Stable balance controller

A robot, comprising:

• a robot body;
• an actuator controlling movement of the robot body;
• and
• a stable balance controller, including:
• a controller receiving an input signal and generating a control effort signal Xref;
• a state-feedback circuit receiving the control effort signal Xref as an input and generating an output signal;
• and
• a feedback loop, including the controller and the state-feedback circuit, transferring the output signal of the state-feedback circuit back to the input of the controller and inputting a tracking error input signal to the controller,
• wherein the tracking error input signal is the difference between the output signal of the state-feedback circuit and the input signal,
• wherein the stable balance controller drives the actuator to control movement of the robot body based on the output signal of the state-feedback circuit,
• wherein:
• S=(I+GK)−1,
• R=K(I+GK)−1,
• T=GK(I+GK)−1,
• y1=W1Sv,
• y2=W2 Rv, and
• y3=W3 Tv,
• wherein I is an identity matrix,
• wherein G is the state-feedback circuit,
• wherein K is the controller,
• wherein R is indicative of control effort,
• wherein S is indicative of a sensitivity function,
• wherein T is indicative of a complementary sensitivity function,
• wherein y1 y2, y3 are auxiliary outputs, W1, W2, W3 are assigned weights, and v is the input signal received by the controller,
• wherein one or more weights of the weights W1, W2, W3 associated with one or more of the auxiliary outputs y1 y2, y3 is assigned based on having a smaller gain at low frequencies to reduce the steady-state error and a larger gain at high frequency to mitigate the effect of noise,
• wherein one or more of the auxiliary outputs y1 y2, y3 is associated with the control effort, the sensitivity function, or the complementary sensitivity function, and
• wherein a circuit of the feedback loop generates the auxiliary outputs y1 y2, y3.

A control system for providing stable balance control, comprising:

• a controller receiving an input signal and generating a control effort signal Xref;
• a state-feedback circuit receiving the control effort signal Xref as an input and generating an output signal;
• and
• a feedback loop, including the controller and the state-feedback circuit, transferring the output signal of the state-feedback circuit back to the input of the controller and inputting a tracking error input signal to the controller,
• wherein the tracking error input signal is the difference between the output signal of the state-feedback circuit and the input signal, and
• wherein the state-feedback circuit includes a second feedback loop nested within the feedback loop of the control system for providing stable balance control,
• wherein the control system for providing stable balance control drives an actuator controlling movement of a robot body based on the output signal of the state-feedback circuit,
• wherein:
• S=(I+GK)−1,
• R=K(I+GK)−1, and
• T=GK(I+GK)−1,
• y1=W1Sv,
• y2=W2 Rv, and
• y3=W3 Tv,
• wherein I is an identity matrix,
• wherein G is the state-feedback circuit,
• wherein K is the controller,
• wherein R is indicative of control effort,
• wherein S is indicative of a sensitivity function,
• wherein T is indicative of a complementary sensitivity function,
• wherein y2, y3 are auxiliary outputs, W1, W2, W3 are assigned weights, and v is the input signal received by the controller,
• wherein one or more weights of the weights W1, W2, W3 associated with one or more of the auxiliary outputs y1, y2, y3 is assigned based on having a smaller gain at low frequencies to reduce the steady-state error and a larger gain at high frequency to mitigate the effect of noise,
• wherein one or more of the auxiliary outputs y1, y2, y3 is associated with the control effort, the sensitivity function, or the complementary sensitivity function, and
• wherein a circuit of the feedback loop generates the auxiliary outputs y1, y2, y3.