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Bring the Heat: Rapid Trajectory optimization With Pseudospectral Techniques and the Affine Geometric Heat Flow Equation

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IEEE ROBOTICS AND AUTOMATION LETTERS 2025年第4期10卷 4148-4155页

作者： Adu, Challen Enninful Chuquiure, Cesar E. Ramos Zhang, Bohao Vasudevan, Ram Univ Michigan Robot Dept Ann Arbor MI 48109 USA

Generating optimal trajectories for high-dimensional robotic systems in a time-efficient manner while adhering to constraints is a challenging task. This letter introduces PHLAME, which applies pseudospectral collocation and spatial vector algebra to efficiently solve the Affine Geometric Heat Flow (AGHF) Partial Differential Equation (PDE) for trajectory optimization. Computing a solution to the AGHF PDE scales efficiently because its solution is defined over a two-dimensional domain. To solve the AGHF one usually applies the Method of Lines (MOL), which works by discretizing one variable of the AGHF PDE, effectively converting the PDE into a system of ordinary differential equations (ODEs) that can be solved using standard time-integration methods. Though powerful, this method requires a fine discretization to generate accurate solutions and still requires evaluating the AGHF PDE which can be computationally expensive for high-dimensional systems. PHLAME overcomes this deficiency by using a pseudospectral method, which reduces the number of function evaluations required to obtain a high-accuracy solution. To further increase computational speed, this letter presents analytical expressions for the AGHF which can be computed efficiently using rigid body dynamics algorithms. The proposed method PHLAME is tested across various dynamical systems, with and without obstacles and compared to a number of state-of-the-art techniques. PHLAME is able to generate trajectories for a 44-dimensional state-space system in $\sim 5$ seconds.

关键词： Heuristic algorithms Heating systems Robots Trajectory optimization Vectors Partial differential equations Dynamic programming Planning optimal control Faces optimization and optimal control motion and path planning integrated planning and control

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Robust and topology-aware motion planning with moving obstacles

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INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2025年

作者： Rousseas, Panagiotis Panagou, Dimitra Kyriakopoulos, Kostas J. Natl Tech Univ Athens Sch Mech Engn Control Syst Lab Athens Greece Univ Michigan Dept Robot Dept Aerosp Engn Ann Arbor MI USA NYU Ctr AI & Robot CAIR Abu Dhabi U Arab Emirates

A novel robust solution to motion planning in the presence of moving obstacles is presented in this paper. The proposed method addresses the uncertainty in the robot state estimate, as well as in the estimate of the a-priori unknown obstacles motion. Our scheme employs the globally optimal state-feedback velocity field for static workspaces and exploits its topological properties to enable moving obstacles avoidance. In contrast to previous relevant contributions, our method tackles polygonal obstacles and accounts for both the obstacles geometry and the approximate motion profile to extract a reactive solution. Furthermore, the proposed kinematic planner is extended to a class of second-order systems. Our multi-layered approach integrates robust safety filtering and exhibits superior performance w.r.t. relevant methods. In summary, this work consists an important step towards bridging the gap between open-loop planning and state-feedback control.

关键词： Motion and path planning optimization and optimal control obstacle avoidance

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Sensitivity-Aware Model Predictive control for Robots With Parametric Uncertainty

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IEEE TRANSACTIONS ON ROBOTICS 2025年 41卷 3039-3058页

作者： Belvedere, Tommaso Cognetti, Marco Oriolo, Giuseppe Giordano, Paolo Robuffo Univ Rennes CNRS IRISA Inria Campus Beaulieu F-35042 Rennes France Univ Toulouse UPS LAAS CNRS F-31031 Toulouse 4 France Sapienza Univ Roma Dipartimento Ingn Informat Automat & Gest I-00185 Rome Italy

