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The delta-gamma Approximation (DGA) is a technique that is often used for hedging options in practice. For its simplicity, it is widely used because it can immediately indicate the number of shares of the underlying assets to be reinvested to hedge the original investments. However, the DGA requires that the change of the underlying asset price to be small for an acceptable performance. Therefore, when this change of the underlying asset price is large, then the hedging performance is not acceptable implying losses, and frequent rebalancing operations of the portfolio may be needed. But, a rebalancing operation has an associated transaction fee and a high frequency of rebalancing operations imply high additional costs. Hence, there is a trade-off between losses due to low performance of the DGA (when the change of the underlying asset price is large) and additional costs due to rebalancing operations to compensate the low performance of the DGA. In the present work, we propose a hedging framework that improves its performance with the purpose to reduce losses by improving the quality of approximating the option prices. This framework consists of estimating the implied volatility using the Markov chain Monte Carlo, predicting the change of the underlying asset price using the functional data analysis, and approximating the option price using the locally weighted regression.

In risk management, the delta-gamma approximation is extensively used, for instance, for derivatives portfolio hedging (such as options). However, this approximation usually works well locally for small changes of the underlying asset price. When these changes become large, then the derivatives prices estimated by the delta-gamma approximation can be significantly different from those that are estimated using the Black-Scholes formula. In this work, we propose a method that allows us to hedge derivatives such as options even for large changes of their underlying asset prices. While the delta-gamma approximation uses the first- and second-order Greeks for derivatives portfolio hedging, our method is based on hedging with a linear combination of some kernel functions. These kernel functions depend in turn on the implied asset price, which in turn is forecasted using the functional data analysis (FDA) approach. Then, both these instances of option prices and the corresponding asset prices are used to find the weights for the linear combination of the kernel functions that allow us to hedge the considered derivative. We then compare the hedging performance of our approach to that obtained using the delta-gamma approximation and other techniques.

The automated trading systems (ATS) are highly interested by traders for their abilities to automatically adapt the embedded decision-making mechanism considering both endogenous and exogenous changes in the financial and economic environments. Their abilities depend greatly on both the choice of the decision-making algorithm and the aspects of the trading environment that are taken into account in the algorithm to make decisions. One of the aspects that significantly influences on the actual profitability obtained using the ATS is the transaction fee. Often, this aspect is neglected or (if considered) is simply modeled as proportional to the trade amount, where this proportionality is maintained constant (that is, linear with respect to the trade amount). However, in reality, a transaction fee is composed by different components such as the flat trade fee, trade fee per share, broker-assisted trade fee, among others. In particular, the trade fee per share often varies nonlinearly with respect to the trade amount and on the trade frequency. In this work, we study how the fact of including this nonlinear variation of the transaction fees (with respect to the transaction amount) affects on the decisions made by the ATS. In particular, we implement the ATS' decision algorithm using a reinforcement learning (RL) such as the Q-learning. The advantage of such an algorithm is that it considers the decision-making problem as a stochastic control problem, and it suggests a sequence of optimal (present and future) actions in order to maximize the expected value of the discounted cumulative rewards. Finally, with the purpose to illustrate the impact of considering the nonlinear variation of transaction fees in the decision-making model, we compare the corresponding results to those that are obtained using the linear variation of transaction fees.

When investing in derivatives portfolios (such as options), the delta-gamma approximation (DGA) is often used as a risk management strategy to reduce the risk associated with the price movements of the underlying asset. However, this approximation is locally accepted only for small changes of the underlying asset price. When these changes become large, the option prices estimated by the DGA significantly differ from those of the market (or those that are estimated using, for instance, the Black-Scholes model). On the other hand, in order to properly hedge the investment in option contracts at any time instant before the maturity, one needs to forecast both the price of the underlying asset price (or, equivalently, its return) and the implied volatility of option contract (for some maturity, risk-free interest rate, and strike). In this work, we first define (and illustrate) the above three problems: 1) the limited performance of the DGA for large changes of the underlying asset price, 2) forecast of the underlying asset price (or, equivalently, its return), and 3) forecast of the implied volatility of option contract. Afterward, we define a framework to resolve each of these problems. 1) We propose to hedge the risk in option contract investment using the locally weighted regression (LWR). 2) We forecast the return of the underlying asset price using the functional data analysis (FDA) techniques. 3) We forecast the implied volatility of option contract using the Markov chain Monte Carlo (MCMC) techniques. Finally, we compare the performance of our method to that of some other existing methods.

