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Volkan Patoglu

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22 papers
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22

IJCAI Conference 2024 Conference Paper

Hybrid planning for challenging construction problems: An Answer Set Programming approach (Abstract Reprint)

  • Faseeh Ahmad
  • Volkan Patoglu
  • Esra Erdem

We study construction problems where multiple robots rearrange stacks of prefabricated blocks to build stable structures. These problems are challenging due to ramifications of actions, true concurrency, and requirements of supportedness of blocks by a surface or a robot and stability of the overall structure at all times. We propose a general elaboration tolerant method to solve a wide range of construction problems, based on the knowledge representation and reasoning paradigm of Answer Set Programming. This method not only (i) determines a stable final configuration of the structure, but also (ii) computes the order of manipulation tasks for multiple autonomous robots to build the structure from an initial configuration, (iii) while simultaneously ensuring the requirements of supportedness and stability at all times. We prove the soundness and completeness of our method with respect to these properties. We introduce a set of challenging construction benchmark instances, including construction of (uneven) bridges and overhangs, and discuss the usefulness of our framework over these instances. Furthermore, we perform experiments to investigate the computational performance of our hybrid method, and demonstrate the applicability of our method using a bimanual Baxter robot.

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AIJ Journal 2023 Journal Article

Hybrid planning for challenging construction problems: An Answer Set Programming approach

  • Faseeh Ahmad
  • Volkan Patoglu
  • Esra Erdem

We study construction problems where multiple robots rearrange stacks of prefabricated blocks to build stable structures. These problems are challenging due to ramifications of actions, true concurrency, and requirements of supportedness of blocks by a surface or a robot and stability of the overall structure at all times. We propose a general elaboration tolerant method to solve a wide range of construction problems, based on the knowledge representation and reasoning paradigm of Answer Set Programming. This method not only (i) determines a stable final configuration of the structure, but also (ii) computes the order of manipulation tasks for multiple autonomous robots to build the structure from an initial configuration, (iii) while simultaneously ensuring the requirements of supportedness and stability at all times. We prove the soundness and completeness of our method with respect to these properties. We introduce a set of challenging construction benchmark instances, including construction of (uneven) bridges and overhangs, and discuss the usefulness of our framework over these instances. Furthermore, we perform experiments to investigate the computational performance of our hybrid method, and demonstrate the applicability of our method using a bimanual Baxter robot.

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ICRA Conference 2020 Conference Paper

A Variable-Fractional Order Admittance Controller for pHRI

  • Doganay Sirintuna
  • Yusuf Aydin
  • Ozan Çaldiran
  • Ozan Tokatli
  • Volkan Patoglu
  • Cagatay Basdogan

In today's automation driven manufacturing environments, emerging technologies like cobots (collaborative robots) and augmented reality interfaces can help integrating humans into the production workflow to benefit from their adaptability and cognitive skills. In such settings, humans are expected to work with robots side by side and physically interact with them. However, the trade-off between stability and transparency is a core challenge in the presence of physical human robot interaction (pHRI). While stability is of utmost importance for safety, transparency is required for fully exploiting the precision and ability of robots in handling labor intensive tasks. In this work, we propose a new variable admittance controller based on fractional order control to handle this trade-off more effectively. We compared the performance of fractional order variable admittance controller with a classical admittance controller with fixed parameters as a baseline and an integer order variable admittance controller during a realistic drilling task. Our comparisons indicate that the proposed controller led to a more transparent interaction compared to the other controllers without sacrificing the stability. We also demonstrate a use case for an augmented reality (AR) headset which can augment human sensory capabilities for reaching a certain drilling depth otherwise not possible without changing the role of the robot as the decision maker.

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IROS Conference 2018 Conference Paper

A Series Elastic Brake Pedal to Preserve Conventional Pedal Feel under Regenerative Braking

  • Umut Caliskan
  • Ardan Apaydin
  • Ata Otaran
  • Volkan Patoglu

We propose a force-feedback brake pedal with series elastic actuation to preserve the conventional brake pedal feel during cooperative regenerative braking. The novelty of the proposed design is due to the deliberate introduction of a compliant element between the actuator and the brake pedal whose deflections are measured to estimate interaction forces and to perform closed-loop force control. Thanks to its series elasticity, the force-feedback brake pedal can utilize robust controllers to achieve high fidelity force control, possesses favorable output impedance characteristics over the entire frequency spectrum, and can be implemented in a compact package using low-cost components. The applicability and effectiveness of the proposed series elastic brake pedal have been tested through human subject experiments that evaluate simulated cooperative regenerative braking scenarios with and without pedal feel compensation. The experimental results and responses to the accompanying questionnaire indicate that pedal feel compensation through the series elastic brake pedal can significantly decrease hard braking instances, improving safety and driver experience.

