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This paper describes a computational method for solving optimal control problems involving large-scale, nonlinear, dynamical systems. Central to the approach is the idea that any optimal control problem can be converted into a standard nonlinear programming problem by parameterizing each control history using a set of nodal points, which then become the variables in the resulting parameter optimization problem. A key feature of the method is that it dispenses with the need to solve the two-point, boundary-value problem derived from the necessary conditions of optimal control theory. Gradient-based methods for solving such problems do not always converge due to computational errors introduced by the highly nonlinear characteristics of the costate variables. Instead, by converting the optimal control problem into a parameter optimization problem, any number of well-developed and proven nonlinear programming algorithms can be used to compute the near-optimal control trajectories. The utility of the parameter optimization approach for solving general optimal control problems for human movement is demonstrated by applying it to a detailed optimal control model for maximum-height human jumping. The validity of the near-optimal control solution is established by comparing it to a solution of the two-point, boundary-value problem derived on the basis of a bang-bang optimal control algorithm. Quantitative comparisons between model and experiment further show that the parameter optimization solution reproduces the major features of a maximum-height, countermovement jump (i.e., trajectories of body-segmental displacements, vertical and fore-aft ground reaction forces, displacement, velocity, and acceleration of the whole-body center of mass, pattern of lower-extremity muscular activity, jump height, and total ground contact time).

We investigated how the human lower-limb joints modulate work and power during walking and running on level ground. Experimental data were recorded from seven participants for a broad range of steadystate locomotion speeds (walking at 1.59±0.09 m s −1 to sprinting at 8.95±0.70 m s −1). We calculated hip, knee and ankle work and average power (i.e. over time), along with the relative contribution from each joint towards the total (sum of hip, knee and ankle) amount of work and average power produced by the lower limb. Irrespective of locomotion speed, ankle positive work was greatest during stance, whereas hip positive work was greatest during swing. Ankle positive work increased with faster locomotion until a running speed of 5.01±0.11 m s ), the ankle's contribution to the average power generated (and positive work done) by the lower limb during stance significantly increased from 52.7±10.4% to 65.3±7.5% (P=0.001), whereas the hip's contribution significantly decreased from 23.0±9.7% to 5.5±4.6% (P=0.004). With faster running, the hip's contribution to the average power generated (and positive work done) by the lower limb significantly increased during stance (P<0.001) and swing (P=0.003). Our results suggest that changing locomotion mode and faster steady-state running speeds are not simply achieved via proportional increases in work and average power at the lower-limb joints.

This paper describes the design, development, implementation, and assessment of a multimedia-based learning module focused on biomechanics. The module is comprised of three challenges and is based on a model of learning and instruction known as the How People Learn (HPL) framework. Classroom assessment of the first challenge was undertaken to test the hypothesis that the HPL approach increases adaptive expertise in movement biomechanics. Student achievement was quantified using pre-and post-test questionnaires designed to measure changes in three facets of adaptive expertise: factual and conceptual knowledge and transfer. The results showed that the HPL approach increased students' conceptual knowledge as well as their ability to transfer knowledge to new situations. These findings indicate that challenge-based instruction, when combined with an intellectually engaging curriculum and principled instructional design, can accelerate the trajectory of novice to expert development in bioengineering education.

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