Leg Use Testing

Experimental Results (Attachments)
  • LegTurnNotes2.doc - indentifies key attributes for each test group and ranks the group turning methods (ADAMS sim and Overhead (OH) robot testing
  • maxsortboth2.xls - contains the top 4 turn setups for each testing group, and statistics for leg use in these top 4 setups
  • legs_turning2.doc - cryptic description of the tests to be performed and the motivation (please ask me for clarification if it seems crazy)
  • Include better description of experiments (?)
  • Include some charts of the data (?)

Observations after leg testing
Front legs seem to have major control over the gait. This is commonly the leg that has the most distinct function of the 3 contralateral leg pairs. The middle legs are used to support and also thrust the body. The rear are mainly used to thrust the body forward. The front leg has been shown (thru Jclark?s sims) to greatly influence the speed and stability of the robot. It alone can cause speed changes and instability. It is generally the odd leg out in terms of its use and longitudinal thrust direction. Because of these observations, it is the single most important leg in maneuvers and body configuration control (pitch and roll).
(Is this behaving as a rear wheel drive car with front axle steering? Most of the thrust is coming from mid and rear, while the front leg can be used to steer.)

The front and rear legs combined seem to play a strong role in control of the robot motion. The front and rear legs can both create the changes necessary to produce maneuvers in the yaw (horizontal), pitch (sagittal) and roll (frontal) planes maneuver analyses previously listed. These two legs can cause a change in force location and magnitude relative to the COM. These changes create turning moments about the COM (H-plane model ? YAW) simply by changing the foot placement and duty cycle. These two legs can also be used to alter the pitch, which is known to be related to velocity. Using this pitch change from leg placement and/or duty cycle changes, two differing velocities can be selected for each side of the body, resulting in a turn (sagittal plane model ? PITCH). The front and rear legs can also be used in contralateral combinations to create roll by leg placement and duty cycle changes. The roll of body is related to various turning methods and can be used as another means to analyze turning (transverse plane model - ROLL). Leg placement changes generally have a more substantial effect on body maneuvers, but duty cycles changes can also be used individually or in concert with leg placement changes to get a desired effect.

Based on observations from leg testing, tripods may provide a unique opportunity for maneuvers. Tripods always contain an ipsilateral set of front and rear legs which have been found to be very influential in maneuvers. By changing the leg placement and duty cycle of legs in a tripod, the turning moment, roll and pitch (depending on the analysis method) can all be controlled to create turns. For example (using the body roll analysis) on the left tripod, the LF and LR legs can be shifted to land more forward, while the duty cycle on the RM can be decreased to cause roll during this tripod stance. In a likewise fashion on the right tripod, the RF and RR legs can be shifted to land more toward the rear, while the duty cycle of the LM can be increased to create a similar roll scenario for the right tripod as the left.

(Test this idea on robot) <DCi-20%?, DCo-20%?>

  • new LT leg positions cause interference
  • above strategy (with LM adjusted for interference) does not turn well
    • lower velocity and slower turning, body rolls, but also tends to drag
    • RF change may cause the gait to be unstable (nosedive on right)
    • minus RF position change creates stability, but still slow
    • minus RM DC change (also RF LA) turns a bit better
    • same DC (35%) throughout still seems to be best turn (LA ips)
    • RM+ and LM- DC changes (separately and combined) both produce poor, non-period 1 turns
    • (Might try more extreme DC values)

Multiple Leg Alterations
It is clear from the leg testing for turning that changing more than one leg will produce a better turn than just using a singular leg, if these legs are changed properly. Thus the method for changing these legs should be further investigated. Using more legs adds more direct control of the turning moment (yaw), body pitch and body roll. (This trend may reach a plateau that tapers off as more than 3 legs are used.) From experiments, it is apparent that changing leg properties on the same side of the body are more effective than changing contralaterally or diagonally leg properties. It is further been shown that when changing these ipsilateral legs, changing them in the same direction (in particular moving the foot placement of multiple legs forward, or increasing the DC on two legs) is more effective than changing the legs in different directions (an increase and a decrease). The nominal settings allow the robot to run very stably and are the results of several rounds of performance analysis. These settings may reflect a very stable region for a forced oscillator with similar mass-spring and damper characteristics as the robot. Thus, when the force is changed, such as by DC or LA alterations, the system may exit the stable (balanced?) forced oscillation region and become unstable (unstable, ie. offset sine). While these unstable gaits may produce turning, the performance can be improved by remaining in the forced oscillation region. This can be accomplished by altering the force direction, or in this case, the leg angles. (Altering all legs by similar angles allows a more uniform force balance than by altering DC or changing the legs in other methods. This retains the leg relationships that are known to the good for normal running) Leg angle changes may retain the oscillation stability by simply redirecting the forces (vector?) and not significantly affecting the net force effect (amplitude?). DC changes alter the net force effects and thus negatively effect the stability.

