Geometric Control of the Trident Snake Robot Based on CGA

Local Geometric Control of a Certain Mechanism with the Growth Vector (4,7)

“…To simulate the bracket motion of the nilpotent approximation, we choose the initial state q 0 and apply the periodic input on couples (N 1 , N 2 ), (N 1 , N 3 ) and (N 1 , N 4 ) to receive the displacement approximately parallel to [N 1 , N 2 ], [N 1 , N 3 ] and [N 1 , N 4 ] respectively [19]. More precisely, for one cycle we apply u 1 (t) = −Aω sin(ωt), u i (t) = Aω cos(ωt), u j (t) = 0, u k (t) = 0 for i ∈ {2, 3, 4} and j, k ∈ {2, 3, 4} − {i}, respectively, all with respect to the control system (10), amplitude A = 0.4 and angular speed ω = 2π 50 . Then we apply the same process to original vector fields X 1 , X 2 , X 3 and X 4 .…”

“…Its simplest non-trivial version, corresponding to one-links, has been mainly discussed, see e.g. [12,10,21]. In this case, the control distribution is that of the growth vector (3,6) [20].…”

On symmetries of a sub--Riemannian structure with growth vector $(4,7)$

“…The mechanism that the authors deal with is a modification of a planar mechanism generally known as trident snake robot. Trident snake robot consists of a root block in the shape of an equilateral triangle together with three one-link branches each of which is connected to one vertex of the root block via revolute joint and has a passive wheel at its very end, [9,6]. The generalized trident snake robot introduced in [8] is a planar mechanism consisting of a root block in the shape of an equilateral triangle together with three one-link branches that have passive wheels at their ends, too.…”

“…This happens e.g. in the case of (3,6) in [12,11] and is generalized for general free distributions in [14].…”

Optimization of Snake-like Robot Locomotion Using GA: Serpenoid Design

“…This method is computationally highly effective [17]. The drawback is the assumption that the wheels only roll, and the shear force is endless [11]. This property disadvantages the direct physical implementation because it computationally leads to singularities.…”