This article introduces a computationally efficient robust model predictive control (MPC) scheme for controlling nonlinear systems affected by parametric uncertainties in their models. The approach leverages the recent notion of closed-loop state sensitivity and the associated ellipsoidal tubes of perturbed trajectories for taking into account online time-varying restrictions on state and input constraints. This makes the MPC controller "aware" of potential additional requirements needed to cope with parametric uncertainty, thus significantly improving the tracking performance and success rates during navigation in constrained environments. One key contribution lies in the introduction of a computationally efficient robust MPC formulation with a comparable computational complexity to a standard MPC (i.e., an MPC not explicitly dealing with parametric uncertainty). An extensive simulation campaign is presented to demonstrate the effectiveness of the proposed approach in handling parametric uncertainties and enhancing task performance, safety, and overall robustness. Furthermore, we also provide an experimental validation that shows the feasibility of the approach in real-world conditions and corroborates the statistical findings of the simulation campaign. The versatility and efficiency of the proposed method make it therefore a valuable tool for real-time control of robots subject to nonnegligible uncertainty in their models.

关键词： Robots Uncertainty Trajectory Sensitivity Robot sensing systems Robustness Planning optimization Navigation Computational efficiency Aerial systems mechanics and control model predictive control (MPC) optimization and optimal control robust/adaptive control of robotic systems

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A Novel Bio-Inspired optimal control Strategy of Heavy-Duty Robots Considering Leg Momentum 17th

A Novel Bio-Inspired Optimal Control Strategy of Heavy-Duty ...

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17th International Conference on Intelligent Robotics and Applications

作者： Qian, Letian Lin, Weixian Chen, Junjie Xu, Zhanhao Luo, Xin Huazhong Univ Sci & Technol Wuhan 430074 Peoples R China

ISBN: (纸本)9789819607976;9789819607983

Heavy-duty legged robots often have robust legs to effectively bear the load. The considerable mass of these robust legs makes agile movements challenging for heavy-duty robots because the legs need to remain as agile as possible without exceeding the actuators' capacity. Animals with robust legs tend to minimize changes in body momentum and leg momentum during rapid running to achieve higher movement efficiency and effectively prevent joint damage. Inspired by this biological locomotion characteristic, we adopted a motion generation criterion based on minimizing leg momentum changes to further optimize the movement of heavy-duty legged robots. This criterion is formulated as a cost function of leg center of mass momentum and incorporated into an optimal control problem (OCP) based on full-kinematics and centroidal dynamics. We derive the Leg Centroidal Momentum Matrix (LCMM) and validate our method through simulations, demonstrating effectiveness across various gaits. Results indicate that using leg centroidal momentum as a cost function reduces the drive forces required for diverse movements.

关键词： Legged Robots Centroidal Dynamics optimization and optimal control Bio-inspired

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Bionic Jumping of Humanoid Robot via Online Centroid Trajectory optimization and High Dynamic Motion controller

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Journal of Bionic Engineering 2024年第6期21卷 2759-2778页

作者： Xiangji Wang Wei Guo Zhicheng He Rongchao Li Fusheng Zha Lining Sun State Key Laboratory of Robotics and System Harbin Institute of Technology(HIT)Harbin150001China Faculty of Computing Harbin Institute of Technology(HIT)Harbin150001China

The dynamic motion capability of humanoid robots is a key indicator for evaluating their ***,as a typical dynamic motion,is of great significance for enhancing the robot’s flexibility and terrain adaptability in unstructured ***,achieving high-dynamic jumping control of humanoid robots has become a challenge due to the high degree of freedom and strongly coupled dynamic *** idea for this paper originated from the human response process to jumping commands,aiming to achieve online trajectory optimization and jumping motion control of humanoid ***,we employ nonlinear optimization in combination with the Single Rigid Body Model(SRBM)to generate a robot’s Center of Mass(CoM)trajectory that complies with physical constraints and minimizes the angular momentum of the ***,a Model Predictive controller(MPC)is designed to track and control the CoM trajectory,obtaining the required contact forces at the robot’s ***,a Whole-Body controller(WBC)is used to generate full-body joint motion trajectories and driving torques,based on the prioritized sequence of tasks designed for the jumping *** control framework proposed in this paper considers the dynamic characteristics of the robot’s jumping process,with a focus on improving the real-time performance of trajectory optimization and the robustness of *** and experimental results demonstrate that our robot successfully executed high jump motions,long jump motions and continuous jump motions under complex working conditions.

