Forward Dynamic Optimization Research Articles

Optimal Control Formulation for Manual Wheelchair Locomotion Simulations: Influence of Anteroposterior Stability.

Manual wheelchair (MWC) locomotion exposes the user's upper-body to large and repetitive loads, which can lead to upper limbs pain and injuries. A thinner understanding of the influence of MWC settings on propulsion biomechanics could allow for a better adaptation of MWC configuration to the user, thus limiting the risk of developing such injuries. Advantageously compared to experimental studies, simulation methods allow numerous configurations to be tested. Recent studies have developed predictive locomotion simulation using optimal control methods. However, those models do not consider MWC anteroposterior stability, potentially resulting in unreasonable propulsion strategies. To this extent, this study aimed at confirming if constraining MWC anteroposterior stability in the optimal control formulation could lead to a different simulated movement. For this purpose, a four-link rigid-body system was used in a forward dynamics optimization paired with an anteroposterior stability constraint to predict MWC locomotion dynamics of the upper limbs during both startup and steady-state propulsion. Simulation results indicated the occurrence of MWC tipping when stability was not constrained, and that the constrained optimal control algorithm predicted different propulsion strategies. Hence, further proceedings of MWC locomotion simulation and optimal control investigations should take the anteroposterior stability into account to achieve more realistic simulations. Additionally, the implementation of the anteroposterior stability constrains unexpectedly resulted in a reduction of the computational time.

Estimation of Joint Moments During Turning Maneuvers in Alpine Skiing Using a Three Dimensional Musculoskeletal Skier Model and a Forward Dynamics Optimization Framework.

In alpine skiing, estimation of the joint moments acting onto the skier is essential to quantify the loading of the skier during turning maneuvers. In the present study, a novel forward dynamics optimization framework is presented to estimate the joint moments acting onto the skier incorporating a three dimensional musculoskeletal model (53 kinematic degrees of freedom, 94 muscles). Kinematic data of a professional skier performing a turning maneuver were captured and used as input data to the optimization framework. In the optimization framework, the musculoskeletal model of the skier was applied to track the experimental data of a skier and to estimate the underlying joint moments of the skier at the hip, knee and ankle joints of the outside and inside leg as well as the lumbar joint. During the turning maneuver the speed of the skier was about 14 m/s with a minimum turn radius of about 16 m. The highest joint moments were observed at the lumbar joint with a maximum of 1.88 Nm/kg for lumbar extension. At the outside leg, the highest joint moments corresponded to the hip extension moment with 1.27 Nm/kg, the knee extension moment with 1.02 Nm/kg and the ankle plantarflexion moment with 0.85 Nm/kg. Compared to the classical inverse dynamics analysis, the present framework has four major advantages. First, using a forward dynamic optimization framework the underlying kinematics of the skier as well as the corresponding ground reaction forces are dynamically consistent. Second, the present framework can cope with incomplete data (i.e., without ground reaction force data). Third, the computation of the joint moments is less sensitive to errors in the measurement data. Fourth, the computed joint moments are constrained to stay within the physiological limits defined by the musculoskeletal model.

Forward dynamic optimization of handle path and muscle activity for handle based isokinetic wheelchair propulsion: A simulation study

Push-rim wheelchair propulsion is biomechanically inefficient and physiologically stressful to the musculoskeletal structure of human body. This study focuses to obtain a new, optimized propulsion shape for wheelchair users, which is within the ergonomic ranges of joint motion, thus reducing the probability of injuries. To identify the propulsion movement, forward dynamic optimization was performed on a 3D human musculoskeletal model linked to a handle based propulsion mechanism, having shape and muscle excitations as optimization variables. The optimization resulted in a handle path shape with a circularity ratio of 0.95, and produced a net propulsion power of 34.7 watts for an isokinetic propulsion cycle at 50 rpm. Compared to push-rim propulsion, the compact design of the new propulsion mechanism along with the ergonomically optimized propulsion shape may help to reduce the risk of injuries and thus improve the quality of life for wheelchair users.

