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Control by Gradient Collocation: Applications to optimal obstacle avoidance and minimum torque control

Paul Ruvolo, Tingfan Wu, Javier R. Movellan
2012 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems  
Our method works by first reducing the problem of obstacle avoidance to a continuous state, action, and time control problem, and then uses efficient collocation methods to solve for an optimal feedback  ...  In addition to contributing a new method for obstacle avoidance, our work contributes to the state-of-the-art in collocation methods for non-linear stochastic optimal control problems in two important  ...  COLLOCATION FOR COMPUTING AN APPROXIMATELY OPTIMAL CONTROLLER Given a description of an obstacle avoidance problem as a controlled stochastic diffusion we seek to compute an optimal controller by finding  ... 
doi:10.1109/iros.2012.6385556 dblp:conf/iros/RuvoloWM12 fatcat:p6bsiinztne2fodfph3x3ke3im

Fast Approximation of Over-Determined Second-Order Linear Boundary Value Problems by Cubic and Quintic Spline Collocation

Philipp Seiwald, Daniel J. Rixen
2020 Robotics  
However, to avoid divergence, collocation sites have to be appropriately chosen.  ...  Moreover, the approximation is forced to fulfill an over-determined set of two-point boundary conditions, which are specified by the given control problem.  ...  Acknowledgments: We would like to express special thanks to Nora-Sophie Staufenberg and Felix Sygulla for the constructive discussions during development, implementation and analysis of the presented method  ... 
doi:10.3390/robotics9020048 fatcat:6t2jejfdhzgjlmwen6wn5vanve

Imitation Learning via Simultaneous Optimization of Policies and Auxiliary Trajectories [article]

Mandy Xie, Anqi Li, Karl Van Wyk, Frank Dellaert, Byron Boots, Nathan Ratliff
2021 arXiv   pre-print
We present simulation results on a 7-degree-of-freedom (DoF) robotic manipulator that learns to exhibit lifting, target-reaching, and obstacle avoidance behaviors.  ...  We circumvent challenges with methods like back-propagation-through-time by introducing an auxiliary trajectory network, which takes inspiration from collocation techniques in optimal control.  ...  inspired by collocation techniques from optimal control (which addresses an analogous problem in the control formulation) to circumvent these issues.  ... 
arXiv:2105.03019v2 fatcat:cxxwyz7fy5bk5pybidsld5uzwm

Adaptive wavelet collocation method on the shallow water model

Shanon M. Reckinger, Oleg V. Vasilyev, Baylor Fox-Kemper
2014 Journal of Computational Physics  
Topographic control of basin and channel flows: The roles of bottom pressure torques and friction. Am. Meteorol. Soc. 36, 1786–805. Kevlahan, K.R., Vasilyev, O.V., 2005.  ...  It also allows a solution to be obtained on a near optimal grid for a given accuracy.  ... 
doi:10.1016/j.jcp.2014.03.043 fatcat:sdc7znw2tvgw5jcyl6hqcahvn4

Autonomous Navigation for Quadrupedal Robots with Optimized Jumping through Constrained Obstacles [article]

Scott Gilroy, Derek Lau, Lizhi Yang, Ed Izaguirre, Kristen Biermayer, Anxing Xiao, Mengti Sun, Ayush Agrawal, Jun Zeng, Zhongyu Li, Koushil Sreenath
2021 arXiv   pre-print
To obtain a dynamic jumping maneuver while avoiding obstacles, dynamically-feasible trajectories are optimized offline through collocation-based optimization where safety constraints are imposed.  ...  Such optimization schematic allows the robot to jump through window-shaped obstacles by considering both obstacles in the air and on the ground.  ...  The authors would like to thank Professor Sangbae Kim, the MIT Biomimetic Robotics Lab, and NAVER LABS for providing the Mini Cheetah simulation software and lending the Mini Cheetah for experiments.  ... 
arXiv:2107.00773v1 fatcat:s2hpu3gzsncljex53lfkd2avwi

Preference-Based Trajectory Generation

Jamie A. Lennon, Ella M. Atkins
2009 Journal of Aerospace Computing Information and Communication  
Numerous techniques exist to optimize aircraft and spacecraft trajectories over cost functions that include terms such as fuel, time, and separation from obstacles.  ...  The system respects hard constraints imposed by system dynamics or by the user, and will not let the user's preferences interfere with the system and user needs.  ...  Optimal Control Trajectory Planning Optimal control methods 37,38 have been extensively used to solve complex trajectory planning problems, and are applicable to linear or nonlinear dynamical systems.  ... 
doi:10.2514/1.36214 fatcat:nwhazbgw45f5fpa2o5nims7zzu

A Consolidated Review of Path Planning and Optimization Techniques: Technical Perspectives and Future Directions

Faiza Gul, Imran Mir, Laith Abualigah, Putra Sumari, Agostino Forestiero
2021 Electronics  
In this paper, a review on the three most important communication techniques (ground, aerial, and underwater vehicles) has been presented that throws light on trajectory planning, its optimization, and  ...  Moreover, optimization techniques suitable for implementing ground, aerial, and underwater vehicles are also a part of this review.  ...  [115] presented the control strategy for trajectory formation by avoiding obstacles.  ... 
doi:10.3390/electronics10182250 fatcat:xxbfslyes5ctpfktnprezb6p6m

