A Vector Algebra Formulation of Mobile Robot Velocity Kinematics

Abstract

Typical formulations of the forward and inverse velocity kinematics of wheeled mobile robots assume flat terrain, consistent constraints, and no slip at the wheels. Such assumptions can sometimes permit the wheel constraints to be substituted into the differential equation to produce a compact, apparently unconstrained result. However, in the general case, the terrain is not flat, the wheel constraints cannot be eliminated in this way, and they are typically inconsistent if derived from sensed information. In reality, the motion of a WMR is restricted to a manifold which more-or-less satisfies the wheel slip constraints while both following the terrain and responding to the inputs. To address these more realistic cases, we have developed a formulation of WMR velocity kinematics as a differential-algebraic system -a constrained differential equation of first order. This paper presents the modeling part of the formulation. The Transport Theorem is used to derive a generic 3D model of the motion at the wheels which is implied by the motion of an arbitrarily articulated body. This wheel equation is the basis for forward and inverse velocity kinematics and for the expression of explicit constraints of wheel slip and terrain following. The result is a mathematically correct method for predicting motion over non-flat terrain for arbitrary wheeled vehicles on arbitrary terrain subject to arbitrary constraints. We validate our formulation by applying it to a Mars rover prototype with a passive suspension in a context where ground truth measurement is easy to obtain. Our approach can constitute a key component of more informed state estimation, motion control, and motion planning algorithms for wheeled mobile robots.

Modular Dynamic Simulation of Wheeled Mobile Robots

“…This is compatible with our prior work on a vector algebra formulation of WMR kinematics [15]. Spatial vectors are 6D and inhabit two vector spaces: motion and force.…”

“…Due to its ease of use, Open Dynamics Engine (ODE) is often used to simulate WMRs [11][17] [6] [15], but it has limited options for wheel-ground contact modeling. ODE can only enforce a rudimentary contact model with Coulomb force limits approximated by a friction pyramid and slip velocities linearly proportional to force.…”

“…Here, "dynamic simulation" means a second-order physicsbased motion model is used, which accounts for inertia and applied forces. This is an expansion on our previously published work on first-order velocity kinematic motion models [15]. "Modular" means that the method accommodates any articulated WMR configuration and any wheel-ground contact model expressed as a function with the specified inputs.…”

Enhanced 3D Kinematic Modeling of Wheeled Mobile Robots

“…Le Menn et al [16] extend a reciprocal screw-based approach to derive the 3D kinematics of multi-monocycle robots. Tarokh et al (in later papers) [26][27], Chang et al [4], and Kelly and Seegmiller [12] use a velocity propagation-based approach, similar to the one used here. Choi and Sreenivasan [5] and Chakraborty and Ghosal [3] do not provide general methods for kinematics derivation, but simulate 3D WMR kinematics to validate mechanism designs.…”

Platooning strategy of mobile robot: simulation and experiment

“…The angular velocity can be used to derive the moving velocity and acceleration of the WMR. The heading of the mobile robot can be determined by analysing the difference between the angular velocities of its wheels [6]. Ignoring dynamic forces in a purely kinematic approach has several known issues.…”