara T, Yamamoto T. Foot-guided agile control of a biped robot through ZMP manipulation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2017. p. 4546–4551.
  • Byl K, Shkolnik A, Prentice S, et al. Reliable dynamic motions for a stiff quadruped. In: Experimental Robotics. 2009. p. 319–328.
  • Horvat T, Melo K, Ijspeert AJ. Model predictive control based framework for CoM control of a quadruped robot. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2017. p. 3372–3378.
  • Orin DE, Goswami A, Lee SH. Centroidal dynamics of a humanoid robot. Auton Robots. 2013;35(2-3):161–176.
  • Audren H, Vaillant J, Kheddar A, et al. Model preview control in multi-contact motion-application to a humanoid robot. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2014. p. 4030–4035.
  • Dai H, Tedrake R. Planning robust walking motion on uneven terrain via convex optimization. In: IEEE-RAS International Conference on Humanoid Robots. 2016. p. 579–586.
  • Fernbach P, Tonneau S, Taïx M. CROC: Convex resolution of centroidal dynamics trajectories to provide a feasibility criterion for the multi contact planning problem. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2018. p. 1–9.
  • Ponton B, Herzog A, Schaal S, et al. A convex model of humanoid momentum dynamics for multi-contact motion generation. In: IEEE-RAS International Conference on Humanoid Robots. 2016. p. 842–849.
  • García G, Griffin R, Pratt J. MPC-based locomotion control of bipedal robots with line-feet contact using centroidal dynamics. In: IEEE-RAS International Conference on Humanoid Robots. 2021. p. 276–282.
  • Caron S, Kheddar A. Multi-contact walking pattern generation based on model preview control of 3D COM accelerations. In: IEEE-RAS International Conference on Humanoid Robots. 2016. p. 550–557.
  • Dai H, Valenzuela A, Tedrake R. Whole-body motion planning with centroidal dynamics and full kinematics. In: IEEE-RAS International Conference on Humanoid Robots. 2014. p. 295–302.
  • Herzog A, Rotella N, Schaal S, et al. Trajectory generation for multi-contact momentum control. In: IEEE-RAS International Conference on Humanoid Robots. 2015. p. 874–880.
  • Kudruss M, Naveau M, Stasse O, et al. Optimal control for whole-body motion generation using center-of-mass dynamics for predefined multi-contact configurations. In: IEEE-RAS International Conference on Humanoid Robots. 2015. p. 684–689.
  • Chignoli M, Kim D, Stanger-Jones E, et al. The MIT humanoid robot: design, motion planning, and control for acrobatic behaviors. In: IEEE-RAS International Conference on Humanoid Robots. 2021. p. 1–8.
  • Ding Y, Pandala A, Park HW. Real-time model predictive control for versatile dynamic motions in quadrupedal robots. In: 2019 International Conference on Robotics and Automation (ICRA). IEEE; 2019. p. 8484–8490.
  • Shah P, Meduri A, Merkt W, et al. Rapid convex optimization of centroidal dynamics using block coordinate descent. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2021. p. 1658–1665.
  • Bellicoso CD, Krämer K, Stäuble M, et al. ALMA-articulated locomotion and manipulation for a torque-controllable robot. In: 2019 International Conference on Robotics and Automation (ICRA). IEEE; 2019. p. 8477–8483.
  • Muico U, Lee Y, Popović J, et al. Contact-aware nonlinear control of dynamic characters. In: Acm siggraph 2009 papers. 2009. p. 1–9.
  • Luh JYS, Walker MW, Paul RPC. On-Line computational scheme for mechanical manipulators. J Dyn Syst Meas Control. 1980;102(2):69–76.06.
  • Featherstone R. The calculation of robot dynamics using articulated-body inertias. Int J Rob Res. 1983;2(1):13–30.
  • Carpentier J, Budhiraja R, Mansard N. Proximal and sparse resolution of constrained dynamic equations. In: Robotics: Science and Systems (RSS 2021). 2021.
  • Neunert M, Giftthaler M, Frigerio M, et al. Fast derivatives of rigid body dynamics for control, optimization and estimation. In: 2016 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR). 2016. p. 91–97.
  • Carpentier J, Mansard N. Analytical derivatives of rigid body dynamics algorithms. In: Robotics: Science and Systems (RSS 2018). 2018. p. hal–01790971v2f.
  • Singh S, Russell R, Wensing PM. Efficient analytical derivatives of rigid-body dynamics using spatial vector algebra. IEEE Robot Autom Lett. 2022;7(2):1776–1783.
