Simple passive dynamic walker integration (ode45) returns discontinuous state estimations

I'm using Andy Ruina's simplest walker simulation (http://ruina.tam.cornell.edu/research/topics/locomotion_and_robotics/ranger/ranger_paper/Reports/Ranger_Robot/control/simulator/index.html) to create an ideal simulation to use as ground truth for further experimentation with model manipulation. The simulation uses a loop to perform integration of a noncontinuous function, as each heelstrike collison creates said discontinuity; however, I was under the assumption that the walker is governed by a system of ODEs that are continuous per gait cycle.

% ODE definition

% y1: theta

% y2: thetadot

% y3: phi

% y4: phidot

% gam: slope of incline (radians)

% First order differential equations for Simplest Walking Model

ydot = [y(2);

sin(y(1)-gam);

y(4);

sin(y(1)-gam)+sin(y(3))*(y(2)*y(2)-cos(y(1)-gam))];

But, when integrated, the plotted states look almost like a linear-piecewise function, but only for the first part of the gait cycle as well as the very end. (First image is theta over 3 gait cycles, each heelstrike denoted by the vertical black line; the second image is a zoomed in plot of theta for one gait cycle.)

I have tried various other ode solvers (simulation does not run), changed the tolerances (simulation does not run), set max step size (still looks like a linear-piecewise function), used forward Euler to gut-check that the system of ODEs are actually continuous (they are), and checked that the linear sections were equal in length (each is 30 points) but I have no idea why that's helpful.

I would appreciate any insight/suggestions and happy to answer any questions or clarifications, as I am counting on continuous time series data for further data science exploration.

[Star Strider]

I wasn’t aware of that site, or the simulaltion. Thank you!

The ‘tspan’ argument in the ‘onestep’ function is a linspace call with 1000 elements, so it appears very smooth when I run it using the included solver, ode113 (in R2019a).

I’m running the code in simplest_walker.m, after deleting the three clc, clear all, and close all statements in the beginning.