关键词： Humanoid robots Jumping motion control Centroid trajectory optimization optimization and optimal control

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How-to Augmented Lagrangian on Factor Graphs

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IEEE ROBOTICS AND AUTOMATION LETTERS 2024年第3期9卷 2806-2813页

作者： Bazzana, Barbara Andreasson, Henrik Grisetti, Giorgio Sapienza Univ Rome Dept Comp Control & Management Engn Antonio Rubert I-00185 Rome Italy Orebro Univ Ctr Appl Autonomous Sensor Syst AASS S-70182 Orebro Sweden

Factor graphs are a very powerful graphical representation, used to model many problems in robotics. They are widely spread in the areas of Simultaneous Localization and Mapping (SLAM), computer vision, and localization. However, the physics of many real-world problems is better modeled through constraints, e.g., estimation in the presence of inconsistent measurements, or optimal control. Constraints handling is hard because the solution cannot be found by following the gradient descent direction as done by traditional factor graph solvers. The core idea of our method is to encapsulate the Augmented Lagrangian (AL) method in factors that can be integrated straightforwardly in existing factor graph solvers. Besides being a tool to unify different robotics areas, the modularity of factor graphs allows to easily combine multiple objectives and effectively exploiting the problem structure for efficiency. We show the generality of our approach by addressing three applications, arising from different areas: pose estimation, rotation synchronization and Model Predictive control (MPC) of a pseudo-omnidirectional platform. We implemented our approach using C++ and ROS. Application results show that we can favorably compare against domain specific approaches.

关键词： optimization Robots Computational modeling Trajectory Simultaneous localization and mapping Synchronization optimal control Localization integrated planning and control optimization and optimal control

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Bundled Gradients Through Contact Via Randomized Smoothing

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IEEE ROBOTICS AND AUTOMATION LETTERS 2022年第2期7卷 4000-4007页

作者： Suh, Hyung Ju Terry Pang, Tao Tedrake, Russ MIT CSAIL Cambridge MA 02139 USA

The empirical success of derivative-free methods in reinforcement learning for planning through contact seems at odds with the perceived fragility of classical gradient-based optimization methods in these domains. What is causing this gap, and how might we use the answer to improve gradient-based methods? We believe a stochastic formulation of dynamics is one crucial ingredient. We use tools from randomized smoothing to analyze sampling-based approximations of the gradient, and formalize such approximations through the bundled gradient. We show that using the bundled gradient in lieu of the gradient mitigates fast-changing gradients of non-smooth contact dynamics modeled by the implicit time-stepping, or the penalty method. Finally, we apply the bundled gradient to optimal control using iterative MPC, introducing a novel algorithm which improves convergence over using exact gradients. Combining our algorithm with a convex implicit time-stepping formulation of contact, we show that we can tractably tackle planning-through-contact problems in manipulation.

关键词： Smoothing methods Planning optimization Convergence optimal control Monte Carlo methods Stochastic processes Contact modeling manipulation planning optimization and optimal control

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Underactuated Motion Planning and control for Jumping With Wheeled-Bipedal Robots

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IEEE ROBOTICS AND AUTOMATION LETTERS 2021年第2期6卷 747-754页

作者： Chen, Hua Wang, Bingheng Hong, Zejun Shen, Cong Wensing, Patrick M. Zhang, Wei Southern Univ Sci & Technol Dept Mech & Energy Engn Shenzhen 518055 Peoples R China Natl Univ Singapore Dept Elect & Comp Engn Singapore 117583 Singapore Univ Notre Dame Dept Aerosp & Mech Engn Notre Dame IN 46556 USA Peng Cheng Lab Shenzhen 201315 Peoples R China