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IROS Conference 2017 Conference Paper

A systematic analysis of spring symmetry on optimality of antagonistic variable stiffness actuation

  • Abdullah Kamadan
  • Güllü Kiziltas
  • Volkan Patoglu

We present a systematic co-design optimization framework that enables comparison of antagonist variable stiffness actuators (VSA) with and without spring symmetry constraints. The proposed framework promotes a fair comparative analysis by maintaining design continuity among system-optimal designs of symmetric and asymmetric VSA configurations. Through a case study of a VSA-powered knee prosthesis, we not only demonstrate that co-design of robots driven by VSAs can provide important performance benefits with respect to sub-system level control-optimal designs, but also provide evidence that relaxing symmetry constraints for certain periodic tasks can result in substantial advantages in performance. Our systematic comparative analysis justifies the use of asymmetric stiffness arrangements for antagonistic VSA-powered robotic systems performing periodic tasks.

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IROS Conference 2016 Conference Paper

A six degrees of freedom haptic interface for laparoscopic training

  • Wisdom C. Agboh
  • Mustafa Yalcin
  • Volkan Patoglu

We present the novel kinematics, workspace characterization, functional prototype and impedance control of a six degrees of freedom haptic interface designed to train surgeons for laparoscopic procedures, through virtual reality simulations. The parallel kinematics of the device is constructed by connecting a 3RRP planar parallel mechanism to a linearly actuated modified delta mechanism with a connecting link. The configuration level forward and inverse kinematics of the device assume analytic solutions, while its workspace can be shaped to enable large end-effector translations and rotations, making it well-suited for laparoscopy operations. Furthermore, the haptic interface features a low apparent inertia with high structural stiffness, thanks to its parallel kinematics with grounded actuators. A model-based open-loop impedance controller with feed-forward gravity compensation has been implemented for the device and various virtual tissue/organ stiffness levels have been rendered.

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IROS Conference 2016 Conference Paper

GRAVITY-ASSIST: A series elastic body weight support system with inertia compensation

  • Hammad Munawar
  • Volkan Patoglu

We present GRAVITY-ASSIST, a series elastic active body weight support and inertia compensation system for use in robot assisted gait rehabilitation. The device consists of a single degree of freedom series elastic actuator that connects to the trunk of a patient. The series elastic system is novel in that, it can provide the desired level of dynamic unloading such that the patient experiences only a percentage of his/her weight and inertia. Inertia compensation is important, since the inertial forces can cause significant deviations from the desired unloading force, specially at low support forces and fast walking speeds. Furthermore, this feature enables the inertia of the harness and force sensing unit attached to the patient to be compensated for, making sure that the device does not interfere with the natural gait cycle. We present a functional prototype of the device, its characterization and experimental verification of the approach.

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ICRA Conference 2016 Conference Paper

Redundant kinematics and workspace centering control of AssistOn-Gait overground gait and balance trainer

  • Hammad Munawar
  • Mustafa Yalcin
  • Volkan Patoglu

We present the redundant kinematics and workspace centering control of AssistOn-Gait, an overground gait and balance trainer designed to deliver pelvis-hip exercises to correct compensatory movements arising from abnormal gait patterns. AssistOn-Gait consists of an impedance controlled pelvis-hip exoskeleton module, supported by a motion controlled holonomic mobile platform. The exoskeleton module possesses 7 active degrees of freedom to independently control the rotation of the each hip in the sagittal plane along with the pelvic tilt, pelvic rotation and the horizontal, vertical and lateral displacements of the pelvis. The holonomic mobile base can track the movements of patients on flat surfaces, allowing patients to walk naturally, start/stop motion, vary their speed, sidestep to maintain balance and turn to change their walking direction. The kinematics of AssistOn-Gait is redundant, as the exoskeleton module spans all the degrees of freedom covered by the mobile platform. The device features dual layer actuation, since the exoskeleton module is designed for force control with good transparency, while the mobile base is designed for motion control to carry the weight of the patient and the exoskeleton. The kinematically redundant dual layer actuation enables the mobile base of the system to be controlled using workspace centering control strategy without the need for any additional sensors, since the patient movements are readily measured by the exoskeleton module. The workspace centering controller ensures that the workspace limits of the exoskeleton module are not reached, decoupling the dynamics of the mobile base from the exoskeleton dynamics. Consequently, AssistOn-Gait possesses virtually unlimited workspace, while featuring the same output impedance and force rendering performance as its exoskeleton module