La couverture d’une option financière de type Européen, utilisée par les praticiens et analysée/étudiée par le monde académique, se base essentiellement sur une approximation que l’on réfère dans la suite par DGA (Delta-Gamma-Approximation). Cette dernière est d’autant plus viable que la variation de l’actif sous-jacent est assez faible. Ce qui justifie le fait que la couverture s’effectue en général de manière journalière. Cependant un nombre élevé d’opérations engendre des coûts qui deviennent à la fin économiquement non viable. Espacer les opérations de couverture permet de limiter les coûts mais pourrait faire exposer de pertes conséquentes sur la position du fait que le sous-jacent aurait subi un décalage important, puisque la DGA utilisée ne s’applique plus. Considérer une approximation du changement de prix d’une option dans le cadre d’une variation conséquente de l’actif sous-jacent devient ainsi un problème capital (encore ouvert) pour les couverture et mesures de risque associées à une position isolée ou sur portefeuille. Cette considération est aussi utile actuellement avec les exigences de stress Test selon les directives réglementaires Bâle 3 pour la Banque et Solvabilité 2 pour l’Assurance. Nous avons apporté au moins trois types de solutions à ce problème de DGA sous de large variations du sous-jacent à l’option que l’on peut noter par DGA-mod, DGA-loc et EDGA que l’on peut comprendre respectivement par « DGA modifiée », « DGA locale » et « Extended DGA ». D’amples « What-If-Else-Analyses » ont été effectuées pour faire comprendre à l’utilisateur les forces et limites de ces solutions. D’abord la DGA-mod a été introduite pour corriger une mauvaise utilisation de la DGA classique faîte par beaucoup (à la fois en pratique et en théorie). Ensuite face à l’impossibilité de la DGA classique (même étendue avec un développement d’ordre élevé) pour de large variations des cours du sous-jacent nous avons proposé la notion de DGA-loc. Ce dernier donne de résultats assez spectaculaires et ouvre ainsi de nouvelles voies, à la fois en stress-test et tout aussi bien dans le cadre de gestion d’option à la fois financière ou réelle. Cependant la DGA-loc nécessite une certaine vue de la part de l’utilisateur. Face à cette limitation, nous avons enfin proposé la EDGA qui permet d’atteindre de résultats comparables à ceux obtenus avec la DGA-loc, mais dont le résultat peut être moins satisfaisant que celui obtenu avec la DGA-mod si jamais la variation relative avérée de l’actif sous-jacent est trop faible. La DGA classique est seulement basée sur une utilisation d’une fonction polynôme du second degré pour remplacer la variation de prix (hautement non linéaire) de l’option. Contrairement aux usages connus à travers la littérature et en cohérence avec les pratiques dans l’industrie financière, nous pensons qu’il est utile d’inclure des vues dans l’outil de base même pour établir un remplacement convenable de la DGA classique. C’est ainsi la raison pour laquelle nous faisons appels à une technique de ML. Cette dernière intervient d’abord pour la prédiction des variations possibles et raisonnables du sous-jacent à l’horizon considéré. Ensuite un nouvel appel à une technique de ML est utilisé pour trouver une substitution convenable de la variation de prix de l’option, qui par la suite nous permet de faire une réplication, en vue d’une finalité de couverture ou juste pour parvenir de manière économique (à la fois en moyen et temps de calcul) des mesures de la position sous divers scénarios d’évolutions du cours du sous-jacent.

