references.bib

@inproceedings{di_carlo_dynamic_2018,
	address = {Madrid},
	title = {Dynamic {Locomotion} in the {MIT} {Cheetah} 3 {Through} {Convex} {Model}-{Predictive} {Control}},
	isbn = {978-1-5386-8094-0},
	url = {https://ieeexplore.ieee.org/document/8594448/},
	doi = {10.1109/IROS.2018.8594448},
	abstract = {This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot. The robot dynamics are simplified to formulate the problem as convex optimization while still capturing the full 3D nature of the system. With the simplified model, ground reaction force planning problems are formulated for prediction horizons of up to 0.5 seconds, and are solved to optimality in under 1 ms at a rate of 20-30 Hz. Despite using a simplified model, the robot is capable of robust locomotion at a variety of speeds. Experimental results demonstrate control of gaits including stand, trot, flying-trot, pronk, bound, pace, a 3-legged gait, and a full 3D gallop. The robot achieved forward speeds of up to 3 m/s, lateral speeds up to 1 m/s, and angular speeds up to 180 deg/sec. Our approach is general enough to perform all these behaviors with the same set of gains and weights.},
	language = {en},
	urldate = {2023-11-28},
	booktitle = {2018 {IEEE}/{RSJ} {International} {Conference} on {Intelligent} {Robots} and {Systems} ({IROS})},
	publisher = {IEEE},
	author = {Di Carlo, Jared and Wensing, Patrick M. and Katz, Benjamin and Bledt, Gerardo and Kim, Sangbae},
	month = oct,
	year = {2018},
	pages = {1--9},
	file = {Di Carlo et al. - 2018 - Dynamic Locomotion in the MIT Cheetah 3 Through Co.pdf:/home/mishmish/Zotero/storage/4M3GG63P/Di Carlo et al. - 2018 - Dynamic Locomotion in the MIT Cheetah 3 Through Co.pdf:application/pdf},
}

@misc{kim_highly_2019,
	title = {Highly {Dynamic} {Quadruped} {Locomotion} via {Whole}-{Body} {Impulse} {Control} and {Model} {Predictive} {Control}},
	url = {http://arxiv.org/abs/1909.06586},
	abstract = {Dynamic legged locomotion is a challenging topic because of the lack of established control schemes which can handle aerial phases, short stance times, and high-speed leg swings. In this paper, we propose a controller combining wholebody control (WBC) and model predictive control (MPC). In our framework, MPC finds an optimal reaction force profile over a longer time horizon with a simple model, and WBC computes joint torque, position, and velocity commands based on the reaction forces computed from MPC. Unlike existing WBCs, which attempt to track commanded body trajectories, our controller is focused more on the reaction force command, which allows it to accomplish high speed dynamic locomotion with aerial phases. The newly devised WBC is integrated with MPC and tested on the Mini-Cheetah quadruped robot. To demonstrate the robustness and versatility, the controller is tested on six different gaits in a number of different environments, including outdoors and on a treadmill, reaching a top speed of 3.7 m/s.},
	language = {en},
	urldate = {2023-12-12},
	publisher = {arXiv},
	author = {Kim, Donghyun and Di Carlo, Jared and Katz, Benjamin and Bledt, Gerardo and Kim, Sangbae},
	month = sep,
	year = {2019},
	note = {arXiv:1909.06586 [cs]},
	keywords = {Computer Science - Robotics},
	file = {Kim et al. - 2019 - Highly Dynamic Quadruped Locomotion via Whole-Body.pdf:/home/mishmish/Zotero/storage/AX96EBRP/Kim et al. - 2019 - Highly Dynamic Quadruped Locomotion via Whole-Body.pdf:application/pdf},
}

