Generate optimal torque driven 2-D gait simulations in below 5s using direct collocation.
NOTE: Running the code requires installation of CasADi (https://web.casadi.org/).
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The model is based on the one presented in "An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation" by Matthew Kelly. (SIAM Review, Vol. 59, No. 4, pp. 849-904)
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The model exists of 5 segments (2 tibia, 2 femur and trunk) and driven by ankle, knee and hip torques. The stance 'foot' is fixed to the ground and the gait pattern is imposed to have no double stance and no flight phase avoiding the implementation of different phases and/or contact models.
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We use CasADi to generate and solve an NLP from our collocation simulation. We don't need to provide analytic gradients of our constraints or cost function as CasADi does this for us using automatic differentiation.
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If you run the 'main' function you will see how the minimial torque walking pattern looks like. There are some options to restrict the gait pattern and look at the effects of for example ('walking without knee muscles'). You can uncomment these and run to observe the effects. The optimization to generate the gait pattern should take between 1s-2s depending on the performance of your computer.
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The functions to generate the equations of motion and heel-strike map constraint (to have a consistent periodic gait) are included ('generateEOM.m').
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The integration scheme is implemented as a backward Euler scheme:: x_k+1 = x_k + f(x_k+1)dt with f(x) = xdot.