In risk management, the delta-gamma approximation is extensively used, for instance, for derivatives portfolio hedging (such as options). However, this approximation usually works well locally for small changes of the underlying asset price. When these changes become large, then the derivatives prices estimated by the delta-gamma approximation can be significantly different from those that are estimated using the Black-Scholes formula. In this work, we propose a method that allows us to hedge derivatives such as options even for large changes of their underlying asset prices. While the delta-gamma approximation uses the first- and second-order Greeks for derivatives portfolio hedging, our method is based on hedging with a linear combination of some kernel functions of higher orders. These kernel functions depend in turn on the implied asset price, which in turn is forecasted using the functional data analysis (FDA) approach. On the other hand, the implied volatility term used in the Black-Scholes model to estimate an option price is often considered as constant, while this is not the case in reality. This issue can be addressed by considering a model for the implied volatility such as the Malz model and its variants. In this work, we propose a Machine Learning algorithm (such as the neural network) to learn the implied volatility of the option price and compare its performance to that of the Malz model. Hence, once the implied volatility is learned, we estimate a number of option prices of an asset using the Black-Scholes model for various times-to-maturities. Then, both these instances of option prices and the corresponding asset prices are used to find the weights for the linear combination of the kernel functions that allow us to hedge the considered derivative. We then compare the hedging performance of our approach to that obtained using the delta-gamma approximation with the Malz model that is used to estimate the implied volatility.

The Delta-Gamma Approximation (DGA) for the option price is a well-known concept, on which the practical hedging is based on. However, the usage of this tool requires that the underlying asset change should be of a small size. Consequently, there is the need to make a very frequent re-balancing of the portfolio made by the hedging instruments. This situation, unfortunately, induces transaction costs, which may be untenable at last. We contribute here by showing that the DGA can be extended in order to handle large variations of the underlying asset price (as for example between -20 % to -10 % or 10 % to 20 %). A first extension is the local version of a DGA suitable for the situation of large asset changes, in some interval with a moderated size and whose the center is far from the origin. A second possible extension, referred to EDGA, is an approximation-based regression. On one hand, the need for full revaluation in risk measurement and stress testing can be circumvented by using a suitable high order EDGA. On the other hand, for various situations, either the local DGA or a low order EDGA can provide a good replication of the option price change. This has the consequence of enabling to replace the (possibly costly) frequent re-balancing hedging operations by probably just a single (or very few) step operation(s).

We address here to the issue related to the bond valuation when the associated underlying shadow rate is assumed to stay inside a given tunnel, but not only above a lower bound as is the case when dealing with the zero lower bound for the interest rate or with the negative interest rates situation. The model considered here is referred to as LUB (Lower and Upper Bound) model and, for the simplicity, the underlying shadow rate is assumed to follow the one-factor Vasicek model for the interest rate. Our consideration of the LUB model is not only done under the willing to deal with a model representation consistent with market situations observed both in developed and emerging countries, but it is also performed with the intention to provide a helping tool when structuring bespoke financial products linked to interest rates. As for the Black’s approach in the context of interest rate zero-lower bound, the LUB restriction on the shadow rate level leads to technical complications in the valuation such that getting tractable zero-coupon bond prices is challenging. We first provide a Monte-Carlo explicit based expression for the zero-coupon price, in the sense that this last is given as a deterministic function of the bond characteristic(s), the model parameters, the underlying state variable and independent realizations of the standard normal Gaussian random variable. Not only the obtained price is helping from the pricing audit point of view, but it has also the advantage to provide a starting point for the derivation of the zero-coupon price sensitivities. Then we provide the definitive closed formula approximation which is the expected solution, at least from the theoretical point of view. To overcome the difficulty linked to the practical implementation of the multidimensional integral associated with this solution, by using a cubature approach, we finally derive another approximated closed form for the zero-coupon price. This last may serve as a quick tool for the LUB model parameter calibration and the underlying shadow rate estimation.