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ICRA Conference 2015 Conference Paper

Integrating hybrid diagnostic reasoning in plan execution monitoring for cognitive factories with multiple robots

  • Esra Erdem 0001
  • Volkan Patoglu
  • Zeynep G. Saribatur

For reliable and fault tolerant operation of cognitive factories, we introduce an algorithm to monitor plan executions. According to this algorithm, when some changes or discrepancies are detected, appropriate decisions are given based on the causes of these changes or discrepancies. To identify these causes (e. g. , broken robots or robot components), we introduce a novel diagnostic reasoning method which synergistically integrates hypothetical reasoning, geometric reasoning, and learning from earlier experiences. Based on these causes, if necessary, new hybrid plans (task plans integrated with feasibility checks) are computed to reach the manufacturing goals by allowing repairs of robots/components. The results of our experiments over reasonably-sized cognitive factory scenarios show the usefulness of (i) diagnostic reasoning for execution monitoring, (ii) allowing repair actions during replanning, and (iii) learning from experiences. We provide a video of dynamic simulation of our execution monitoring algorithm with Kuka youBots and a Nao humanoid robot as the supplementary material.

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IROS Conference 2015 Conference Paper

Stability of haptic systems with fractional order controllers

  • Ozan Tokatli
  • Volkan Patoglu

Fractional order calculus is a generalization of the familiar integer order calculus in that, it allows for differentiation/integration with orders of any real number. The use of fractional order calculus in systems and control applications provides the user an extra design variable, the order of differointegration, which can be tuned to improve the desired behavior of the overall system. We propose utilization of fractional order models/controllers in haptic systems and study the effect of fractional differentiation order on the stability robustness of the overall sampled-data system. Our results demonstrate that fractional calculus generalization has a significant impact on both the shape and area of stability region of a haptic system and inclusion of fractional order impedances may improve the stability robustness of haptic rendering. Our results also include experimental verification of the stability regions predicted by the theoretical analysis.

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IROS Conference 2014 Conference Paper

Cognitive factories with multiple teams of heterogeneous robots: Hybrid reasoning for optimal feasible global plans

  • Zeynep G. Saribatur
  • Esra Erdem 0001
  • Volkan Patoglu

We consider cognitive factories with multiple teams of heterogenous robots, and address two key challenges of these domains, hybrid reasoning for each team and finding an optimal global plan (with minimum makespan) for multiple teams. For hybrid reasoning, we propose (i) modeling each team's workspace taking into account capabilities of heterogeneous robots, (ii) embedding continuous external computations into discrete symbolic representation and reasoning by combining different methods of integration, (iii) not only optimizing the makespans of local plans but also minimizing the total cost of robotic actions, where costs of actions can be defined in various ways. To find a global plan with minimum makespan, we propose a semi-distributed approach: we formulate the problem of finding an optimal coordination of teams that can help each other, prove its intractability, and describe how to solve this problem using existing automated reasoners. As a case study, we show applications of our hybrid reasoning and coordination approaches on a cognitive toy factory with dynamic simulations and physical implementation utilizing KuKa youBots and Lego NXT robots (supplementary video provided). We also present experimental results to discuss the scalability of these methods.

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AAAI Conference 2014 Conference Paper

Coordination of Multiple Teams of Robots for an Optimal Global Plan

  • Zeynep Saribatur
  • Esra Erdem
  • Volkan Patoglu

We consider multiple teams of heterogeneous robots, where each team is given a feasible task to complete in its workspace on its own, and where teams are allowed to transfer robots between each other. We study the problem of finding a coordination of robot transfers between teams to ensure an optimal global plan (with minimum makespan) so that all tasks can be completed as soon as possible by helping each other. We propose to solve this problem using answer set programming.

