We present an analytical method for the concurrent calculation of optimal parallel compliant elements and frequency of reference trajectories for serial manipulators performing cyclic tasks. In this approach, we simultaneously shape and exploit the robot's natural dynamics by finding a set of compliant elements and task frequency that result in minimization of an energy-based cost function. The cost function is the integral of a weighted squared norm of the generalized forces. We prove that the generalized force needed for tracking the reference trajectory is a linear function of compliance coefficients and a quadratic function of task frequency. Therefore, the cost function is quadratic with respect to stiffness coefficients and quartic with respect to the task frequency. These properties lead to a well-posed optimization problem with a closed-form solution. Using three case studies, we elucidate the properties of our method.

Human population density is globally three times higher along the coasts than inland, and thus environmental impacts of human activities are greater in magnitude on coastal ecosystems such as beaches and dunes. Vulnerability assessment (the loss of capacity to return to the original dynamic state after system displacement) is thus necessary to evaluate the conservation status and determine the most relevant disturbance events. Twenty-six sites along 902 km of Gulf of Mexico coastline, varying in conservation status and sedimentary dynamics, were sampled. At each site a vulnerability index (VI) was calculated based on variables that described geomorphological condition, marine influence, aeolian influence, vegetation condition and human effects. Vulnerability was very variable along the coast and only 19% of the sampled locations (mostly in the central Gulf of Mexico) displayed low vulnerability. Cluster analyses of the values assigned to the checklists for each location grouped the studied sites into three, according to their VI values. Low vulnerability locations had abundant sediment supply and low human impact. Locations with medium to high VI were mostly affected by their natural geomorphological and marine features and had medium to intense human activities. Management strategies should consider the observed variability in vulnerability, the natural dynamics of these systems and the role of human activities and interests, in order to achieve adequate policies and establish well-informed priorities for integrated coastal zone management.

A real-time joint trajectory generator for planar walking bipeds is proposed. This trajectory planner generates dynamically stable motion patterns by using a set of objective locomotion parameters as its input, and by tuning and exploiting the natural upper body dynamics. The latter can be determined and manipulated by using the angular momentum equation. Basically, trajectories for hip and swing foot motion are generated, which guarantee that the objective locomotion parameters attain certain prescribed values. Additionally, the hip trajectories are slightly modified such that the upper body motion is steered naturally, meaning that it requires practically no actuation. This has the advantage that the upper body actuation hardly influences the position of the Zero Moment Point. The effectiveness of the developed strategy is demonstrated by simulation results.