On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors

A Motion Planning Strategy for a Spherical Rolling Robot Driven by Two Internal Rotors

“…However, since the robot dynamics are not nilpotent, this is not an exact representation of the system and it can result to inaccuracies. An exact motion planning algorithm was described in [8], but the trajectories generated by that algorithm are not always dynamically realizable [15]. This paper continues our study undertaken in [15], where we developed a mathematical model of a rolling robot actuated by internal rotors and analyzed the model's properties.…”

“…For the kinematic model with pure rolling constraint, tracing geodesic lines on the sphere results in geodesic lines in the contact plane and vice versa, and many algorithms exploit this property explicitly [9], [12], [13] or implicitly as a part of a more general procedure [14]. However, if the rolling is constrained dynamically, this propertygeodesic-to-geodesic mapping-does not, in general, hold true [15]. For this reason, the aforementioned algorithms cannot be used without essential modifications because the trajectories they produce are not, in general, dynamically realizable.…”

“…However, for the minimal number of two actuators, such a decomposition is impossible because there appears a constraint on the component of the angular velocity of the sphere and this constraint depends on the inertia distribution [15]. For this reason, the assigned trajectories for the angular velocity, including those corresponding to pure rolling, are not necessarily dynamically feasible and realizable by the robot actuators [15].…”

“…Even in the case of pure rolling, the structure of the optimal control exhibits several qualitatively different types of solutions corresponding to Euler's elastica [10]. One may expect that the solution structure becomes more complex if rolling is not restricted to nospinning but constrained dynamically [15]. This makes a systematic construction of the initial guess for the optimal control very difficult.…”

The dynamic of a spherical robot with an internal omniwheel platform

“…Укажем работы по динамике сферороботов, перемещающихся за счет со-здания переменного гиростатического момента (с помощью внутренних роторов) [16][17][18][19][20][21] и за счет смещения собственного центра масс [22][23][24][25][26][27]. В указанных работах приведены раз-нообразные формы уравнений динамики сферороботов и получены управляющие воздей-ствия для реализации движения по типовым траекториям.…”