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ICRA Conference 2014 Conference Paper

Geometric rearrangement of multiple movable objects on cluttered surfaces: A hybrid reasoning approach

  • Giray Havur
  • Guchan Ozbilgin
  • Esra Erdem 0001
  • Volkan Patoglu

We introduce a novel computational method for geometric rearrangement of multiple movable objects on a cluttered surface, where objects can change locations more than once by pick and/or push actions. This method consists of four stages: (i) finding tentative collision-free final configurations for all objects (all the new objects together with all other objects in the clutter) while also trying to minimize the number of object relocations, (ii) gridization of the continuous plane for a discrete placement of the initial configurations and the tentative final configurations of objects on the cluttered surface, (iii) finding a sequence of feasible pick and push actions to achieve the final discrete placement for the objects in the clutter from their initial discrete place, while simultaneously minimizing the number of object relocations, and (iv) finding feasible final configurations for all objects according to the optimal task plan calculated in stage (iii). For (i) and (iv), we introduce algorithms that utilize local search with random restarts; for (ii), we introduce a mathematical modeling of the discretization problem and use the state-of-the-art ASP reasoners to solve it; for (iii) we introduce a formal hybrid reasoning framework that allows embedding of geometric reasoning in task planning, and use the expressive formalisms and reasoners of ASP. We illustrate the usefulness of our integrated AI approach with several scenarios that cannot be solved by the existing approaches. We also provide a dynamic simulation for one of the scenarios, as supplementary material.

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ICRA Conference 2013 Conference Paper

A case study on the Tower of Hanoi challenge: Representation, reasoning and execution

  • Giray Havur
  • Kadir Haspalamutgil
  • Can Palaz
  • Esra Erdem 0001
  • Volkan Patoglu

The Tower of Hanoi puzzle, has recently been established as a robotics challenge as a part of EU Robotics coordination action in 2011 and IEEE IROS Conference in 2012. It provides a good standardized test bed to evaluate integration of high-level reasoning capabilities of robots together with their manipulation and perception aspects. We address this challenge within a general planning and monitoring framework: we represent the puzzle in a logic-based formalism, integrate task planning and motion planning, solve this hybrid planning problem with a state-of-the-art automated reasoner (e. g. , a SAT solver), execute the computed plans under feedback control while also monitoring for failures, and recover from failures as required. We show the applicability of this framework by implementing it using two robotic manipulators on a physical experimental setup.

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IROS Conference 2013 Conference Paper

AssistOn-Knee: A self-aligning knee exoskeleton

  • Besir Celebi
  • Mustafa Yalcin
  • Volkan Patoglu

We present kinematics, actuation, detailed design, characterization results and initial user evaluations of AssistOn-Knee, a novel self-aligning active exoskeleton for robot-assisted knee rehabilitation. AssistOn-Knee can, not only assist flexion/extension movements of the knee joint but also accommodate its translational movements in the sagittal plane. Automatically aligning its joint axes, AssistOn-Knee enables an ideal match between human knee axis and the exoskeleton axis, guaranteeing ergonomy and comfort throughout the therapy. Self-aligning feature significantly shortens the setup time required to attach the patient to the exoskeleton, allowing more effective time spent on exercises. The proposed exoskeleton actively controls the rotational degree of freedom of the knee through a Bowden cable-driven series elastic actuator, while the translational movements of the knee joints are passively accommodated through use of a 3 degrees of freedom planar parallel mechanism. AssistOn-Knee possesses a lightweight and compact design with significantly low apparent inertia, thanks to its Bowden cable based transmission that allows remote location of the actuator and reduction unit. Furthermore, thanks to its series-elastic actuation, AssistOn-Knee enables high-fidelity force control and active backdrive-ability within its control bandwidth, while featuring passive elasticity for excitations above this bandwidth, ensuring safety and robustness throughout the whole frequency spectrum.

