Bézier Curve Implementation

“The problem of finding a feasible collision free path, from start to goal, can be solved by applying Bézier technique; a number of intermediate points will be found and used for path planning.” (Shabeeb, 2013, p. 80)

Path Planning 

“Bézier Curves have useful properties for path planning" (Choi, Curry and Elkaim, 2009, p. 1):

The curve “always passes through the first and last control point” (Dixit and Silakari, 2015, p. 319) as the first and last control points are interpolated and the interior control point(s) approximated.
This property will allow me to easily define the first control point with the foot position at the start of swing phase, and the fourth control point as the desired end position as the double support phase begins – leaving the interior control points to define any features of the trajectory including step height or obstacle avoidance.

Catmull-Rom Implementation

A “Catmull-Rom spline is preferred over other techniques due to ease of computation and local control” (George et al., 2018, p. 7)

As discussed by Breen et al. (not dated) a Catmull-Rom spline is created from a series of linear Hermite curves with tension modified at each control point which can increase the order of continuity. This explains many of the properties of a Catmull-Rom spline.

Trajectory Planning

Path Planning 

“path planning problem formulation involves searching the configuration space (C-space) of a robotic system for a collision-free path that connects a start configuration a goal configuration” (Bertram et al., 2006, p.1874).

Having implemented a suitable knee joint with simple end effector to target seeking behaviour, a method of imitating accurate movement of leg limbs during the swing phase is required.

Project Milestones Adjustment

Current progress 

Reviewing my current progress against my estimated milestones created before beginning development reveals that my early expectations were inaccurate.

While the contents of my initial milestones largely remain essential, what I have already learnt has shown that I have underestimated the size of several goals and had not fully understood the relationship between some of the necessary functionality.

Biped Gait Analysis

Human Gait Cycle 

To attempt to replicate human gait I first need to understand the stages of a normal bipedal gait cycle.

“A typical gait involves one foot placed forward with the second placed the same distance beyond the first” (Kong and Tomizuka, 2008, p. 3678).
This process repeated is the human gait.