Modeling and Control for Efficient Bipedal Walking Robots: A by Vincent Duindam

By Vincent Duindam

Walking robots are complicated machines with many levels of freedom. Designing effective controllers for such robots could be a daunting job, and the differential equations by means of themselves frequently don't support a lot while attempting to comprehend the dynamics. nonetheless, examine on passive dynamic jogging robots has proven that it's attainable to make robot mechanisms stroll very certainly and successfully with no utilizing any regulate! the distance among theoretically well-understood position-controlled strolling robots and experimentally-designed out of control passive-dynamic walkers is however huge, and lengthening a passive-dynamic walker to be extra strong and flexible is non-trivial.

The function of this paintings is to offer a suite of mathematical instruments which can simplify learning robot strolling motions and designing energy-efficient controllers. The authors expand classical dynamic modeling equipment and consider robots and controllers as energy-exchanging actual structures, which kinds the basisof the so-called port-based strategy. They exhibit how such equipment can be utilized to research jogging mechanisms, locate effective strolling trajectories, and layout controllers that raise robustness and balance with minimum power rate. vast examples and illustrations are used with the target to make the maths intuitive and available to everybody with an engineering background.

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53), which, using the Jacobian, can be expressed as 1 (AdH∅i Ti∅,∅ )T I i,i (AdH∅i Ti∅,∅ ) 2 1 = v T JiT (Q) AdTH i I i,i AdH∅i Ji (Q) v ∅ 2 (Uk )i = Summing this expression for all rigid bodies gives the total kinetic co-energy of the mechanism. 3 Dynamic Equations of Rigid Mechanisms For the derivation of the dynamics of a rigid mechanism, we start from the Euler-Lagrange equations (Goldstein 1980). 60) with the Lagrangian L(q, q) ˙ = Uk (q, q)−U ˙ p (q). 61) ∂H ∂q ∂H ∂p with the Hamiltonian equal to H(q, p) = pT q−L(q, ˙ q) ˙ = 12 pT M −1 (q)p+Up (q), and (u, y) defining a power port.

37) hence just two rotational joints as in (a), but now both depending on the same states q and q. ˙ In a similar way, this approach can be used for systems of more than two gears. (e) Free (6 DoF) relative motion of two rigid bodies can be seen as a degenerate joint (since in fact nothing is joined), but can still be described as a globally parameterized rigid joint. We can just take Q = H21 and v = T21,1 , and ˙ as the vector representation of QQ ˙ −1 . 3. (f) The spherical joint allows two bodies to have a fixed relative displacement, but arbitrary rotation.

E. 21. 22. 10 shows the snakeboard, an interesting mechanical system with nonholonomic constraints. A. 2005), very similar to the skateboard, but with extra degrees of freedom that allow rotation of the front and rear wheel bases around the vertical axis, such that the direction of motion of the wheels can be changed. Using certain combinations of motion of the feet (to control the wheel base angles) and of the upper body, the person riding the snakeboard can increase the total forward momentum, without touching the ground or directly driving the wheels.

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