Working with Dan Levine and Ken Nakagaki from the Tangible Media group.
In this project we designed a 1 DOF robot to perform a forward flip. For inspiration we drew insights from the forward pike move in gymnastics. During the arial phase of this move, rotation is generated as the gymnast bends forward at the waist, with the legs kept straight. This moves the center of mass away from the hips. Our robot mimics this by including two rigid links that are actuated about a central DC motor. We generate the forward momentum by dropping the robot with an inital rotation from the vertical axis.
To fabricate the robot linkages we created a sheet metal assembly using Fusion 360, the Fablight fiber laser cutter and metal bending tools. Finally the parts were assembled using rivets. I had some trouble getting the folds in the correct place, I overcame this by tapering the relief holes so that the weakness as a result of the reliefs was centered along a single axis.
Below is a log of summaries written in response to weekly assigned paper readings.
Walking and Running - Alexander - 1984 - Human walking can be modelled as a point mass at the pelvis with two legs, rigidly straight that pivot around the hip. In this way the maximum velocity of walking is limited as follows $v \leqslant \sqrt{gl}$, therefore people with longer legs (i.e. adults) have a greater maximum walking pace. In the same way, race walkers increase their maximum walking pace by tilting their hips when their feet make contact with the ground, thereby increasing the apparent length of their leg fo each step. Studies carried out with horses (Hoyt and Taylors 1981) have shown that mammals adopt the gait that expends the minimum amount of energy for the required speed. The slightly disturbing video below shows a decerebrated cat changing gaits at different speeds, thereby demonstrating that this adaptation occurs passively.
Different gaits at different speeds can be characterized by the duty factor, $\beta$, which describes the duration of the stride for which the foot is in contact with the ground and the shape factor, $q$, which describes the magnitude of the force imparted on the ground over time. Analysis of the different muscles and tendons that are active during running shows that tendons store elastic-strain energy during running and it is this that makes running more efficient that walking above certain speeds.
Impedance Control - Hogan - 1987 - Summary - This paper presents uses a method of control based on impedance which can be used to control robots in situations where they make physical contact with their environment. When a robot makes contact with an external object it experiences interaction forces. Force based methods have been used to manage these interactions however they often lead to contact instability because they do not take into consideration the dynamics of the system and therefore they do not model how the dynamics of the system may affect the robot when it makes contact with something else.
The concept of impedance is described in a more detail in this paper. Hogan describes impedances in the following way: "admittances, which accept effort (e.g., force) inputs and yield flow (e.g., motion) outputs; and impedances, which accept flow (e.g., motion) inputs and yield effort (e.g., force) outputs".
All that is required to implement this control is a set of constants that describe the robot including masses, lengths and moments of inertia. During operation, you then take measurements of the joint motions (angle and angular velocity) and external forces on the end effector and feed these into a nonlinear impedance control algorithm. The algorithm then generates outputs (which in most cases translates to torques from motors) to make the robot end-effector exhibit a specified target impedance.
There are many benefits of using this approach including the elimination of the need to perform complex and difficult inverse kinematic calculations. Another key benefit of this method is it's suitability to all parts of a robot's task including free motion, the constrained motion (when it makes contact something) and the transitions between these two situations.
Role of Compliance - McMahon - 1985 - This paper extends beyond the first reading of the semester to investigate quadrupedal animals and the impact of compliance in the interaction between legs and the ground. Furthermore this paper includes in it's investigation into the sequence of leg placements and how this effects different gaits. The paper draws interesting conclusions about the role of compliance in the characteristics of walking and running, "if the surface under a runner's feet is soft and compliant, more time is required to reverse the runner's downward velocity as he or she rebounds into the air" which makes me wonder how it is that people are able to run 100m fastest on a compliant running track in comparison to a non-compliant concrete floor? In order to understand the impact of the sequence of leg placements, the paper decomposes various gaits into the number of rebounds per stride, the number of legs in contact with the as well as the stiffness of the whole-animal and individual legs. This analysis leads to the conclusion that for higher speed gaits the legs and body become less stiff and the bumpiness of the ride reduces. The paper then goes on to redo the analysis by making different assumptions and holding different characteristics constant and in this way provides a good demonstration of the approach one can take to understanding a complex behaviour such as locomotion.
Running with Symmetry - Raibert - 1986 - This paper uses the fact that gaits have symmetric qualities to determine simplified control strategies for legged robots. Symmetry is assessed in terms of the vertical position, forward position and pitch angle and used to understand the symmetry of forces and torques throughout a stride. Having understood types of symmetry present, the paper describes methods for generating symmetric motion using approximations for future foot placement. One such method is using the scissor algorithm which uses the previous leg's movement to influence the next step. Towards the end of the paper there's a good quote that encapsulates the values of this type of approach - "Perhaps most important is the idea that symmetry and balance give us tools for dealing with a dynamic system without requiring detailed solutions to complex formulations.".