We address here to the issue related to the bond valuation when the associated underlying shadow rate is assumed to stay inside a given tunnel, but not only above a lower bound as is the case when dealing with the zero lower bound for the interest rate or with the negative interest rates situation. The model considered here is referred to as LUB (Lower and Upper Bound) model and, for the simplicity, the underlying shadow rate is assumed to follow the one-factor Vasicek model for the interest rate. Our consideration of the LUB model is not only done under the willing to deal with a model representation consistent with market situations observed both in developed and emerging countries, but it is also performed with the intention to provide a helping tool when structuring bespoke financial products linked to interest rates. As for the Black’s approach in the context of interest rate zero-lower bound, the LUB restriction on the shadow rate level leads to technical complications in the valuation such that getting tractable zero-coupon bond prices is challenging. We first provide a Monte-Carlo explicit based expression for the zero-coupon price, in the sense that this last is given as a deterministic function of the bond characteristic(s), the model parameters, the underlying state variable and independent realizations of the standard normal Gaussian random variable. Not only the obtained price is helping from the pricing audit point of view, but it has also the advantage to provide a starting point for the derivation of the zero-coupon price sensitivities. Then we provide the definitive closed formula approximation which is the expected solution, at least from the theoretical point of view. To overcome the difficulty linked to the practical implementation of the multidimensional integral associated with this solution, by using a cubature approach, we finally derive another approximated closed form for the zero-coupon price. This last may serve as a quick tool for the LUB model parameter calibration and the underlying shadow rate estimation.

In this work, we provide an approach to derive a distribution forecast for the stock price, without resorting to any presumed (complex) parametric model. The representation learning approach presented in this work can be seen as a nonlinear autoregressive (NAR) model that takes into account the volatility, skewness and kurtosis of the underlying asset price distribution. Aside from the forecasting aspect, we explore a way to represent the asset price that avoids the recourse to any well-established volatility model, such as the GARCH family. Finally, this work is realized with the intention to provide various formulas that can empower the reader to implement an immediately usable stock price forecasting tool.

A fish ladder (or fishway, fish pass) is a hydraulic structure constructed near dams. Such fish passage permits to immigrant fishes to cross to theirs productions and feeding areas or from the cold area to the hot one for species which do not withstand the cold period. Our purpose is to establish an optimal structure that allows fish to pass through the dams with less effort. In order to achieve this challenge, we will give a mathematical formulation of channel composed of ten pools with vertical slots for obtaining a flow pattern effective for a wide range of species. We proceed with the study of the state system given by the shallow water equations and the objective function which is related to fish's swimming aptitudes. Numerical simulations for ten pools channel are given to illustrate the efficiency and viability of the technique.

Negative interest rates are present in various marketplaces since mid-2014, following the negative interest rate policy (NIRP) adopted by the European Central Bank in order to lift the economic growth (and, therefore, the inflation). However, this policy involves difficulties for market practitioners as there is no model that enables to forecast negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable models, the well-known Historical Approach (HA) appears to be a good resource. By tweaking the HA, we derive a data-driven and very tractable tool that allows practitioners to generate yield-curve distribution at future discrete time horizons. So, we provide a robust and easy-to-understand forecasting model, suitable for the NIRP context, allowing to appreciate its prediction power. Besides the methodology development that we present in this work, various numerical illustrations are reported in order to shed light on the benefit (and the limit) of our forecasting approach.

Since the 2007 financial crisis, many central banks adopted policies to lower their interest rates, whose dynamics can not be captured using classical models. Recently, Meucci and Loregian (2016) proposed an approach to estimate nonnegative interest rates using the inverse-call transformation. Despite the fact that their work distinguishes from others in the literature by their consideration of practical aspects, some technical difficulties still remain, such as the lack of the analytic expression for the zero-coupon bond (ZCB) price. In this work, we provide approximate closed formulae for the ZCB price in the zero lower bound (ZLB) framework, when the underlying shadow rate is assumed to follow the classical one-factor Vasicek model. Then, a filtering procedure is performed using the Unscented Kalman Filter (UKF) to estimate the unobservable state variable (the shadow rate), and the model calibration is proceeded by estimating the model parameters using the Particle Swarm Optimization (PSO) algorithm. Lastly, empirical illustrations are given and discussed using (as input data) the interest rates of the AAA-rated bonds compiled by the European Central Bank ranging from September 6, 2004 to June 21, 2012.

