In this article, a new model for 3D motion planning, applicable to aerial vehicles, is proposed to connect an initial and final configuration subject to pitch rate and yaw rate constraints. The motion planning problem for a curvature-constrained vehicle over the surface of a sphere is identified as an intermediary problem to be solved, and it is the focus of this paper. In this article, the optimal path candidates for a vehicle with a minimum turning radius$r$moving over a unit sphere are derived using a phase portrait approach. We show that the optimal path is$CGC$or concatenations of$C$segments through simple proofs, where$C = L, R$denotes a turn of radius$r$and$G$denotes a great circular arc. We generalize the previous result of optimal paths being$CGC$and$CCC$paths for$r \in (0, \frac{1}{2}]\bigcup \lbrace \frac{1}{\sqrt{2}}\rbrace$to$r \leq \frac{\sqrt{3}}{2}$to account for vehicles with a larger$r$. We show that the optimal path is$CGC, CCCC,$for$r \leq \frac{1}{\sqrt{2}},$and$CGC, CC_\pi C, CCCCC$for$r \leq \frac{\sqrt{3}}{2}.$Additionally, we analytically construct all candidate paths and provide the code in a publicly accessible repository.

In this paper, we propose a new modeling approach and a fast algorithm for 3D motion planning, applicable for fixed-wing unmanned aerial vehicles. The goal is to construct the shortest path connecting given initial and final configurations subject to motion constraints. Our work differs from existing literature in two ways. First, we consider full vehicle orientation using a body-attached frame, which includes roll, pitch, and yaw angles. However, existing work uses only pitch and/or heading angle, which is insufficient to uniquely determine orientation. Second, we use two control inputs to represent bounded pitch and yaw rates, reflecting control by two separate actuators. In contrast, most previous methods rely on a single input, such as path curvature, which is insufficient for accurately modeling the vehicle's kinematics in 3D. We use a rotation minimizing frame to describe the vehicle's configuration and its evolution, and construct paths by concatenating optimal Dubins paths on spherical, cylindrical, or planar surfaces. Numerical simulations show our approach generates feasible paths within 10 seconds on average and yields shorter paths than existing methods in most cases.

This article studies the time-optimal path planning problem for a convexified Reeds-Shepp (CRS) vehicle on a unit sphere, capable of both forward and backward motion, with speed bounded in magnitude by 1 and turning rate bounded in magnitude by a given constant. For the case in which the turning-rate bound is at least 1, using Pontryagin's Maximum Principle and a phase-portrait analysis, we show that the optimal path connecting a given initial configuration to a desired terminal configuration consists of at most six segments drawn from three motion primitives: tight turns, great circular arcs, and turn-in-place motions. A complete classification yields a finite sufficient list of 23 optimal path types with closed-form segment angles derived. The complementary case in which the turning-rate bound is less than 1 is addressed via an equivalent reformulation. The proposed formulation is applicable to underactuated satellite attitude control, spherical rolling robots, and mobile robots operating on spherical or gently curved surfaces. The source code for solving the time-optimal path problem and visualization is publicly available at https://github.com/sixuli97/Optimal-Spherical-Convexified-Reeds-Shepp-Paths.

This paper presents a dynamic brake force distribution (BFD) control strategy that allocates the brake force to each wheel based on the normal loads and coefficients of friction for a two-axle heavy commercial road vehicle (HCRV) for straightline braking. A three degree of freedom half car pitch model was used to calculate the dynamic load transfer on each wheel, which was corroborated using IPG TruckMaker. The Magic Formula tire model with load-dependent coefficients was utilized to obtain instantaneous coefficient of friction at all four tires. The BFD strategy was then compared with two static BFD strategies: one which employs a 50:50 BFD and another which employs a BFD corresponding to ideal BFD curve (I curve) for the fully laden vehicle between the front and rear wheels. The test cases for a comparative evaluation of the dynamic and static BFD strategies were generated from the IS 11852 standard. The dynamic BFD strategy was found to reduce braking distance in the range of 1 % to 27 % when compared to the static BFD strategies. Further, all the strategies resulted in stable braking with no wheel lock.