arXiv subjects

Chris Manzie

Publications and source records attributed to Chris Manzie.

54 records · Page 3Linked to original sources

arXiv2020

Interior Point Differential Dynamic Programming

This paper introduces a novel Differential Dynamic Programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely Feasible- and Infeasible-IPDDP algorithms, are developed using primal-dual interior-point methodology, and their local quadratic convergence properties are characterised. We show that the stationary points of the algorithms are the perturbed KKT points, and thus can be moved arbitrarily close to a locally optimal solution. Being free from the burden of the active-set methods, it can handle nonlinear state and input inequality constraints without a discernible increase in its computational complexity relative to the unconstrained case. The performance of the proposed algorithms is demonstrated using numerical experiments on three different problems: control-limited inverted pendulum, car-parking, and unicycle motion control and obstacle avoidance.

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arXiv2020

Exploiting Structure in the Bottleneck Assignment Problem

An assignment problem arises when there exists a set of tasks that must be allocated to a set of agents. The bottleneck assignment problem (BAP) has the objective of minimising the most costly allocation of a task to an agent. Under certain conditions the structure of the BAP can be exploited such that subgroups of tasks are assigned separately with lower complexity and then merged to form a combined assignment. In particular, we discuss merging the assignments from two separate BAPs and use the solution of the subproblems to bound the solution of the combined problem. We also provide conditions for cases where the solution of the subproblems produces an exact solution to the BAP over the combined problem. We then introduce a particular algorithm for solving the BAP that takes advantage of this insight. The methods are demonstrated in a numerical case study.

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arXiv2020

Optimization with Zeroth-Order Oracles in Formation

In this paper, we consider the optimisation of time varying functions by a network of agents with no gradient information. The proposed a novel method to estimate the gradient at each agent's position using only neighbour information. The gradient estimation is coupled with a formation controller, to minimise gradient estimation error and prevent agent collisions. Convergence results for the algorithm are provided for functions which satisfy the Polyak-Lojasiewicz inequality. Simulations and numerical results are provided to support the theoretical results.

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arXiv2020

Collision Avoidance Based on Robust Lexicographic Task Assignment

Traditional task assignment approaches for multi-agent motion control do not take the possibility of collisions into account. This can lead to challenging requirements for path planning. We derive an assignment method that not only minimises the largest distance between an agent and its assigned destination but also provides local constraints for guaranteed collision avoidance. To this end, we introduce a sequential bottleneck optimisation problem and define a notion of robustness of an optimising assignment to changes of individual assignment costs. Conditioned on a sufficient level of robustness in relation to the size of the agents, we construct time-varying position bounds for every individual agent. These local constraints are a direct byproduct of the assignment procedure and only depend on the initial agent positions, the destinations that are to be visited, and a timing parameter. We prove that no agent that is assigned to move to one of the target locations collides with any other agent if all agents satisfy their local position constraints. We demonstrate the method in a illustrative case study.

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arXiv2020

Global Sensitivity Analysis for the Linear Assignment Problem

In this paper, the following question is addressed: given a linear assignment problem, how much can the all of the individual assignment weights be perturbed without changing the optimal assignment? The extension of results involving perturbations in just one edge or one row/column are presented. Algorithms for the derivation of these bounds are provided. We also show how these bounds may be used to prevent assignment churning in a multi-vehicle guidance scenario.

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arXiv2020

Uncertainty Intervals for Robust Bottleneck Assignment

We examine the robustness of bottleneck assignment problems to perturbations in the assignment weights. We derive two algorithms that provide uncertainty bounds for robust assignment. We prove that the bottleneck assignment is guaranteed to be invariant to perturbations which lie within the provided bounds. We apply the method to an example of task assignment for a multi-agent system.

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arXiv2020

Active Learning for Linear Parameter-Varying System Identification

Active learning is proposed for selection of the next operating points in the design of experiments, for identifying linear parameter-varying systems. We extend existing approaches found in literature to multiple-input multiple-output systems with a multivariate scheduling parameter. Our approach is based on exploiting the probabilistic features of Gaussian process regression to quantify the overall model uncertainty across locally identified models. This results in a flexible framework which accommodates for various techniques to be applied for estimation of local linear models and their corresponding uncertainty. We perform active learning in application to the identification of a diesel engine air-path model, and demonstrate that measures of model uncertainty can be successfully reduced using the proposed framework.

