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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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Tendon elastic strain energy is the dominant contributor to muscle-tendon work during steady-state running. Does this behaviour also occur for sprint accelerations? We used experimental data and computational modelling to quantify muscle fascicle work and tendon elastic strain energy for the human ankle plantar flexors (specifically soleus and medial gastrocnemius) for multiple foot contacts of a maximal sprint as well as for running at a steady-state speed. Positive work done by the soleus and medial gastrocnemius muscle fascicles decreased incrementally throughout the maximal sprint and both muscles performed more work for the first foot contact of the maximal sprint (FC1) compared with steady-state running at 5 m s 21 (SS5). However, the differences in tendon strain energy for both muscles were negligible throughout the maximal sprint and when comparing FC1 to SS5. Consequently, the contribution of muscle fascicle work to stored tendon elastic strain energy was greater for FC1 compared with subsequent foot contacts of the maximal sprint and compared with SS5. We conclude that tendon elastic strain energy in the ankle plantar flexors is just as vital at the start of a maximal sprint as it is at the end, and as it is for running at a constant speed.

This paper presents a dynamical analysis of quadrupedal locomotion, with specific reference to an adult Nubian goat. Measurements of ground reaction forces and limb motion are used to assess variations in intersegmental forces, joint moments, and instantaneous power for three discernible gaits: walking, running, and jumping. In each case, inertial effects of the torso are shown to dominate to the extent that lower-extremity contributions may be considered negligible. Footforces generated by the forelimbs exceed those exerted by the hindlimbs; and, in general, ground reactions increase with speed. The shoulder and hip dominate mechanical energy production during walking, while the knee plays a more significant role in running. In both cases, however, the elbow absorbs energy, and by so doing functions primarily as a damping (control) element. As opposed to either walking or running, jumping requires total horizontal retardation of the body's center of mass. In this instance, generating the necessary vertical thrust amounts to energy absorption at all joints of the lower extremities.

To understand how humans perform non-ballistic movements, we have developed an optimal control model to simulate rising from a chair. The human body was modeled as a three-segment, articulated, planar linkage, with adjacent links joined together by frictionless revolutes. The skeleton was actuated by eight musculotendinous units with each muscle modeled as a three-element entity in series with tendon. Because rising from a chair presents a relatively ambiguous performance criterion, we chose to evaluate a number of different performance criteria, each based upon a fundamental dynamical property of movement; muscle force. Through a quantitative comparison of model and experiment, we found that neither a minimum-impulse nor a minimum-energy criterion is able to reproduce the major features of standing up. Instead, we introduce a performance criterion based upon an important and previously overlooked dynamical property of muscle: the time derivative of force. Our motivation for incorporating such a quantity into a mathematical description of the goal of a motor task is founded upon the belief that non-ballistic movements are controlled by gradual increases in muscle force rather than by rapid changes in force over time. By computing the optimal control solution for rising from a static squatting position, we show that minimizing the integral of a quantity which depends upon the time derivative of muscle force meets an important physiological requirement: it minimizes the peak forces developed by muscles throughout the movement. Furthermore, by computing the optimal control solution for rising from a chair, we demonstrate that multi-joint coordination is dictated not only by the choice of a performance criterion but by the presence of a motion constraint as well.