Robot Design by Animation

overview

intro

data

model

optimization

simulation

hybrid_1

hybrid_2

conclusions

Model

Figure 8
Close up of Sprawlita Leg The dynamic model considered here is a rigid body with six legs in the horizontal plane. Each leg is a prismatic joint with a spring and a damper element in parallel. Each leg is attached to the body through a rotational spring and a rotational damper.
This model is motivated by the simplified configuration of our robots. Each leg in the robot consists of a prismatic pneumatic piston attached to a compliant viscoelastic hip joint (see Figure 8). This configuration, in turn, was motivated by findings that legs in the cockroach act as "thrusters", where the leg reaction forces tend to align along the hip joint.

Each leg in the model exerts forces and a moment on the body when it is in contact with the ground. This force is the result of the damping terms and the deflections of the hip and linear springs.

The timing of the system is modeled as a feedforward motor pattern. The dynamics of the model proceed as follow:

At the beginning of the stride period, one tripod of support is activated. When activated, each leg appears in the ground at a predetermined position with respect to the body. This allows for legs to be activated with a pre-compression.
The system then proceeds under the influence of these three legs.
Halfway into the stride period, the current tripod of legs is deactivated and the other tripod of legs is activated. The state of the system (X, Y and rotational positions and velocities) is continous between mode changes.
The cycle is repeated at the end of the stride period.

Each leg is attached to the body at a predetermined position in the body with respect to the center of mass.

Thus, the unknowns at this point to be solved for are:

Linear leg stiffnesses (ki) and nominal lengths (Li)
Rotational hip stiffnesses (Ki) and nominal angles (Ai)
Linear leg (bi) and hip (Bi) damping coefficients

Which makes our search vector consist of 18 unknowns:

X = [k1 k2 k3 b1 b2 b3 K1 K2 K3 B1 B2 B3 L1 L2 L3 A1 A2 A3]

Surprisingly, for a range of parameter values, this model results in self-stabilizing behavior. That is, when simulated, the model converges to a particular orientation and forward velocity and is robust to certain pertubations.

Model
Figure 8 Close up of Sprawlita Leg	The dynamic model considered here is a rigid body with six legs in the horizontal plane. Each leg is a prismatic joint with a spring and a damper element in parallel. Each leg is attached to the body through a rotational spring and a rotational damper. This model is motivated by the simplified configuration of our robots. Each leg in the robot consists of a prismatic pneumatic piston attached to a compliant viscoelastic hip joint (see Figure 8). This configuration, in turn, was motivated by findings that legs in the cockroach act as "thrusters", where the leg reaction forces tend to align along the hip joint. Each leg in the model exerts forces and a moment on the body when it is in contact with the ground. This force is the result of the damping terms and the deflections of the hip and linear springs.
	The timing of the system is modeled as a feedforward motor pattern. The dynamics of the model proceed as follow: At the beginning of the stride period, one tripod of support is activated. When activated, each leg appears in the ground at a predetermined position with respect to the body. This allows for legs to be activated with a pre-compression. The system then proceeds under the influence of these three legs. Halfway into the stride period, the current tripod of legs is deactivated and the other tripod of legs is activated. The state of the system (X, Y and rotational positions and velocities) is continous between mode changes. The cycle is repeated at the end of the stride period. Each leg is attached to the body at a predetermined position in the body with respect to the center of mass.
	Thus, the unknowns at this point to be solved for are: Linear leg stiffnesses (ki) and nominal lengths (Li) Rotational hip stiffnesses (Ki) and nominal angles (Ai) Linear leg (bi) and hip (Bi) damping coefficients Which makes our search vector consist of 18 unknowns: X = [k1 k2 k3 b1 b2 b3 K1 K2 K3 B1 B2 B3 L1 L2 L3 A1 A2 A3]
	Surprisingly, for a range of parameter values, this model results in self-stabilizing behavior. That is, when simulated, the model converges to a particular orientation and forward velocity and is robust to certain pertubations.