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arXiv2020

The Use of Implicit Human Motor Behaviour in the Online Personalisation of Prosthetic Interfaces

In previous work, the authors proposed a data-driven optimisation algorithm for the personalisation of human-prosthetic interfaces, demonstrating the possibility of adapting prosthesis behaviour to its user while the user performs tasks with it. This method requires that the human and the prosthesis personalisation algorithm have same pre-defined objective function. This was previously ensured by providing the human with explicit feedback on what the objective function is. However, constantly displaying this information to the prosthesis user is impractical. Moreover, the method utilised task information in the objective function which may not be available from the wearable sensors typically used in prosthetic applications. In this work, the previous approach is extended to use a prosthesis objective function based on implicit human motor behaviour, which represents able-bodied human motor control and is measureable using wearable sensors. The approach is tested in a hardware implementation of the personalisation algorithm on a prosthetic elbow, where the prosthetic objective function is a function of upper-body compensation, and is measured using wearable IMUs. Experimental results on able-bodied subjects using a supernumerary prosthetic elbow mounted on an elbow orthosis suggest that it is possible to use a prosthesis objective function which is implicit in human behaviour to achieve collaboration without providing explicit feedback to the human, motivating further studies.

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arXiv2020

Personalized On-line Adaptation of Kinematic Synergies for Human-Prosthesis Interfaces

Synergies have been adopted in prosthetic limb applications to reduce complexity of design, but typically involve a single synergy setting for a population and ignore individual preference or adaptation capacity. However, personalization of the synergy setting is necessary for the effective operation of the prosthetic device. Two major challenges hinder the personalization of synergies in human-prosthesis interfaces. The first is related to the process of human motor adaptation and the second to the variation in motor learning dynamics of individuals. In this paper, a systematic personalization of kinematic synergies for human-prosthesis interfaces using on-line measurements from each individual is proposed. The task of reaching using the upper-limb is described by an objective function and the interface is parameterized by a kinematic synergy. Consequently, personalizing the interface for a given individual can be formulated as finding an optimal personalized parameter. A structure to model the observed motor behavior that allows for the personalized traits of motor preference and motor learning is proposed, and subsequently used in an on-line optimization scheme to identify the synergies for an individual. The knowledge of the common features contained in the model enables on-line adaptation of the human-prosthesis interface to happen concurrently to human motor adaptation without the need to re-tune the personalization algorithm for each individual. Human-in-the-loop experimental results with able-bodied subjects, performed in a virtual reality environment to emulate amputation and prosthesis use, show that the proposed personalization algorithm was effective in obtaining optimal synergies with a fast uniform convergence speed across a group of individuals.

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arXiv2020

Tuning of multivariable model predictive controllersthrough expert bandit feedback

For certain industrial control applications an explicit function capturing the nontrivial trade-off between competing objectives in closed loop performance is not available. In such scenarios it is common practice to use the human innate ability to implicitly learn such a relationship and manually tune the corresponding controller to achieve the desirable closed loop performance. This approach has its deficiencies because of individual variations due to experience levels and preferences in the absence of an explicit calibration metric. Moreover, as the complexity of the underlying system and/or the controller increase, in the effort to achieve better performance, so does the tuning time and the associated tuning cost. To reduce the overall tuning cost, a tuning framework is proposed herein, whereby a supervised machine learning is used to extract the human-learned cost function and an optimization algorithm that can efficiently deal with a large number of variables, is used for optimizing the extracted cost function. Given the interest in the implementation across many industrial domains and the associated high degree of freedom present in the corresponding tuning process, a Model Predictive Controller applied to air path control in a diesel engine is tuned for the purpose of demonstrating the potential of the framework.

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arXiv2019

Fast Calibration of a Robust Model Predictive Controller for Diesel Engine Airpath

A significant challenge in the development of control systems for diesel airpath applications is to tune the controller parameters to achieve satisfactory output performance, especially whilst adhering to input and safety constraints in the presence of unknown system disturbances. Model-based control techniques, such as model predictive control (MPC), have been successfully applied to multivariable and highly nonlinear systems, such as diesel engines, while considering operational constraints. However, efficient calibration of typical implementations of MPC is hindered by the high number of tuning parameters and their non-intuitive correlation with the output response. In this paper, the number of effective tuning parameters is reduced through suitable structural modifications to the controller formulation and an appropriate redesign of the MPC cost function to aid rapid calibration. Furthermore, a constraint tightening-like approach is augmented to the control architecture to provide robustness guarantees in the face of uncertainties. A switched linear time-varying MPC strategy with recursive feasibility guarantees during controller switching is proposed to handle transient operation of the engine. The robust controller is first implemented on a high fidelity simulation environment, with a comprehensive investigation of its calibration to achieve desired transient response under step changes in the fuelling rate. An experimental study then validates and highlights the performance of the proposed controller architecture for selected tunings of the calibration parameters for fuelling steps and over drive cycles.