Optimization-based motor control of a Paralympic wheelchair athlete

The following research approximated how the central nervous system of Paralympic wheelchair athletes resolve kinematic redundancies during upper-limb movements. A multibody biomechanical model of a tetraplegic Paralympic athlete was developed using subject-specific body segment parameters. The angular joint kinematics throughout a specified Paralympic sport movement (i.e., wheelchair curling) were experimentally measured using inertial measurement units. The motor control system of the Paralympian was mathematically modelled and simulated using forward dynamics optimization. The predicted kinematics from different optimization objective functions (i.e., minimizing resultant joint moments, mechanical joint power, and angular joint velocities and accelerations) were compared with those experimentally measured throughout the wheelchair curling movement. Of the optimization objective functions under consideration, minimizing angular joint accelerations produced the most accurate predictions of the kinematic trajectories (i.e., characterized with the lowest overall root mean square deviations) and the shortest optimization computation time. The implications of these control findings are discussed with regards to optimal wheelchair design through predictive dynamic simulations.

Optimal Dynamic Liquidation of an Inventory via Forward Markets

In commodity markets, a trader selling her inventory over a finite time horizon has access not only to the spot market but also to forward contracts. The trader has the choice to sell at the spot price, or to short a forward contract for later delivery, or a combination of both. While the commodity is hedged with the forward contract and carried in the inventory, the trader can dynamically adjust the maturity of the forward contract at each time step until the inventory is completely depleted. This paper investigates the optimal liquidation strategy for such a trader in the above framework, which can be considered a dynamic extension of the cash and carry arbitrage that may arise in contango markets. It is proved, independent of the underlying stochastic forward price model, that a ‘partial sale’ strategy involving the sale of the inventory across different contracts is not optimal. In addition, under a linearity assumption on the forward price differences, the optimally selected forward maturity is limited to a subset comprising the immediate (spot), next, or last time stage. The theoretical results imply that the optimal actions set is considerably smaller than the feasible set. An Approximate Dynamic Programming (ADP) policy is developed, and compared to the solution achieved by an exact grid-based technique and a Forward Dynamic Optimization (FDO) approach. The risk and return characteristics of ADP and FDO methods are contrasted. The theoretical propositions are verified numerically, and found to reduce computational times significantly.

A forward dynamic optimization strategy under contango storage arbitrage with frictions

The goal of this paper is to explain and improve the offshore oil storage trade observed in a contango market using a forward dynamic optimization strategy. The strategy is developed using trades in forward contracts and contrasted with the literature. By simulating forward prices based on realistic May 2009 market conditions, our strategy, when compared with selling the oil on the spot in a base case scenario, gains an extra US$8.99/barrel, which is comprised of US$6.19 generated by the initial forward maximization and US$2.80 achieved by the subsequent trades. The impact of the forward curve dynamics is studied by examining the trading decisions based on the realized slope and mean level of the forward curve. The path of the realized slope and stepwise changes in the slope are found to be able to explain most of the trading decisions. The effect of initial conditions, the frequency with which the position is readjusted and the storage cost are also examined. The optimal frequency depends on the storage cost. Friction is introduced into the problem by penalizing the refund of the storage cost when a decision to advance the short position in time is made, where its influence, which depends on the storage cost, is at most US$1.40.

A Model of Muscle–Tendon Function in Human Walking at Self-Selected Speed

Although joint biomechanics and whole-body energetics are well documented for human walking, the underlying mechanisms that govern individual muscle-tendon behaviors are not fully understood. Here, we present a computational model of human walking that unifies muscle and joint biomechanics with whole-body metabolism for level-ground walking at self-selected speed. In the model, muscle-tendon units that dorsiflex the ankle, and flex and extend the knee, are assumed to act as linear springs upon neural activation; each muscle-tendon is modeled as a tendon spring in series with an isometric force source. To provide the mechanical power lost in step-to-step gait transitions, a Hill-type soleus muscle is modeled to actively plantar flex the ankle using muscle state and force as reflex feedback signals. Finally, to stabilize the trunk during stance, and to protract and retract each leg throughout the swing phase, two mono-articular Hill-type muscles actuate the model's hip joint. Following a forward dynamics optimization procedure, the walking model is shown to predict muscle and joint biomechanics, as well as whole-body metabolism, supporting the idea that the preponderance of leg muscles operate isometrically, affording the relatively high metabolic walking economy of humans.

