Analysis of Underactuated Dynamic Locomotion Systems Using Perturbation Expansion: The Twistcar Toy Example

Chakon, Ofir; Or, Yizhar

doi:10.1007/s00332-016-9357-y

Cited by 8 publications

(27 citation statements)

References 26 publications

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“…For micro-swimmers, where inertial effects are negligible, these relations originate from imposing quasistatic equilibrium [18,19], whereas they come from added-mass effect and momentum conservation for inertiadominated swimming in ideal fluid [20,21]. Several works have analyzed such systems utilizing methods of differential geometry [22], optimal control [23,24,25] and perturbation expansion [26,27,28].…”

Section: Scientific Backgroundmentioning

confidence: 99%

Nonholonomic dynamics of the Twistcar vehicle: asymptotic analysis and hybrid dynamics of frictional skidding

Halvani

2022

Nonlinear Dyn

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The Twistcar vehicle is a classic example of a nonholonomic dynamical system. The vehicle model consists of two rigid links connected by an actuated rotary joint and supported by wheeled axles, where nonholonomic constraints are assumed to impose no skidding of the wheels. Recent experimental measurements conducted with a robotic Twistcar prototype have shown disagreements with previous theoretical analyses. In particular, significant skidding has been observed, in addition to discrepancies with respect to theoretical predictions of divergence in oscillations of the vehicle's speed and orientation, as well as direction reversal depending on the vehicle's structure. The goal of our research is to resolve this disagreement by generalizing the theoretical analysis. First, we extend previous asymptotic analysis by incorporating the effects of links' inertia and oscillation amplitude of the input angle on the direction of net motion. Next, we formulate the vehicle's hybrid dynamics under frictional bounds and skid-state transitions. Using numerical analysis, we obtain optimal values for the vehicle's mean speed and energetic cost-of-transport as a function of the input frequency. Our results improve the agreement between theory and experiments and suggest directions for further experimental investigation.

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Section: Scientific Backgroundmentioning

confidence: 99%

Nonholonomic dynamics of the Twistcar vehicle: asymptotic analysis and hybrid dynamics of frictional skidding

Halvani

2022

Nonlinear Dyn

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“…Fig. 2 shows typical simulation results from [27] under parameter values of l 1 = 0.5m, l 2 = 0.1m, b 1 = 0.3m, φ 0 = π, ε = 0.6rad, and ω = 1rad/s. Time plot of the speed of rear axle midpoint v 1 (t) = [27].…”

Section: Twistcar -Review Of Recent Relevant Workmentioning

confidence: 99%

“…In cases where these conditions are not satisfied, they have demonstrated a numerical simulation example where the direction of motion can be reversed for a vehicle with specific values of m i , l i by only modulating the input's amplitude and frequency of the steering angle φ (t) oscillating about φ 0 = π as in (1). This interesting effect has not been captured by the leading-order asymptotic analysis in [27]. Finally, the work [31] also considered a relaxation of the no-skid assumption by using the "skid-angle" model [30,32,33] , which accounts for non-dissipative smooth changes in the skidding velocities.…”

Section: Analysis Of the Landshark Modelmentioning

confidence: 99%

“…Note that a 2 reduces to the simple expression in [27] for the point-mass case, by substituting κ = η 1 = η 2 = 0. Expansion to the next order of ε 4 -terms, which has not been considered previously in [27], gives equation of the forṁ v 4 (t) = F 4 (v 0 , v 2 ,t). Assuming v 0 = 0, integrating in time and substituting the expression for v 2 from (20), one obtains:…”

Section: Asymptotic Analysis -Perturbation Expansionmentioning

confidence: 99%

“…First, consider the case where the no-skid constraint (3) at the i th wheel axle is satisfied. The constraint force λ i must satisfy Coulomb's dry friction inequality (27), where the normal reaction force N i (φ ) is obtained from solving (29). When the friction bound in ( 27) is reached for the i th axle, it begins to skid, so that σ i (t) = w i (q) •q = 0, and the constraint force reaches its maximal value, λ i = −µ sgn(σ i )N i .…”

Section: Hybrid Dynamics With Skid-state Transitionsmentioning

confidence: 99%

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Nonholonomic Dynamics of the Twistcar Vehicle: Asymptotic Analysis and Hybrid Dynamics of Frictional Skidding

Halvani

2021

Preprint

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The Twistcar vehicle is a classic example of a nonholonomic dynamical system. The vehicle model consists of two rigid links connected by an actuated rotary joint and supported by wheeled axles, where nonholonomic constraints are assumed to impose no skidding of the wheels. Recent experimental measurements conducted with a robotic Twistcar prototype have shown disagreements with previous theoretical analyses. In particular, significant skidding has been observed, in addition to discrepancies with respect to theoretical predictions of divergence in oscillations of the vehicle’s speed and orientation, as well as direction reversal depending on the vehicle’s structure. The goal of our research is to resolve this disagreement by generalizing the theoretical analysis. First, we extend previous asymptotic analysis by incorporating the effects of links’ inertia and oscillation amplitude of the input angle on the direction of net motion. Next, we formulate the vehicle’s hybrid dynamics under frictional bounds and skid-state transitions. Using numerical analysis, we obtain optimal values for the vehicle’s mean speed and energetic cost-of-transport as a function of the input frequency. Our results improve the agreement between theory and experiments and suggest directions for further experimental investigation.

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Sinusoidal control and limit cycle analysis of the dissipative Chaplygin sleigh

Fedonyuk

Tallapragada

2018

Nonlinear Dyn

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Analysis of Underactuated Dynamic Locomotion Systems Using Perturbation Expansion: The Twistcar Toy Example

Cited by 8 publications

References 26 publications

Nonholonomic dynamics of the Twistcar vehicle: asymptotic analysis and hybrid dynamics of frictional skidding

Nonholonomic dynamics of the Twistcar vehicle: asymptotic analysis and hybrid dynamics of frictional skidding

Nonholonomic Dynamics of the Twistcar Vehicle: Asymptotic Analysis and Hybrid Dynamics of Frictional Skidding

Sinusoidal control and limit cycle analysis of the dissipative Chaplygin sleigh

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