  • Ayusawa K, Yoshida E. Comprehensive theory of differential kinematics and dynamics towards extensive motion optimization framework. Int J Rob Res. 2018;37(13-14):1554–1572.
  • Nganga JN, Wensing PM. Accelerating second-order differential dynamic programming for rigid-body systems. IEEE Robot Autom Lett. 2021;6(4):7659–7666.
  • Quirynen R, Houska B, Diehl M. Efficient symmetric Hessian propagation for direct optimal control. J Process Control. 2017;50:19–28.
  • Frigerio M, Buchli J, Caldwell DG, et al. RobCoGen: a code generator for efficient kinematics and dynamics of articulated robots, based on domain specific languages. J Softw Eng Robot. 2016;7(1):36–54.
  • Carpentier J, Saurel G, Buondonno G, et al. The Pinocchio C++ library – a fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives. In: International Symposium on System Integration (SII). 2019. p. 614–619.
  • Mordatch I, Todorov E, Popović Z. Discovery of complex behaviors through contact-invariant optimization. ACM Trans Graph. 2012;31(4):1–8.
  • Budhiraja R, Carpentier J, Mastalli C, et al. Differential dynamic programming for multi-phase rigid contact dynamics. In: 2018 IEEE-RAS 18th International Conference on Humanoid Robots (Humanoids). IEEE; 2018. p. 1–9.
  • Schultz G, Mombaur K. Modeling and optimal control of human-like running. IEEE ASME Trans Mechatron. 2010;15(5):783–792.
  • Andersson JAE, Gillis J, Horn G, et al. CasADi – a software framework for nonlinear optimization and optimal control. Math Program Comput. 2019;11(1):1–36.
  • Giftthaler M, Neunert M, Stäuble M, et al. The control toolbox – an open-source C++ library for robotics, optimal and model predictive control. In: 2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR). IEEE; 2018. p. 123–129.
  • Galliker MY, Grandia R, Farshidian F, et al. OCS2: an open source library for optimal control of switched systems. 2017–2022. Available from: https://github.com/leggedrobotics/ocs2
  • Farshidian F, Kamgarpour M, Pardo D, et al. Sequential linear quadratic optimal control for nonlinear switched systems. IFAC-PapersOnLine. 2017;50(1):1463–1469. 20th IFAC World Congress.
  • Katayama S. robotoc. 2020–2022. Available from: https://github.com/mayataka/robotoc
  • Grandia R, Taylor AJ, Singletary A, et al. Nonlinear model predictive control of robotic systems with control Lyapunov functions. In: Robotics: Science and Systems (RSS 2020). 2020.
  • Henze B, Roa MA, Ott C. Passivity-based whole-body balancing for torque-controlled humanoid robots in multi-contact scenarios. Int J Rob Res. 2016;35(12):1522–1543.
  • Englsberger J, Dietrich A, Mesesan GA, et al. MPTC-modular passive tracking controller for stack of tasks based control frameworks. In: Robotics: Science and Systems (RSS 2020). 2020.
  • Ramuzat N, Boria S, Stasse O. Passive inverse dynamics control using a global energy tank for torque-controlled humanoid robots in multi-contact. IEEE Robotics and Automation Letters; 2022.
  • Ames AD, Xu X, Grizzle JW, et al. Control barrier function based quadratic programs for safety critical systems. IEEE Trans Automat Contr. 2016;62(8):3861–3876.
  • Scokaert PO, Mayne DQ. Min-max feedback model predictive control for constrained linear systems. IEEE Trans Automat Contr. 1998;43(8):1136–1142.
  • Köhler J, Soloperto R, Müller MA, et al. A computationally efficient robust model predictive control framework for uncertain nonlinear systems. IEEE Trans Automat Contr. 2020;66(2):794–801.
  • Lorenzen M, Dabbene F, Tempo R, et al. Constraint-tightening and stability in stochastic model predictive control. IEEE Trans Automat Contr. 2016;62(7):3165–3177.
  • Minniti MV, Grandia R, Fäh K, et al. Model predictive robot-environment interaction control for mobile manipulation tasks. In: 2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE; 2021. p. 1651–1657.
  • Minniti MV, Grandia R, Farshidian F, et al. Adaptive CLF-MPC with application to quadrupedal robots. IEEE Robot Autom Lett. 2022;7(1):565–572.
  • Zanon M, Gros S. Safe reinforcement learning using robust MPC. IEEE Trans Automat Contr. 2020;66(8):3638–3652.