Sell Spot or Sell Forward? Analysis of Oil-Trading Decisions With the Two-Factor Price Model and Simulation

Summary In oil and gas markets, the relationships between the spot and futures prices reveal important opportunities for value creation. When oil prices are in contango (i.e., when futures prices are higher than the expected future spot prices), it may be profitable for a trader to hold oil in storage and enter into a futures contract instead of selling oil in the spot market. The decision to either sell oil in the spot market or use the storage to sell oil in the future is usually challenging because the future spot prices and futures prices are uncertain. In this paper, we discuss the storage trading decisions by use of a realistic example, and we propose an analysis methodology on the basis of a two-factor price process for modeling spot and futures oil prices. The dynamic decision problem, sell spot or sell forward, is analyzed with a forward dynamic optimization algorithm and the least-squares Monte Carlo simulation.

A Robotic Model of Transfemoral Amputee Locomotion for Design Optimization of Knee Controllers

A two-dimensional, seven link, nine degrees of freedom biped model was developed to investigate the dynamic characteristics of normal and transfemoral amputee locomotion during the entire gait cycle. The equations of motion were derived using the Lagrange method and the stance foot-ground contact was simulated using a five-point penetration model. The joint driving torques were obtained using forward dynamic optimization of the normal human gait and applied to the intact joints of the amputee. Three types of motion controllers; frictional, elastic and hydraulic were considered for the prosthetic joints of the amputee and their design parameters were optimized to achieve the closest kinematics to that of the normal gait. It was found that, if optimally designed, all three passive controllers could reasonably reproduce a normal kinematical pattern in the swing phase. However, the stance phase kinematics could only be replicated by the hydraulic and elastic controllers; the performance of the latter was highly sensitive to the design parameters. It was concluded that an appropriately designed hydraulic motion controller can provide reasonably normal kinematics and reliable stability for stance knee flexion prostheses.

A modular and efficient approach to computational modeling and sensitivity analysis of robot and human motion dynamics

AbstractIn this paper a new class library for the computation of the forward multi‐body‐system (MBS) dynamics of robots and biomechanical models of human motion is presented. By the developed modular modeling approach the library can be flexibly extended by specific modeling elements like joints with specific geometry or different muscle models and thus can be applied efficiently for a number of dynamic simulation and optimization problems. The library not only provides several methods for solving the forward dynamics problem (like articulated body or composite rigid body algorithms) which can transparently be exchanged. Moreover, the numerical solution of optimal control problems, like in the forward dynamics optimization of human motion, is significantly facilitated by the computation of the sensitivity matrix with respect to the control variables. Examples are given to demonstrate the efficiency of the approach. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Model-based estimation of muscle forces exerted during movements

Estimation of individual muscle forces during human movement can provide insight into neural control and tissue loading and can thus contribute to improved diagnosis and management of both neurological and orthopaedic conditions. Direct measurement of muscle forces is generally not feasible in a clinical setting, and non-invasive methods based on musculoskeletal modeling should therefore be considered. The current state of the art in clinical movement analysis is that resultant joint torques can be reliably estimated from motion data and external forces (inverse dynamic analysis). Static optimization methods to transform joint torques into estimates of individual muscle forces using musculoskeletal models, have been known for several decades. To date however, none of these methods have been successfully translated into clinical practice. The main obstacles are the lack of studies reporting successful validation of muscle force estimates, and the lack of user-friendly and efficient computer software. Recent advances in forward dynamics methods have opened up new opportunities. Forward dynamic optimization can be performed such that solutions are less dependent on measured kinematics and ground reaction forces, and are consistent with additional knowledge, such as the force-length-velocity-activation relationships of the muscles, and with observed electromyography signals during movement. We conclude that clinical applications of current research should be encouraged, supported by further development of computational tools and research into new algorithms for muscle force estimation and their validation.