We address in this paper the issue of a bond valuation when the underlying shadow rate is assumed to stay inside a given tunnel, but not only above a lower bound as is considered by various authors when dealing with the zero-lower bound for the interest rate or as with the negative interest rates situation arisen after the policy adopted by the European Central Bank from 2014. The model considered here is referred to as LUB (Lower and Upper Bound) model, and for the simplicity, the underlying shadow rate is assumed to follow the one-factor Vasicek model for the interest rate. Our consideration of the LUB model is not only done under the willing to deal with a model epresentation consistent with market situations observed both in developed and emerging countries, but it is also performed with the intention to provide a helping tool when structuring bespoke financial products linked to interest rates. Indeed, discarding the ranges of interest rate levels not attainable under the market regime may mildly/drastically lower or rise zero-coupon prices. As is well-known for the Black's approach in the context of interest rate zero-lower bound, the LUB restriction on the shadow rate level leads to technical complications in the bond valuation such that getting tractable zero-coupon bond prices is challenging. We first provide a Monte-Carlo explicit based expression for the zero-coupon price, in the sense that this last is given as a deterministic function of the bond characteristics, the model parameters, the underlying state variable and independent realizations of the standard normal Gaussian random variable. Not only the obtained price is helping from the pricing audit point of view, but it has also the advantage to provide a starting point for the derivation of the zero-coupon price sensitivities. Next, using a cubature approach, we derive an approximate closed form for the zero-coupon price which has the advantage to be free of any standard Gaussian random variable realizations and may serve as a quick tool for the LUB model parameter calibration and the underlying shadow rate estimation.

Negative interest rates are present in various market places since mid-2014, following the Negative Interest Rate Policy (NIRP) adopted by the European Central Bank in order to lift growth or inflation. This spans difficulties for many market practitioners as there is not yet any model which enables to handle negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable model, the well-known Historical Approach (HA) appears to be a good recourse. By tweaking the HA, we derive a data-driven and very tractable tool allowing various users to generate a distribution forecast of the yield curves at future discrete time horizon. So we provide here a robust and easy-to-understand reference forecasting model, suitable for the NIRP context, allowing to appreciate the prediction power of any ongoing alternative parametric model. Besides the methodology development, various experiments are also reported here in order to shed light in depth on the benefit and limit of our forecasting approach.

Many approaches proposed in the literature to forecast stock prices are based on pointwise forecasts for a single-time horizon. Although the forecast performance obtained from these approaches might provide an acceptable guideline for buying or selling stocks, for the purpose of position management and risk management, one needs to have a notion of a confident range of possible forecasts of stock prices at multiple-time horizons. In this work, we show that the forecast performance can be improved from that of traditional approaches by working along two directions: by generating joint forecast distributions (instead of pointwise forecasts) and by forecasting for multiple-time horizons (instead of a single-time horizon). In particular, we formulate various types of historical-approach based methods (parametric and non-parametric), with various forecast methods (auto-regressive and recurrent neural networks) with various types of probability functions (exogenous and endogenous). Further, we compare the forecast performance achieved from each of these methods from their respective statistical results using real stock prices corresponding to various assets.

Negative interest rates are present in various market places since mid-2014, following the Negative Interest Rate Policy (NIRP) adopted by the European Central Bank in order to lift growth or inflation. This spans difficulties for many market practitioners as there is not yet any model which enables to handle negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable model, the well-known Historical Approach (HA) appears to be a good recourse. By tweaking the HA, we derive a data-driven and very tractable tool allowing various users to generate a distribution forecast of the yield curves at future discrete time horizon. So we provide here a robust and easy-to-understand reference forecasting model, suitable for the NIRP context, allowing to appreciate the prediction power of any ongoing alternative parametric model. Besides the methodology development, various experiments are also reported here in order to shed light in depth on the benefit and limit of our forecasting approach.

Negative interest rates are present in various market places since mid-2014, following the Negative Interest Rate Policy (NIRP) adopted by the European Central Bank in order to lift growth or inflation. This spans difficulties for many market practitioners as there is not yet any model which enables to handle negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable model, the well-known Historical Approach (HA) appears to be a good recourse. By tweaking the HA, we derive a data-driven and very tractable tool allowing various users to generate a distribution forecast of the yield curves at future discrete time horizon. So we provide here a robust and easy-to-understand reference forecasting model, suitable for the NIRP context, allowing to appreciate the prediction power of any ongoing alternative parametric model. Besides the methodology development, various experiments are also reported here in order to shed light in depth on the benefit and limit of our forecasting approach.

