Polynomial mechanics and optimal control

We describe a new algorithm for trajectory optimization of mechanical systems. Our method combines pseudo-spectral methods for function approximation with variational discretization schemes that exactly preserve conserved mechanical quantities such as momentum. We thus obtain a global discretization of the Lagrange-d'Alembert variational principle using pseudo-spectral methods. Our proposed scheme inherits the numerical convergence characteristics of spectral methods, yet preserves momentum-conservation and symplecticity after discretization. We compare this algorithm against two other established methods for two examples of underactuated mechanical systems; minimum-effort swing-up of a two-link and a three-link acrobot.Comment: Final version to EC

Optimal strategies for throwing accurately

Accuracy of throwing in games and sports is governed by how errors at projectile release are propagated by flight dynamics. To address the question of what governs the choice of throwing strategy, we use a simple model of throwing with an arm modelled as a hinged bar of fixed length that can release a projectile at any angle and angular velocity. We show that the amplification of deviations in launch parameters from a one parameter family of solution curves is quantified by the largest singular value of an appropriate Jacobian. This allows us to predict a preferred throwing style in terms of this singular value, which itself depends on target location and the target shape. Our analysis also allows us to characterize the trade-off between speed and accuracy despite not including any effects of signal-dependent noise. Using nonlinear calculations for propagating finite input-noise, we find that an underarm throw to a target leads to an undershoot, but an overarm throw does not. Finally, we consider the limit of the arm-length vanishing, i.e. shooting a projectile, and find that the most accurate shooting angle bifurcates as the ratio of the relative noisiness of the initial conditions crosses a threshold.Comment: 18 pages, 8 figure

Spatially distributed force measurement for small terrestrial animals

The 11th International Symposium on Adaptive Motion of Animals and Machines. Kobe University, Japan. 2023-06-06/09. Adaptive Motion of Animals and Machines Organizing Committee.Poster Session P7

Effects of neuromuscular lags on controlling contact transitions

We present a numerical exploration of contact transitions with the fingertip. When picking up objects our fingertips must make contact at specific locations, and—upon contact—maintain posture while producing well-directed force vectors. However, the joint torques for moving the fingertip towards a surface (τm) are different from those for producing static force vectors (τf). We previously described the neural control of such abrupt transitions in humans, and found that unavoidable errors arise because sensorimotor time delays and lags prevent an instantaneous switch between different torques. Here, we use numerical optimization on a finger model to reveal physical bounds for controlling such rapid contact transitions. Resembling human data, it is necessary to anticipatorily switch joint torques to τf at about 30 ms before contact to minimize the initial misdirection of the fingertip force vector. This anticipatory strategy arises in our deterministic model from neuromuscular lags, and not from optimizing for robustness to noise/uncertainties. Importantly, the optimal solution also leads to a trade-off between the speed of force magnitude increase versus the accuracy of initial force direction. This is an alternative to prevailing theories that propose multiplicative noise in muscles as the driver of speed–accuracy trade-offs. We instead find that the speed–accuracy trade-off arises solely from neuromuscular lags. Finally, because our model intentionally uses idealized assumptions, its agreement with human data suggests that the biological system is controlled in a way that approaches the physical boundaries of performance

Elastic energy storage in the shoulder and the evolution of high-speed throwing in Homo

Although some primates, including chimpanzees, throw objects occasionally1,2, only humans regularly throw projectiles with high speed and great accuracy. Darwin noted that humans’ unique throwing abilities, made possible when bipedalism emancipated the arms, enabled foragers to effectively hunt using projectiles3. However, there has been little consideration of the evolution of throwing in the years since Darwin made his observations, in part because of a lack of evidence on when, how, and why hominins evolved the ability to generate high-speed throws4-8. Here, we show using experimental studies of throwers that human throwing capabilities largely result from several derived anatomical features that enable elastic energy storage and release at the shoulder. These features first appear together approximately two million years ago in the species Homo erectus. Given archaeological evidence that suggests hunting activity intensified around this time9, we conclude that selection for throwing in order to hunt likely played an important role in the evolution of the human genus

Curvature-induced stiffening of a fish fin

How fish modulate their fin stiffness during locomotive manoeuvres remains unknown. We show that changing the fin's curvature modulates its stiffness. Modelling the fin as bendable bony rays held together by a membrane, we deduce that fin curvature is manifested as a misalignment of the principal bending axes between neighbouring rays. An external force causes neighbouring rays to bend and splay apart, and thus stretches the membrane. This coupling between bending the rays and stretching the membrane underlies the increase in stiffness. Using analysis of a 3D reconstruction of a Mackerel (Scomber japonicus) pectoral fin, we calculate the range of stiffnesses this fin is expected to span by changing curvature. The 3D reconstruction shows that, even in its geometrically flat state, a functional curvature is embedded within the fin microstructure owing to the morphology of individual rays. Since the ability of a propulsive surface to transmit force to the surrounding fluid is limited by its stiffness, the fin curvature controls the coupling between the fish and its surrounding fluid. Thereby, our results provide mechanical underpinnings and morphological predictions for the hypothesis that the spanned range of fin stiffnesses correlates with the behaviour and the ecological niche of the fish