@article{raibert_experiments_1984,
	title = {Experiments in {Balance} with a {3D} {One}-{Legged} {Hopping} {Machine}.},
	volume = {3},
	issn = {02783649},
	url = {https://search.ebscohost.com/login.aspx?direct=true&AuthType=ip,sso&db=bth&AN=4707675&site=eds-live&scope=site&custid=umaah},
	doi = {10.1177/027836498400300207},
	abstract = {In order to explore the balance in legged locomotion, we are studying systems that hop and run on one springy leg. Previous work has shown that relatively simple algorithms can achieve balance on one leg for the special case of a system that is constrained mechanically to operate in a plane (Raibert, in press; Raibert and Brown, in press). Here we generalize the approach to a three-dimensional (3D) one-legged machine that runs and balances on an open floor without physical support. We decompose control of the machine into three separate parts: one part that controls forward running velocity, one part that controls attitude of the body, and a third part that controls hopping height. Experiments with a physical 3D one-legged hopping machine showed that this control scheme, while simple to implement, is powerful enough to permit hopping in place, running at a desired rate, and travel along a simple path. These algorithms that control locomotion in 3D are direct generalizations of those in 2D, with surprisingly little additional complication. [ABSTRACT FROM AUTHOR]},
	number = {2},
	journal = {International Journal of Robotics Research},
	author = {Raibert, Marc H. and Brown Jr., H. Benjamin and Chepponis, Michael},
	year = {1984},
	keywords = {Locomotion, Mathematics, Postural balance},
	pages = {75},
	annote = {Accession Number: 4707675; Raibert, Marc H.; Brown Jr., H. Benjamin; Chepponis, Michael; Issue Info: Summer84, Vol. 3 Issue 2, p75; Thesaurus Term: Mathematics; Subject Term: Locomotion; Subject Term: Postural balance; Number of Pages: 18p; Illustrations: 8 Black and White Photographs, 8 Diagrams, 1 Chart, 14 Graphs; Document Type: Article},
}

@article{azevedo_line_2002,
	title = {{ON} {LINE} {OPTIMAL} {CONTROL} {FOR} {BIPED} {ROBOTS}},
	volume = {35},
	issn = {14746670},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S1474667015392661},
	doi = {10.3182/20020721-6-ES-1901.00845},
	abstract = {This paper deals with the control of walking biped robots. An on line optimal control approach based on moving horizon strategy is developed. The problem is stated as an optimization one subject to physical coherent constraints issued from human behavior observation. The strategy is tested with a model of the BIP robot designed by INRIA.},
	language = {en},
	number = {1},
	urldate = {2023-12-12},
	journal = {IFAC Proceedings Volumes},
	author = {Azevedo, Christine and Poignet, Philippe and Espiau, Bernard},
	year = {2002},
	pages = {199--204},
	file = {Azevedo et al. - 2002 - ON LINE OPTIMAL CONTROL FOR BIPED ROBOTS.pdf:/home/mishmish/Zotero/storage/GKU67MID/Azevedo et al. - 2002 - ON LINE OPTIMAL CONTROL FOR BIPED ROBOTS.pdf:application/pdf},
}

@article{chestnut_predictive-control_1961,
	title = {Predictive-control system application},
	volume = {80},
	issn = {0097-2185},
	url = {https://ieeexplore.ieee.org/document/6371731/},
	doi = {10.1109/TAI.1961.6371731},
	language = {en},
	number = {3},
	urldate = {2023-12-12},
	journal = {Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry},
	author = {Chestnut, H. and Sollecito, W. E. and Troutman, P. H.},
	month = jul,
	year = {1961},
	pages = {128--139},
	file = {Chestnut et al. - 1961 - Predictive-control system application.pdf:/home/mishmish/Zotero/storage/Z7FCXIFA/Chestnut et al. - 1961 - Predictive-control system application.pdf:application/pdf},
}