Negative interest rates are present in various market places since mid-2014, following the Negative Interest Rate Policy (NIRP) adopted by the European Central Bank in order to lift growth or inflation. This spans difficulties for many market practitioners as there is not yet any model which enables to handle negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable model, the well-known Historical Approach (HA) appears to be a good recourse. By tweaking the HA, we derive a data-driven and very tractable tool allowing various users to generate a distribution forecast of the yield curves at future discrete time horizon. So we provide here a robust and easy-to-understand reference forecasting model, suitable for the NIRP context, allowing to appreciate the prediction power of any ongoing alternative parametric model. Besides the methodology development, various experiments are also reported here in order to shed light in depth on the benefit and limit of our forecasting approach.

A novel path-planning algorithm is proposed for a tracked mobile robot to traverse uneven terrains, which can efficiently search for stability sub-optimal paths. This algorithm consists of combining two RRT-like algorithms (the Transition-based RRT (T-RRT) and the Dynamic-Domain RRT (DD-RRT) algorithms) bidirectionally and of representing the robot–terrain interaction with the robot’s quasi-static tip-over stability measure (assuming that the robot traverses uneven terrains at low speed for safety). The robot’s stability is computed by first estimating the robot’s pose, which in turn is interpreted as a contact problem, formulated as a linear complementarity problem (LCP), and solved using the Lemke’s method (which guarantees a fast convergence). The present work compares the performance of the proposed algorithm to other RRT-like algorithms (in terms of planning time, rate of success in finding solutions and the associated cost values) over various uneven terrains and shows that the proposed algorithm can be advantageous over its counterparts in various aspects of the planning performance.

Since the 2007 financial crisis, the levels of interest rates in many countries are time-to-time so low such that the common and classical models fail to be functional. Recently, Meucci A. and Loregian A. (2014) have proposed an interest rates approach, based on the inverse-call transformation, which is very transparent from the practical point of view, in comparison with other available models allowing to avoid negative interest rates. However, some technical difficulties remain as for example the non-availability of analytic expression for the zero-coupon bond (ZCB) price. Our purpose in this paper is to provide approximated closed formulas for the ZCB price when the underlying shadow rate is assumed to follow the classical one-factor Vasicek model. Moreover we derive formulas allowing the user to filter the unobservable state variable involved in the ZCB price, as well as the model parameters.

Since the 2007 financial crisis, the levels of interest rates in many countries are time-to-time so low such that the common and classical models fail to be functional. Recently, Meucci A. and Loregian A. (2014) have proposed an interest rates approach, based on the inverse-call transformation, which is very transparent from the practical point of view, in comparison with other available models allowing to avoid negative interest rates. However, some technical difficulties remain as for example the non-availability of analytic expression for the zero-coupon bond (ZCB) price. Our purpose in this paper is to provide approximated closed formulas for the ZCB price when the underlying shadow rate is assumed to follow the classical one-factor Vasicek model. Moreover we derive formulas allowing the user to filter the unobservable state variable involved in the ZCB price, as well as the model parameters.

We propose an approach to the synthesis of safety controllers for a class of switched systems, based on the use of multiscale symbolic models that describe transitions of various durations and whose sets of states are given by a sequence of embedded lattices approximating the state-space, the finer lattices being accessible only by transitions of shorter duration. We prove that these multiscale symbolic models are approximately bisimilar to the original switched system provided it enjoys an incremental stability property attested by the existence of a common Lyapunov function or of multiple Lyapunov functions with a minimal dwell-time. Then, for specifications given by a safety automaton, we present a controller synthesis algorithm that exploits the specificities of multiscale symbolic models. We formalize the notion of maximal lazy safety controller which gives priority to transitions of longer durations; the shorter transitions and thus the finer scales of the symbolic model are effectively explored only when safety cannot be ensured at the coarser level and fast switching is needed. We propose a synthesis algorithm where symbolic models can be computed on the fly, this allows us to keep the number of symbolic states as low as possible. We provide computational evidence that shows drastic improvements of the complexity of controller synthesis using multiscale symbolic models instead of uniform ones.

