Dynamical and Optimization Trade-offs of Levi--Civita Coordinates for Learned Close-Encounter Dynamics

Classical regularization removes the binary-collision singularity from the Kepler problem, but its value as a representation for learned Hamiltonian dynamics has not been systematically isolated. We compare Cartesian and planar Levi--Civita formulations of a perturbed Kepler system with a smooth quadrupole potential. With the perturbation supplied analytically, a Levi--Civita Hamiltonian splitting holds the maximum relative energy error near $2.1\times10^{-5}$ through eccentricity $e=0.99$, while the Cartesian splitting becomes unstable. This advantage persists at matched physical horizon and force-evaluation budget, where the regularized baseline is $3\times10^{-5}$, about $4.7$--$8.3$ orders of magnitude below the Cartesian arm depending on eccentricity. In held-out high-eccentricity tests with matched sampling, regularized models produce finite rollouts in $40/40$ runs versus $0/40$ for Cartesian. However, the fixed-shell construction supplies the regularized model with the exact initial orbit energy, and survival still carries $\mathcal{O}(1)$ energy error. Four neural residual objectives fail to approach the analytic result. Exact-feature controls show that the regularized residual is a four-monomial degree-6 polynomial that a direct least-squares solve fits to the baseline. The remaining exact-feature gap is due to severe raw-basis ill-conditioning: orthogonalization restores baseline fitting for L-BFGS in two iterations. Small MLPs remain at $\mathcal{O}(1)$ rollout error even after gauge symmetrization. Levi--Civita coordinates therefore improve dynamical conditioning while worsening raw-basis optimization conditioning; accurate neural residual learning remains unresolved. This is a controlled falsification-plus-trade-off study, not a solution to learned close-encounter dynamics.

Autonomous Control of a Novel Closed Chain Five Bar Active Suspension via Deep Reinforcement Learning

Planetary exploration requires traversal in environments with rugged terrains. In addition, Mars rovers and other planetary exploration robots often carry sensitive scientific experiments and components onboard, which must be protected from mechanical harm. This paper deals with an active suspension system focused on chassis stabilisation and an efficient traversal method while encountering unavoidable obstacles. Soft Actor-Critic (SAC) was applied along with Proportional Integral Derivative (PID) control to stabilise the chassis and traverse large obstacles at low speeds. The model uses the rover's distance from surrounding obstacles, the height of the obstacle, and the chassis' orientation to actuate the control links of the suspension accurately. Simulations carried out in the Gazebo environment are used to validate the proposed active system.