Once turning has been narrowed to just ipsilateral legs moving in the same direction, various methods for changing these leg angles can be investigated. There are 3 legs on each side giving 3 degrees of freedom for independent control. The dimension of the control parameters can be reduced by introducing dependencies between the legs and other supplemental parameters. To reduce the dimension to 2, one logical method is to have a mean leg angle (MA) and a sprawl angle (SA) that will dictate the angles for all 3 legs. The SA is the angle between the front and rear legs. The sprawl angle acts to change the difference between the function of the front and rear legs (braking at one extreme and acceleration at the other). For a small sprawl angle, the leg angles are very similar and thus the legs generally act in a similar fashion. For a large sprawl angle, the leg angles are very different between front and rear and lead to varied functionality (for example, front legs may be mostly braking, mid legs are supporting and thrusting, while rear primarily thrust). (Add some diagrams here for clarity) The mean angle is the angle of the middle leg whose projection will intersect with the intersection of the other two legs? projections (May want to add diagram here, confusing) The mean angle controls what regions of functionality the various legs will fall in. By selecting the mean angle, some legs may end up near vertical (mostly providing support) while others are at substantial angles (inclines?) (mostly either braking or accelerating). In 2 dimension turning, both parameters can have an effect on body dynamics such as performance and stability.


Figure. Mean angle and sprawl angle

Another 2 dimensional method for turning simply involves a Cartesian coordinate system on the sagittal plane. By selecting an X and Y intersection point for the 3 legs in the sagittal plane, the leg angles of these three legs become uniquely defined. The location of the intersection point relative to the body will determine the performance of the robot. Unfortunately, the calculation of intersection points requires the use of trigonometric functions, and a floating point processor or a lookup table. While a floating point processor was not available for the Sprawlettes, a lookup table was not thoroughly investigated in the initial turning investigation. Later work showed that similar results could be obtained by using a 1 parameter based turn. Aside from these two methods, there are many ways to reduce the task of selecting 3 leg angles to a task of selecting 2 other parameters.


Figure. Workspace shapes for cartesion and cylindrical coordinate systems

In a similar fashion, the 3 dimensional problem can be reduced to a 1 dimensional problem by simply having a fixed set of leg angles, then altering all three relative to some linear parameter. A decent choice of the fixed leg angles would be those found from previous research to be the best for straight ahead running on level ground. Then, for turning, legs on one side of the body can be shifted relative to some single parameter. For the Sprawlettes, this parameter has been called the turnfactor, and it alters all ipsilateral leg angles by equal amounts. Just as this mapping has been set to change all legs linearly, the mapping could have changed the legs by some percentage relative to the ground normal, or by the square root of the parameter, or any other imaginable function. There are several advantages to changing all legs in linear fashion. The linear change prevents leg collision, retains leg relations that are known to be stable for standard running and provides a smooth, predictable turn mapping. In the sagittal plane, this isometric-ipsilateral (1D) turn method traces a gentle curve above the robot. This curve is fairly fixed and can be shifted up or down by altering the leg angles of the standard running pose. The turnfactor parameter selects where on the line the effective leg intersection point will fall.

For the 2D case, the selection of SA and MA (or other 2D parameters) will allow 2D control of the intersection in the sagittal plane to affect turning. The 1D and 2D case are just two mappings that allow turning by the selection of the effective leg intersection point. The functional regions in the sagittal plane are traversed by both 1D and 2D methods, just via differing curves (with similar gradients). Both 1 and 2 parameter-based turning have the same general effect for effective initial leg positions. (Include Matlab plots of curves)


Figure. Mappings for 1D (left) and 2D (right) turn methods

Effective Intersection
Another method of analyzing 2 dimensional leg positioning involves effective leg angles and intersection distance, and can be applied to any dimensional turning method. For the Sprawlette robots, if you extend the projections of the three legs, they will either intersect in one point or at three (provided no 2 lines are parallel). For the case of 3 intersections, the effective intersection point for all 3 legs can be considered to be the center of this triangle. The angle of the line between the middle leg mount (hip) and the (effective) intersection point can be viewed as the effective leg angle for the 3 legs. Likewise, the distance from the middle leg mount (hip) to the (effective) intersection point can be called the effective intersection distance. These two parameters can be used to describe the majority of the leg configurations on one side of the robot, no matter what n-dimensional turning method is used. It is hypothesized that the effective leg intersection point is a measure of the operation and performance of legs on one side of the body (no matter how the intersection point is derived, either by direct intersection (intersection based turn) or triangulation (non-intersection based, ie 1D iso-ips, other 2D or 3D)).


Figure. Effective distance (d) and effective leg angle (theta)


  • May have to consider servo/body dynamics in extreme turn (may have to use instant interim strategy until servos rotate or momentum builds for cont. turn strategy)

May want to investigate turning via LA increases, and also look at DC increases separately

-- AMcClung? - 06 Aug 2003

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