This study presents a liquidity risk management model allows to assess the impact of stress scenarios on a banking system within a top-down approach. The impact of stress scenarios on a banking system includes: (i) individual bank reactions to the shock, (ii) the shock transmission across banks, through interbank networks and nancial markets channels and (iii) the recover rate, the proportion of the debt a creditor receives in an event of a default. The macro economic model is estimated and simulated quarterly and the data in balance sheet is yearly for the Vietnamese banking system. The results show a high vulnerability of the trading portfolios and interbank market.

University of Genova, Italy Conference Evolutionary Political Economics

Running with compliant curved legs involves the progression of the center of pressure, the changes of both the leg's stiffness and effective rest length, and the shift of the location of the maximum stress point along the leg. These phenomena are product of the geometric and material properties of these legs, and the rolling motion produced during stance. We examine these aspects with several reduced-order dynamical models to relate the leg's design parameters (such as normalized foot radius, leg's effective stiffness, location of the maximum stress point and leg shape) to running performance (such as robustness and efficiency). By using these models, we show that running with compliant curved legs can be more efficient, robust with fast recovery behavior from perturbations than running with compliant straight legs. Moreover, the running performance can be further improved by tuning these design parameters in the context of running with rolling. The results shown in this work may serve as potential guidance for future compliant curved leg designs that may further improve the running performance.

The problem of improving the stability of a mobile manipulator over a sloped terrain is addressed in the present work. Such an improvement is achieved by finding the location of the manipulator's center of mass that maximizes the overall quasi-static stability, defined here as the force-angle stability, using a stochastic optimization approach known as the Covariance Matrix Adaptation. The tracking of both trajectories for the robot base and for the manipulator is achieved by using an inverse-kinematics controller in simulation.

A skid-steering mobile robot steers by creating a moment that is larger than the frictional moment which results in a lateral slippage also known as skidding. This moment is in turn generated by a difference of the forces originated from the two sides of the robot. Tracking a given trajectory using this type of steering mechanism is not easy since it requires to relate skidding to steering. A necessary condition for the stability of skid-steering mobile robots is that the longitudinal component of the instantaneous center of rotation (ICR) resides within the robot dimension. In the present work, we propose a novel trajectory-tracking control design using a backstepping technique that guarantees the Lyapunov stability and that satisfies this necessary condition by relating the longitudinal component of the “desired ICR” to the curvature of a given trajectory and the reference linear speed. Finally, we compare the performance of the proposed controller to that of other existing controllers for skid-steering mobile robots and show the robustness of the proposed controller even in the presence of modeled sensory noise and control time delay in simulation.

Most of the existing path planners for traversing over rough terrains use the single-valued probabilistic properties of the terrain with the extension of considering the robot’s dimensions to build the cost function. The present work proposes a path planner for a tracked mobile robot to traverse over rough terrains using the robot’s tip-over stability as its cost function. The contacts that the robot makes with the terrain determine the pose of the robot and in turn its tip-over stability. The estimation of the robot’s pose is formulated as a linear complementary problem (LCP) and solved using the Lemke’s method. We show some examples on searching paths that optimize for various cost functions over a randomly generated rough terrain. We also validate the performance of our pose estimator by comparing their results to those obtained from a dynamic simulator (MSC Adams).

The groundbreaking running performances of RHex-like robots are analyzed from the perspective of their leg designs. In particular, two-segment-leg models are used both for studying the running with the legs currently employed and for suggesting new leg designs that could improve the gait stability, running efficiency and forward speed. New curved compliant monolithic legs are fabricated from these models, and the running with these legs is tested by using a newly designed running test robot. Both the simulations and the experimental trials seem to suggest that running with legs with unity-ratio of the leg segments is faster and more efficient than running with the leg that is currently used on the RHex-like robots. The simulation model predictions seem to match closely to experimental trials in some instances but not always. In the future, a more sophisticated model is needed to capture the actual running with curved legs more accurately.

We introduce CoSyMA, a tool for automatic controller synthesis for incrementally stable switched systems based on multi-scale discrete abstractions. The tool accepts a description of a switched system represented by a set of differential equations and the sampling parameters used to define an approximation of the state-space on which discrete abstractions are computed. The tool generates a controller - if it exists - for the system that enforces a given safety or time-bounded reachability specification. We illustrate by examples the synthesized controllers and the significant performance gains during their computation.