@inproceedings{erez_integrated_2013,
	address = {Atlanta, GA},
	title = {An integrated system for real-time model predictive control of humanoid robots},
	isbn = {978-1-4799-2617-6 978-1-4799-2619-0},
	url = {http://ieeexplore.ieee.org/document/7029990/},
	doi = {10.1109/HUMANOIDS.2013.7029990},
	abstract = {Generating diverse behaviors with a humanoid robot requires a mix of human supervision and automatic control. Ideally, the user’s input is restricted to high-level instruction and guidance, and the controller is intelligent enough to accomplish the tasks autonomously. Here we describe an integrated system that achieves this goal. The automatic controller is based on real-time model-predictive control (MPC) applied to the full dynamics of the robot. This is possible due to the speed of our new physics engine (MuJoCo), the efficiency of our trajectory optimization algorithm, and the contact smoothing methods we have developed for the purpose of control optimization. In our system, the operator specifies subtasks by selecting from a menu of predefined cost functions, and optionally adjusting the mixing weights of the different cost terms in runtime. The resulting composite cost is sent to the MPC machinery which constructs a new locally-optimal timevarying linear feedback control law once every 30 msec, while planning 500 msec into the future. This control law is evaluated at 1 kHz to generate control signals for the robot, until the next control law becomes available. Performance is illustrated on a subset of the tasks from the DARPA Virtual Robotics Challenge.},
	language = {en},
	urldate = {2023-12-12},
	booktitle = {2013 13th {IEEE}-{RAS} {International} {Conference} on {Humanoid} {Robots} ({Humanoids})},
	publisher = {IEEE},
	author = {Erez, Tom and Lowrey, Kendall and Tassa, Yuval and Kumar, Vikash and Kolev, Svetoslav and Todorov, Emanuel},
	month = oct,
	year = {2013},
	pages = {292--299},
	file = {Erez et al. - 2013 - An integrated system for real-time model predictiv.pdf:/home/mishmish/Zotero/storage/BGG2NNJC/Erez et al. - 2013 - An integrated system for real-time model predictiv.pdf:application/pdf},
}

@article{neunert_whole-body_2018,
	title = {Whole-{Body} {Nonlinear} {Model} {Predictive} {Control} {Through} {Contacts} for {Quadrupeds}},
	volume = {3},
	issn = {2377-3766, 2377-3774},
	url = {https://ieeexplore.ieee.org/document/8276298/},
	doi = {10.1109/LRA.2018.2800124},
	abstract = {In this letter, we present a whole-body nonlinear model predictive control approach for rigid body systems subject to contacts. We use a full-dynamic system model which also includes explicit contact dynamics. Therefore, contact locations, sequences, and timings are not prespecified but optimized by the solver. Yet, using numerical and software engineering allows for running the nonlinear Optimal Control solver at rates up to 190 Hz on a quadruped for a time horizon of half a second. This outperforms the state-of-the-art by at least one order of magnitude. Hardware experiments in the form of periodic and nonperiodic tasks are applied to two quadrupeds with different actuation systems. The obtained results underline the performance, transferability, and robustness of the approach.},
	language = {en},
	number = {3},
	urldate = {2023-12-12},
	journal = {IEEE Robotics and Automation Letters},
	author = {Neunert, Michael and Stauble, Markus and Giftthaler, Markus and Bellicoso, Carmine D. and Carius, Jan and Gehring, Christian and Hutter, Marco and Buchli, Jonas},
	month = jul,
	year = {2018},
	pages = {1458--1465},
	file = {Neunert et al. - 2018 - Whole-Body Nonlinear Model Predictive Control Thro.pdf:/home/mishmish/Zotero/storage/INPKZHTG/Neunert et al. - 2018 - Whole-Body Nonlinear Model Predictive Control Thro.pdf:application/pdf},
}

@article{posa_direct_2014,
	title = {A direct method for trajectory optimization of rigid bodies through contact},
	volume = {33},
	issn = {0278-3649},
	url = {https://doi.org/10.1177/0278364913506757},
	doi = {10.1177/0278364913506757},
	abstract = {Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform.},
	number = {1},
	urldate = {2023-12-12},
	journal = {The International Journal of Robotics Research},
	author = {Posa, Michael and Cantu, Cecilia and Tedrake, Russ},
	month = jan,
	year = {2014},
	note = {Publisher: SAGE Publications Ltd STM},
	pages = {69--81},
	file = {Full Text PDF:/home/mishmish/Zotero/storage/YDLM7WTU/Posa et al. - 2014 - A direct method for trajectory optimization of rig.pdf:application/pdf},
}