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arXiv2019

Model Predictive Controller with Average Emissions Constraints for Diesel Airpath

Diesel airpath controllers are required to deliver good tracking performance whilst satisfying operational constraints and physical limitations of the actuators. Due to explicit constraint handling capabilities, model predictive controllers (MPC) have been successfully deployed in diesel airpath applications. Previous MPC implementations have considered instantaneous constraints on engine-out emissions in order to meet legislated emissions regulations. However, the emissions standards are specified over a drive cycle, and hence, can be satisfied on average rather than just instantaneously, potentially allowing the controller to exploit the trade-off between emissions and fuel economy. In this work, an MPC is formulated to maximise the fuel efficiency whilst tracking boost pressure and exhaust gas recirculation (EGR) rate references, and in the face of uncertainties, adhering to the input, safety constraints and constraints on emissions averaged over some finite time period. The tracking performance and satisfaction of average emissions constraints using the proposed controller are demonstrated through an experimental study considering the new European drive cycle.

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arXiv2019

Control Barrier Functions for Mechanical Systems: Theory and Application to Robotic Grasping

Control barrier functions have been demonstrated to be a useful method of ensuring constraint satisfaction for a wide class of controllers, however existing results are mostly restricted to continuous time systems of relative degree one. Mechanical systems, including robots, are typically second-order systems in which the control occurs at the force/torque level. These systems have velocity and position constraints (i.e. relative degree two) that are vital for safety and/or task execution. Additionally, mechanical systems are typically controlled digitally as sampled-data systems. The contribution of this work is two-fold. First, is the development of novel, robust control barrier functions that ensure constraint satisfaction for relative degree two, sampled-data systems in the presence of model uncertainty. Second, is the application of the proposed method to the challenging problem of robotic grasping in which a robotic hand must ensure an object remains inside the grasp while manipulating it to a desired reference trajectory. A grasp constraint satisfying controller is proposed that can admit existing nominal manipulation controllers from the literature, while simultaneously ensuring no slip, no over-extension (e.g. singular configurations), and no rolling off of the fingertips. Simulation and experimental results validate the proposed control for the robotic hand application.

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arXiv2019

Adaptive Scan for Atomic Force Microscopy Based on Online Optimisation: Theory and Experiment

A major challenge in Atomic Force Microscopy (AFM) is to reduce the scan duration while retaining the image quality. Conventionally, the scan rate is restricted to a sufficiently small value in order to ensure a desirable image quality as well as a safe tip-sample contact force. This usually results in a conservative scan rate for samples that have a large variation in aspect ratio and/or for scan patterns that have a varying linear velocity. In this paper, an adaptive scan scheme is proposed to alleviate this problem. A scan line-based performance metric balancing both imaging speed and accuracy is proposed, and the scan rate is adapted such that the metric is optimised online in the presence of aspect ratio and/or linear velocity variations. The online optimisation is achieved using an extremum-seeking (ES) approach, and a semi-global practical asymptotic stability (SGPAS) result is shown for the overall system. Finally, the proposed scheme is demonstrated via both simulation and experiment.

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arXiv2019

Robust Object Manipulation for Tactile-based Blind Grasping

Tactile-based blind grasping addresses realistic robotic grasping in which the hand only has access to proprioceptive and tactile sensors. The robotic hand has no prior knowledge of the object/grasp properties, such as object weight, inertia, and shape. There exists no manipulation controller that rigorously guarantees object manipulation in such a setting. Here, a robust control law is proposed for object manipulation in tactile-based blind grasping. The analysis ensures semi-global asymptotic and exponential stability in the presence of model uncertainties and external disturbances that are neglected in related work. Simulation and experimental results validate the effectiveness of the proposed approach.

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arXiv2018

Grasp Constraint Satisfaction for Object Manipulation using Robotic Hands

For successful object manipulation with robotic hands, it is important to ensure that the object remains in the grasp at all times. In addition to grasp constraints associated with slipping and singular hand configurations, excessive rolling is an important grasp concern where the contact points roll off of the fingertip surface. Related literature focus only on a subset of grasp constraints, or assume grasp constraint satisfaction without providing guarantees of such a claim. In this paper, we propose a control approach that systematically handles all grasp constraints. The proposed controller ensures that the object does not slip, joints do not exceed joint angle constraints (e.g. reach singular configurations), and the contact points remain in the fingertip workspace. The proposed controller accepts a nominal manipulation control, and ensures the grasping constraints are satisfied to support the assumptions made in the literature. Simulation results validate the proposed approach.

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arXiv2018

Closeness of Solutions for Singularly Perturbed Systems via Averaging

This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order O(\sqrt(ε)), where εis the perturbation parameter.

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arXiv2016

Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem.

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