This letter studies jumping for wheeled-bipedal robots, a motion that takes full advantage of the benefits from the hybrid wheeled and legged design features. A comprehensive hierarchical scheme for motion planning and control of jumping with wheeled-bipedal robots is developed. Underactuation of the wheeled-bipedal dynamics is the main difficulty to be addressed, especially in the planning problem. To tackle this issue, a novel wheeled-spring-loaded inverted pendulum (W-SLIP) model is proposed to characterize the essential dynamics of wheeled-bipedal robots during jumping. Relying on a differential-flatness-like property of the W-SLIP model, a tractable quadratic programming based solution is devised for planning jumping motions for wheeled-bipedal robots. Combined with a kinematic planning scheme accounting for the flight phase motion, a complete planning scheme for the W-SLIP model is developed. To enable accurate tracking of the planned trajectories, a linear quadratic regulator based wheel controller and a task-space whole-body controller for the other joints are blended through disturbance observers. The overall planning and control scheme is validated using V-REP simulations of a prototype wheeled-bipedal robot.

关键词： Robots Mobile robots Planning Wheels Dynamics Load modeling Legged locomotion optimization and optimal control underactuated robots whole-body motion planning and control

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Time-optimal Path Tracking for Jerk controlled Robots

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IEEE ROBOTICS AND AUTOMATION LETTERS 2019年第4期4卷 3932-3939页

作者： Palleschi, Alessandro Garabini, Manolo Caporale, Danilo Pallottino, Lucia Univ Pisa Res Ctr Enrico Piaggio I-56126 Pisa Italy Univ Pisa Dipartimento Ingn Informaz I-56126 Pisa Italy

This letter presents a new approach to solve the time-optimal path tracking under limited joint range and bounds on velocity, acceleration, and jerk. To obtain smooth and continuous accelerations, with beneficial effects for the load and wear on the actuators but a limited impact on performance, we state the minimum-time path tracking problem with the jerk as the control input. The main contribution of this letter is a formulation that includes the jerk constraints in the optimization problem and that, even if the resulting non-linear programming problem is non-convex, allows to perform an efficient and reliable convex relaxation using McCormick envelopes. Simulations and experimental tests on two 7-DoF manipulators have been carried out to show the benefits of the proposed approach and to compare it to state-of-the-art techniques.

关键词： Motion and path planning optimization and optimal control motion control

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optimal Design of Continuum Robots With Reachability Constraints

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IEEE ROBOTICS AND AUTOMATION LETTERS 2021年第2期6卷 3902-3909页

作者： Cheong, Hyunmin Ebrahimi, Mehran Duggan, Timothy Autodesk Inc Autodesk Res Toronto ON M5G 1M1 Canada Otherlab Inc San Francisco CA 94017 USA

While multi-joint continuum robots are highly dexterous and flexible, designing an optimal robot can be challenging due to its kinematics involving curvatures. Hence, the current work presents a computational method developed to find optimal designs of continuum robots, given reachability constraints. First, we leverage both forward and inverse kinematic computations to perform reachability analysis in an efficient yet accurate manner. While implementing inverse kinematics, we also integrate torque minimization at joints such that robot configurations with the minimum actuator torque required to reach a given workspace could be found. Lastly, we apply an estimation of distribution algorithm (EDA) to find optimal robot dimensions while considering reachability, where the objective function could be the total length of the robot or the actuator torque required to operate the robot. Through three application problems, we show that the EDA is superior to a genetic algorithm (GA) in finding better solutions within a given number of iterations, as the objective values of the best solutions found by the EDA are 4-15% lower than those found by the GA.

关键词： Kinematics methods and tools for robot system design optimization and optimal control soft robot applications

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