@inproceedings{melon_receding-horizon_2021,
	address = {Xi'an, China},
	title = {Receding-{Horizon} {Perceptive} {Trajectory} {Optimization} for {Dynamic} {Legged} {Locomotion} with {Learned} {Initialization}},
	isbn = {978-1-72819-077-8},
	url = {https://ieeexplore.ieee.org/document/9560794/},
	doi = {10.1109/ICRA48506.2021.9560794},
	abstract = {To dynamically traverse challenging terrain, legged robots need to continually perceive and reason about upcoming features, adjust the locations and timings of future footfalls and leverage momentum strategically. We present a pipeline that enables flexibly-parametrized trajectories for perceptive and dynamic quadruped locomotion to be optimized in an online, receding-horizon manner. The initial guess passed to the optimizer affects the computation needed to achieve convergence and the quality of the solution. We consider two methods for generating good guesses. The first is a heuristic initializer which provides a simple guess and requires significant optimization but is nonetheless suitable for adaptation to upcoming terrain. We demonstrate experiments using the ANYmal C quadruped, with fully onboard sensing and computation, to cross obstacles at moderate speeds using this technique. Our second approach uses latent-mode trajectory regression (LMTR) to imitate expert data—while avoiding invalid interpolations between distinct behaviors—such that minimal optimization is needed. This enables high-speed motions that make more expansive use of the robot’s capabilities. We demonstrate it on flat ground with the real robot and provide numerical trials that progress toward deployment on terrain. These results illustrate a paradigm for advancing beyond short-horizon dynamic reactions, toward the type of intuitive and adaptive locomotion planning exhibited by animals and humans.},
	language = {en},
	urldate = {2023-12-12},
	booktitle = {2021 {IEEE} {International} {Conference} on {Robotics} and {Automation} ({ICRA})},
	publisher = {IEEE},
	author = {Melon, Oliwier and Orsolino, Romeo and Surovik, David and Geisert, Mathieu and Havoutis, Ioannis and Fallon, Maurice},
	month = may,
	year = {2021},
	pages = {9805--9811},
	file = {Melon et al. - 2021 - Receding-Horizon Perceptive Trajectory Optimizatio.pdf:/home/mishmish/Zotero/storage/2G46TQRX/Melon et al. - 2021 - Receding-Horizon Perceptive Trajectory Optimizatio.pdf:application/pdf},
}

@inproceedings{bledt_extracting_2020,
	address = {Paris, France},
	title = {Extracting {Legged} {Locomotion} {Heuristics} with {Regularized} {Predictive} {Control}},
	isbn = {978-1-72817-395-5},
	url = {https://ieeexplore.ieee.org/document/9197488/},
	doi = {10.1109/ICRA40945.2020.9197488},
	abstract = {Optimization based predictive control is a powerful tool that has improved the ability of legged robots to execute dynamic maneuvers and traverse increasingly difficult terrains. However, it is often challenging and unintuitive to design meaningful cost functions and build high-fidelity models while adhering to timing restrictions. A novel framework to extract and design principled regularization heuristics for legged locomotion optimization control is presented. By allowing a simulation to fully explore the cost space offline, certain states and actions can be constrained or isolated. Data is fit with simple models relating the desired commands, optimal control actions, and robot states to identify new heuristic candidates. Basic parameter learning and adaptation laws are then applied to the models online. This method extracts simple, but powerful heuristics that can approximate complex dynamics and account for errors stemming from model simplifications and parameter uncertainty without the loss of physical intuition while generalizing the parameter tuning process. Results on the Mini Cheetah robot verify the increased capabilities due to the newly extracted heuristics without any modification to the controller structure or gains.},
	language = {en},
	urldate = {2023-12-12},
	booktitle = {2020 {IEEE} {International} {Conference} on {Robotics} and {Automation} ({ICRA})},
	publisher = {IEEE},
	author = {Bledt, Gerardo and Kim, Sangbae},
	month = may,
	year = {2020},
	pages = {406--412},
	file = {Bledt and Kim - 2020 - Extracting Legged Locomotion Heuristics with Regul.pdf:/home/mishmish/Zotero/storage/C7ZVJEZT/Bledt and Kim - 2020 - Extracting Legged Locomotion Heuristics with Regul.pdf:application/pdf},
}