Some of the unique properties associated with running with curved legs or feet (as opposed to point-contact feet) are examined in this work, including the rolling contact motion, the change of the leg's effective stiffness and rest length, the shift of the effective flexion point along the leg, and the compliant-vaulting motions over its tiptoe during stance. To examine these factors, a novel torque-driven reduced-order dynamical model with a clock-based control scheme and with a simple motor model is developed (named as torque-driven and damped half-circle-leg model (TD-HCL)). The controller parameters are optimized for running efficiency and forward speed using a direct search method, and the results are compared to those of other existing dynamical models such as the torque-driven and damped spring-loaded-inverted-pendulum (TD-SLIP) model, the torque-driven and damped two-segment-leg (TD-TSL) model, and the TD-SLIP with a rolling foot (TD-SLIP-RF) model. The results show that running with rolling is more efficient and more stable than running with legs that involve pin joint contact model. This work begins to explain why autonomous robots using curved legs run efficiently and robustly. New curved legs are designed and manufactured in order to validate these results.

Humans and terrestrial legged animals can travel with great degree of stability, agility and maneuverability over a large number of terrains such as gravel, grass, sand, rock, mud, snow, asphalt, river-beds and more. They can also perform many locomotive tasks elegantly and seemingly effortlessly, showing their rich structural and dynamic readiness in rejecting even large, rapid and unexpected disturbances. However, despite significant advances in the robotic legged locomotion field during the last three decades since Raibert introduced the first self-balancing hopping robot, there are not yet any robots that can run over real outdoor rough terrains as humans and animals do. During rapid locomotion, animals seem to use passive mechanisms such as sprawled posture or tuned mechanical impedances to self-stabilize and reject unexpected disturbances before the neural reflexes take place. These mechanisms allow for immediate response to perturbations, and, in this way, humans and animals are able to move with great stability and maneuverability over various types of terrains. With the purpose of designing robotic legs with similar passive mechanisms that biological legged systems have embedded, the present work focuses on relating the robotic leg's passive properties to various running performance measures. In particular, curved legs are chosen for this study motivated by the exceptional running performance achieved by some autonomous robots and human amputees using this type of leg. The relevant aspects of running with this type of leg are characterized by using various reduced-order dynamical models. Then, by associating the design parameters of each model to the running performance, these parameters are optimized to obtain new curved leg designs. The results of the present work reveal that, in the presence of changes in the environmental conditions, the approach of mechanical impedance adaptation is a more effective and realistic strategy than the controller optimization method for stable and efficient running. In addition, this work shows that running with curved legs is more efficient and robust and can recover from perturbations more quickly than with straight legs. These results are justified by the richer running dynamics involved with curved legs than with straight legs such as variable passive compliance and variable rest length due to the rolling motion involved during stance. In essence, the results obtained in this work show the importance of (actively or passively) tuning the mechanical properties of the leg to achieve stable and efficient running. These approaches do not only apply to robotic platforms with curved legs but can be generalized for any robotic legged system.

The present work investigates the effect of rolling contact during stance phase in running by relating the variation of foot curvature radii to running efficiency, stability and forward speed. Both a conservative reduced-order running model and one with a simple motor and friction model are used to simulate running with a rolling foot. We find that having a larger foot radius implies smoother peak vertical ground reaction forces. Increased foot radius also yields, up to a point, a larger region of stable gaits for the conservative system, and more stable, fast, and efficient gaits for the actuated version. These results motivate the design of a new set of legs to test these findings on a dynamic running platform.

This paper presents the ongoing effort of setting up a model based on interactions between Agents in the banking sector endowed with some heterogeneous mechanism of learning and optimizing independently their differentiated utilities. The construction of the system is presented in detail, as are the components starting from a mini set of DSGE equations, and going through the reasons for adopting Q-Learning, part of Adaptive Learning mechanism, to animate these agents. An Interacting Particle System filter is also justified to serve as a human psychological bias generator for each type of agents who then can behave differently even though presented with the same arriving online bit of news. Finally a quick overview of the rough results obtained so far is presented at high level.