A corridor \(Y\) for the motion of an object is given in the space \(X=\mathbb{R}^{N}\) (\(N=2,3\)). A finite number of emitters \(s_{i}\) with fixed convex radiation cones \(K(s_{i})\) are located outside the corridor. The intensity of radiation \(F(y)\), \(y>0\), satisfies the condition \(F(y)\geq\lambda F(\lambda y)\) for \(y>0\) and \(\lambda>1\). It is required to find a trajectory minimizing the value

\(J({\mathcal{T}})=\displaystyle\sum_{i}\displaystyle\intop\limits_{0}^{1}F\big{ (}\|s_{i}-t(\tau)\|\big{)}\,d\tau\)

in the class of uniform motion trajectories \({\mathcal{T}}=\big{\{}t(\tau)\colon 0\leq\tau\leq 1,\ t(0)=t_{*},\ t(1)=t^{*} \big{\}}\subset Y\), \(t_{*},t^{*}\in\partial Y\), \(t_{*}\neq t^{*}\). We propose methods for the approximate construction of optimal trajectories in the case where the multiplicity of covering the corridor \(Y\) with the cones \(K(s_{i})\) is at most 2.

在空间\(X=\mathbb{R}^{N}\) ( \(N=2,3\) ) 中给出了用于物体运动的走廊 \(Y\ )。有限数量的发射器 \(s_{i}\)具有固定的凸辐射锥\(K(s_{i})\)位于走廊外。辐射的强度\（F（y）的\） ，\（Y> 0 \） ，满足条件\（F（y）的\ GEQ \拉姆达F（\拉姆达Y）\） 为\（Y> 0 \）和\(\lambda>1\)。需要找到最小化值的轨迹

\(J({\mathcal{T}})=\displaystyle\sum_{i}\displaystyle\intop\limits_{0}^{1}F\big{ (}\|s_{i}-t(\tau )\|\big{)}\,d\tau\)

在匀速运动轨迹类\({\mathcal{T}}=\big{\{}t(\tau)\colon 0\leq\tau\leq 1,\ t(0)=t_{*}, \ t(1)=t^{*} \big{\}}\subset Y\) , \(t_{*},t^{*}\in\partial Y\) , \(t_{*}\ neq t^{*}\)。我们提出了在覆盖走廊\(Y\) 与锥体\(K(s_{i})\)的多重性最多为 2的情况下近似构建最佳轨迹的方法 。