@misc{cleach_fast_2023,
	title = {Fast {Contact}-{Implicit} {Model}-{Predictive} {Control}},
	url = {http://arxiv.org/abs/2107.05616},
	abstract = {We present a general approach for controlling robotic systems that make and break contact with their environments. Contact-implicit model predictive control (CI-MPC) generalizes linear MPC to contact-rich settings by utilizing a bi-level planning formulation with lower-level contact dynamics formulated as time-varying linear complementarity problems (LCPs) computed using strategic Taylor approximations about a reference trajectory. These dynamics enable the upper-level planning problem to reason about contact timing and forces, and generate entirely new contact-mode sequences online. To achieve reliable and fast numerical convergence, we devise a structure-exploiting interior-point solver for these LCP contact dynamics and a custom trajectory optimizer for the tracking problem. We demonstrate real-time solution rates for CI-MPC and the ability to generate and track non-periodic behaviours in hardware experiments on a quadrupedal robot. We also show that the controller is robust to model mismatch and can respond to disturbances by discovering and exploiting new contact modes across a variety of robotic systems in simulation, including a pushbot, planar hopper, planar quadruped, and planar biped.},
	urldate = {2023-12-12},
	publisher = {arXiv},
	author = {Cleac'h, Simon Le and Howell, Taylor and Yang, Shuo and Lee, Chi-Yen and Zhang, John and Bishop, Arun and Schwager, Mac and Manchester, Zachary},
	month = jan,
	year = {2023},
	note = {arXiv:2107.05616 [cs, eess]},
	keywords = {Computer Science - Robotics, Electrical Engineering and Systems Science - Systems and Control},
	annote = {Comment: submitted to Transactions on Robotics (T-RO), under review},
	file = {arXiv.org Snapshot:/home/mishmish/Zotero/storage/K3X8NWIB/2107.html:text/html;Full Text PDF:/home/mishmish/Zotero/storage/M6S47C4N/Cleac'h et al. - 2023 - Fast Contact-Implicit Model-Predictive Control.pdf:application/pdf},
}

@misc{toussaint_sequence--constraints_2022,
	title = {Sequence-of-{Constraints} {MPC}: {Reactive} {Timing}-{Optimal} {Control} of {Sequential} {Manipulation}},
	shorttitle = {Sequence-of-{Constraints} {MPC}},
	url = {http://arxiv.org/abs/2203.05390},
	abstract = {Task and Motion Planning has made great progress in solving hard sequential manipulation problems. However, a gap between such planning formulations and control methods for reactive execution remains. In this paper we propose a model predictive control approach dedicated to robustly execute a single sequence of constraints, which corresponds to a discrete decision sequence of a TAMP plan. We decompose the overall control problem into three sub-problems (solving for sequential waypoints, their timing, and a short receding horizon path) that each is a non-linear program solved online in each MPC cycle. The resulting control strategy can account for long-term interdependencies of constraints and reactively plan for a timing-optimal transition through all constraints. We additionally propose phase backtracking when running constraints of the current phase cannot be fulfilled, leading to a fluent re-initiation behavior that is robust to perturbations and interferences by an experimenter.},
	urldate = {2023-12-12},
	publisher = {arXiv},
	author = {Toussaint, Marc and Harris, Jason and Ha, Jung-Su and Driess, Danny and Hönig, Wolfgang},
	month = sep,
	year = {2022},
	note = {arXiv:2203.05390 [cs]},
	keywords = {Computer Science - Robotics},
	annote = {Comment: IROS 2022 - Int. Conf. on Intelligent Robots and Systems},
	file = {arXiv.org Snapshot:/home/mishmish/Zotero/storage/8WBCAQY7/2203.html:text/html;Full Text PDF:/home/mishmish/Zotero/storage/YX9AM43F/Toussaint et al. - 2022 - Sequence-of-Constraints MPC Reactive Timing-Optim.pdf:application/pdf},
}