Iterative local dynamic programming

Emanuel Todorov, Yuval Tassa
2009 2009 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning  
We develop an iterative local dynamic programming method (iLDP) applicable to stochastic optimal control problems in continuous high-dimensional state and action spaces.  ...  we use general basis functions rather than quadratics to approximate the optimal value function; (b) we introduce a collocation method that dispenses with explicit differentiation of the cost and dynamics  ...  In Fig 2 we show the solution to simple obstacle avoidance task, under deterministic and stochastic conditions.  ... 
doi:10.1109/adprl.2009.4927530 dblp:conf/adprl/TodorovT09 fatcat:sk3rytm3gjgsfh6dghdaoxxdhe

On the synthesis of driver inputs for the simulation of closed-loop handling manoeuvres

T.J. Gordon, M.C. Best
2006 International Journal of Vehicle Design  
GENERALISED OPTIMAL CONTROL Generalized Optimal Control (GOC) is an independent approach to providing driver inputs for the 'optimal' obstacle avoidance problem, and is used here to provide a baseline  ...  An early version of this method was presented previously though in a different context and with a general application to lap optimization rather than obstacle avoidance.  ... 
doi:10.1504/ijvd.2006.008453 fatcat:7rkcugdnhvhtbpuv6h5lvboxga

Online deformation of optimal trajectories for constrained nonprehensile manipulation

Alexander Pekarovskiy, Thomas Nierhoff, Jochen Schenek, Yoshihiko Nakamura, Sandra Hirche, Martin Buss
2015 2015 IEEE International Conference on Robotics and Automation (ICRA)  
By creating optimal trajectories offline and deforming them online, computational complexity during execution is reduced considerably.  ...  This paper discusses an online dynamic motion generation scheme for nonprehensile object manipulation by using a set of predefined motions and a trajectory deformation algorithm capable of incorporating  ...  ACKNOWLEDGMENT This work is supported in part within the ERC Advanced Grant SHRINE Agreement No. 267877 (www.shrineproject.eu) and in part by the Technische Universität München -Institute for Advanced  ... 
doi:10.1109/icra.2015.7139531 dblp:conf/icra/PekarovskiyNSNH15 fatcat:kek5txozrrf6thhobdikameaui

Reward-Adaptive Reinforcement Learning: Dynamic Policy Gradient Optimization for Bipedal Locomotion [article]

Changxin Huang, Guangrun Wang, Zhibo Zhou, Ronghui Zhang, Liang Lin
2021 arXiv   pre-print
Controlling a non-statically bipedal robot is challenging due to the complex dynamics and multi-criterion optimization involved.  ...  In this work, we propose a novel reward-adaptive reinforcement learning for biped locomotion, allowing the control policy to be simultaneously optimized by multiple criteria using a dynamic mechanism.  ...  avoid the abnormal states, such as falling down, XK over-torque and strange posture.  ... 
arXiv:2107.01908v2 fatcat:ey2t3vncprayzmvh2h3otk7hru

Efficient Trajectory Planning for UAVs Using Hierarchical Optimization

Shikai Shao, Chenglong He, Yuanjie Zhao, Xiaojing Wu
2021 IEEE Access  
The main challenge is to avoid collisions with environmental obstacles and other members and to provide a capable guidance for the tracking control system.  ...  One can see that the trajectories generated by IPSO-GPM are all flyable and can avoid conflicting with obstacles, while those by GPM with 30 and 50 collocation points conflict with the obstacles.  ... 
doi:10.1109/access.2021.3073420 fatcat:vwzyizh26jfypfgenll7zj2boi

Online Motion Planning based on Nonlinear Model Predictive Control with Non-Euclidean Rotation Groups [article]

Christoph Rösmann, Artemi Makarow, Torsten Bertram
2020 arXiv   pre-print
Realizations include but are not limited to quadratic form and time-optimal objectives.  ...  This paper proposes a novel online motion planning approach to robot navigation based on nonlinear model predictive control. Common approaches rely on pure Euclidean optimization parameters.  ...  Our provided open-source C++ MPC framework with ROS integration is highly modular, versatile and computationally efficient.  ... 
arXiv:2006.03534v1 fatcat:trqroetg55fzdbnoz4ewevl4zm

PYROBOCOP : Python-based Robotic Control Optimization Package for Manipulation and Collision Avoidance [article]

Arvind U. Raghunathan, Devesh K. Jha, Diego Romeres
2021 arXiv   pre-print
PYROBOCOP is a lightweight Python-based package for control and optimization of robotic systems described by nonlinear Differential Algebraic Equations (DAEs).  ...  In particular, the package can handle systems with contacts that are described by complementarity constraints and provides a general framework for specifying obstacle avoidance constraints.  ...  The dynamics provided by the user to create a MPCC which is then optimized using IPOPT and the gradients are evaluated using automatic differentiation via ADOL-C.  ... 
arXiv:2106.03220v1 fatcat:mqgfeztidvfcvp2du5h2brnp2a

Walking, Running and Kicking of Humanoid Robots and Humans [chapter]

M. Stelzer, O. von Stryk
2008 From Nano to Space  
Numerical and experimental results are presented for modelbased optimal control as well as for hardware-in-the-loop optimization of humanoid robot walking and for forward dynamics simulation and optimization  ...  In this paper key aspects and several methods for modeling, simulation, optimization and control of the locomotion of humanoid robots and humans are discussed.  ...  The successful investigation of the methods and case studies presented in this paper would not have been possible without the major contributions of the following coauthors whose most valuable contributions  ... 
doi:10.1007/978-3-540-74238-8_14 fatcat:oxpbrtbhkjbmvai6u7ejw6xw4m
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