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IROS Conference 2013 Conference Paper

VnSA: Variable negative stiffness actuation based on nonlinear deflection characteristics of buckling beams

  • Mustafa Yalcin
  • Bircan Uzunoglu
  • Elif Altintepe
  • Volkan Patoglu

We present variable negative stiffness actuation (VnSA), an alternative method of achieving variable stiffness actuation based on the nonlinear deflection characteristics of buckling beams. The approach exploits transverse stiffness variations of axially loaded beams around their critical buckling load to achieve an actuator with adjustable stiffness. In particular, transverse stiffness of buckled beams are positive under tensile loading and for compressive loading below their first critical buckling load, while they display negative stiffness above this critical value. Furthermore, for small deflections transverse stiffness of buckled beams depends linearly on the amount of axial loading. Consequently, the stiffness of a variable stiffness actuator can be modulated (i) by decreasing the transverse stiffness through an increase of the axial compressive loading on a beam, up to values above the first critical buckling load where the overall stiffness of the actuator approaches its lowest negative value, and (ii) by increasing the transverse stiffness through application of tensile axial loading. Capitalizing on the concept of negative stiffness, the lowest stiffness of VnSA can be set arbitrarily close to zero or even to negative values (when counterbalanced), while very high stiffness values are also achievable by tensile loading of the beam. As a result, VnSA can modulate its stiffness over a uniquely large range that includes zero and negative stiffness values. Furthermore, thanks to the negative stiffness characteristics, the stiffness of VnSA can be kept very low without sacrificing the mechanical integrity and load bearing capacity of the actuator. We introduce the design of VnSA, theoretically analyze its stiffness modulation response, and provide implementation details of a prototype. We also provide experimental results detailing range of stiffness modulation and force tracking performance achieved with this prototype and discuss its correspondence with the theory.

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ICRA Conference 2012 Conference Paper

ASSISTON-SE: A self-aligning shoulder-elbow exoskeleton

  • Mehmet Alper Ergin
  • Volkan Patoglu

We present AssistOn-SE: , a novel powered exoskeleton for robot-assisted rehabilitation that allows for movements of the shoulder girdle as well as shoulder rotations. Automatically adjusting its joint axes, AssistOn-SE: can enable a perfect match between human joint axes and the device axes, not only guaranteeing ergonomy and comfort throughout the therapy, but also extending the usable range of motion for the shoulder joint. Moreover, the adjustability feature significantly shortens the setup time required to attach the patient to the exoskeleton, allowing more effective time be spend on exercises instead of wasting this valuable resource for adjustments. Back-driveable design of AssistOn-SE: supports both passive translational movements of the center of glenohumeral joint and independent active control of these degrees of freedom. Thanks to this property, glenohumeral mobilization and scapular stabilization exercises can also be delivered with AssistOn-SE: , extending the type of therapies that can be administered using upper-arm exoskeletons. We introduce the design of the exoskeleton and present the kinematic analysis of its self-aligning joint. We also provide implementation details for an early prototype as well as some experimental results detailing range of motion of the device and its ability to track movements of the shoulder girdle.

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IROS Conference 2012 Conference Paper

Slacking prevention during assistive contour following tasks with guaranteed coupled stability

  • Ahmetcan Erdogan
  • Volkan Patoglu

Passive velocity field control is advantageous to deliver human-in-the-loop contour tracking rehabilitation exercises, since patients can be allowed to proceed with their preferred pace, while assistance can still be provided as determined by the therapist with ensured coupled stability. We introduce a framework based on passive velocity field control for robot assisted rehabilitation that includes prevention mechanisms against undesired slacking behavior of patients. This framework not only provides systematic approaches to prevent slacking, but also can do so while ensuring coupled stability of the overall robot patient system, a property that cannot be assured with any of the other ad-hoc slacking prevention methods. In particular, the proposed approach enables seamless on-line modification of the task difficulty, speed of contour following, and the level of assistance, while preserving passivity of the system with respect to external forces. The proposed slacking prevention schemes encourage active participation of the patients in rehabilitation protocols with even increased number of repetitions and thanks to flexibility introduced by the controller, render delivery of “repetitive tasks without repeating the same task” possible. Experiments with an haptic interface are included to demonstrate the passivity of the proposed control framework and preliminary human subject experiments with healthy volunteers are presented to validate feasibility and usability of the proposed approaches.

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IROS Conference 2011 Conference Paper

A self-adjusting knee exoskeleton for robot-assisted treatment of knee injuries

  • Mehmet Alper Ergin
  • Volkan Patoglu

In this study, we present a novel active device for robot-assisted rehabilitation that accommodates transitional movements of the knee joint as well as its rotation, enabling a perfect match between human joint axes and the device axes. Automatically adjusting its joint axes, the proposed device is not only capable of guaranteeing ergonomy and comfort throughout the therapy, but also extends the usable range of motion for the knee joint. Moreover, the adjustability feature significantly shortens the setup time required to attach the patient to the exoskeleton, allowing more effective time be spend on exercises instead of wasting it for adjustments. The proposed system is different from the similar works in literature in that it supports both passive translational movements of the knee joint and independent active control of these degrees of freedom. In particular, we introduce implementation details of a prototype that features compact design and combines the power of three actuators to achieve high rotational torques, detail the model based impedance controller utilized to adjust interaction forces and present the experimental characterization of the exoskeleton.

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ICRA Conference 2011 Conference Paper

Combining high-level causal reasoning with low-level geometric reasoning and motion planning for robotic manipulation

  • Esra Erdem 0001
  • Kadir Haspalamutgil
  • Can Palaz
  • Volkan Patoglu
  • Tansel Uras

We present a formal framework that combines high-level representation and causality-based reasoning with low-level geometric reasoning and motion planning. The frame-work features bilateral interaction between task and motion planning, and embeds geometric reasoning in causal reasoning, thanks to several advantages inherited from its underlying components. In particular, our choice of using a causality-based high-level formalism for describing action domains allows us to represent ramifications and state/transition constraints, and embed in such formal domain descriptions externally defined functions implemented in some programming language (e. g. , C++). Moreover, given such a domain description, the causal reasoner based on this formalism (i. e. , the Causal Calculator) allows us to compute optimal solutions (e. g. , shortest plans) for elaborate planning/prediction problems with temporal constraints. Utilizing these features of high-level representation and reasoning, we can combine causal reasoning, motion planning and geometric planning to find feasible kinematic solutions to task-level problems. In our framework, the causal reasoner guides the motion planner by finding an optimal task-plan; if there is no feasible kinematic solution for that task-plan then the motion planner guides the causal reasoner by modifying the planning problem with new temporal constraints. Furthermore, while computing a task-plan, the causal reasoner takes into account geometric models and kinematic relations by means of external predicates implemented for geometric reasoning (e. g. , to check some collisions); in that sense the geometric reasoner guides the causal reasoner to find feasible kinematic solutions. We illustrate an application of this framework to robotic manipulation, with two pantograph robots on a complex assembly task that requires concurrent execution of actions. A short video of this application accompanies the paper.

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IROS Conference 2007 Conference Paper

Development of a micromanipulation mystem with force sensing

  • Shahzad Khan 0003
  • Ahmet Ozcan Nergiz
  • Asif Sabanoviç
  • Volkan Patoglu

This article provides in-depth knowledge about our undergoing effort to develop an open architecture micromanipulation system with force sensing capabilities. The major requirement to perform any micromanipulation task effectively is to ensure the controlled motion of actuators within nanometer accuracy with low overshoot even under the influence of disturbances. Moreover, to achieve high dexterity in manipulation, control of the interaction forces is required. In micromanipulation, control of interaction forces necessitates force sensing in milli-Newton range with nano-Newton resolution. In this paper, we present a position controller based on a discrete time sliding mode control architecture along with a disturbance observer. Experimental verifications for this controller are demonstrated for 100, 50 and 10 nanometer step inputs applied to PZT stages. Our results indicate that position tracking accuracies up to 10 nanometers, without any overshoot and low steady state error are achievable. Furthermore, the paper includes experimental verification of force sensing within nano-Newton resolution using a piezoresistive cantilever end- effector. Experimental results are compared to the theoretical estimates of the change in attractive forces as a function of decreasing distance and of the pull off force between a silicon tip and a glass surface, respectively. Good agreement among the experimental data and the theoretical estimates has been demonstrated.

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ICRA Conference 2002 Conference Paper

Extremal Distance Maintenance for Parametric Curves and Surfaces

  • Volkan Patoglu
  • R. Brent Gillespie

A new extremal distance tracking algorithm is presented for parametric curves and surfaces undergoing rigid body motion. The essentially geometric extremization problem is transformed into a dynamical control problem by differentiating with respect to time. Extremization is then solved with the design of a stabilizing controller. We use a feedback linearizing controller. The controller simultaneously accounts for the surface shape and motion while asymptotically achieving (and maintaining) the extremal pair. Thus collision detection takes place in a framework fully analogous to the framework used for the simulation of dynamical response.

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