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Hironobu Sasaki

Publications and source records attributed to Hironobu Sasaki.

12 recordsLinked to original sources

Transporting Unsecured Stacked Payloads with a Quadrupedal Robot via Multi-Objective Reinforcement Learning

Transporting unsecured payloads with legged robots over uneven terrain requires balancing locomotion performance and payload stability, since aggressive motion can destabilize the payload even when the robot remains stable. We study quadrupedal transportation of unsecured stacked boxes on an edgeless torso-mounted board without dedicated payload sensors or active carrier mechanisms. To address this trade-off, we propose Payload-Adaptive Multi-Objective Reinforcement learning for Transportation (PAMORT). PAMORT trains a multi-objective base policy conditioned on a preference vector that weights locomotion and payload-stability reward groups, then trains a weight adjuster on the frozen policy to adapt this preference online from proprioception. In simulation, PAMORT achieves comparable or better overall transportation success than a corresponding single-objective baseline across different payload configurations, including an unseen three-box stack, despite training only with two boxes. Real-world experiments on a Unitree Go2 demonstrate zero-shot transfer to slopes and steps at or beyond the training difficulty, with mean success rates of 0.850 for PAMORT and 0.675 for the baseline across eight tasks. These results demonstrate robust unsecured-payload transportation with online adaptation of the locomotion--payload trade-off from proprioceptive information.

cs.RO↗

On inverse scattering for the one-dimensional nonlinear Dirac equation

The inverse scattering problem for the one-dimensional nonlinear Dirac equation \begin{align*} \begin{cases} i(u_t+u_x)+v=\mathcal{N}_1(u,v),\\ i(v_t-v_x)+u=\mathcal{N}_2(u,v) \end{cases} \end{align*} is studied. We assume that the unknown nonlinearities $\mathcal{N}_j(u,v)$ ($j=1,2$) of the equation belong to $C^\infty(\mathbb{C}^2;\mathbb{C})$ and satisfy $(\partial_\mathbf{z}^α\mathcal{N}_j)(\mathbf{z})=O(|\mathbf{z}|^{\max\{ 5-|α|,0 \}})$ ($|\mathbf{z}|\to 0$) for any multi-index $α\in (\mathbb{N} \cup \{ 0 \})^4$. Here, $\mathbf{z}=(z_1,z_2)\in \mathbb{C}^2$, $ \partial_\mathbf{z}^α= (\partial_{z_1},\partial_{\overline{z_1}},\partial_{z_2},\partial_{\overline{z_2}})^α, $ and $\partial_{z_1},\partial_{\overline{z_1}},\partial_{z_2},\partial_{\overline{z_2}}$ are the Wirtinger differential operators. Under some additional assumptions on $\mathcal{N}_j$, we establish a reconstruction formula for $(\partial_\mathbf{z}^α\mathcal{N}_j)(0)$ ($|α|\ge 5$) using the knowledge of the scattering operator for the equation. Although such results were established for the nonlinear Schrödinger equation [Sasaki 2024] and the nonlinear Klein-Gordon equation [Sasaki 2025], the methods in [Sasaki 2024, 2025] are not directly applicable to the nonlinear Dirac equation due to its system nature. Specifically, it is quite difficult to prove the invertibility of a matrix associated with the input data. To overcome this difficulty, we introduce a new method based on the massless limit for the free solutions.

math.AP↗

On inverse scattering for the two-dimensional nonlinear Klein-Gordon equation

The inverse scattering problem for the two-dimensional nonlinear Klein-Gordon equation $u_{tt}-Δu + u = \mathcal{N}(u)$ is studied. We assume that the unknown nonlinearity $\mathcal{N}$ of the equation satisfies $\mathcal{N}\in C^\infty(\mathbb{R};\mathbb{R})$, $\mathcal{N}^{(k)}(y)=O(|y|^{\max\{ 3-k,0 \}})$ ($y \to 0$) and $\mathcal{N}^{(k)}(y)=O(e^{c y^2})$ ($|y| \to \infty$) for any $k=0,1,2,\cdots$. Here, $c$ is a positive constant. We establish a reconstraction formula of $\mathcal{N}^{(k)}(0)$ ($k=3,4,5,\cdots$) by the knowledge of the scattering operator for the equation. As an application, we also give an expression for higher order Gâteaux differentials of the scattering operator at 0.

math.AP↗

Dispersive estimates for quantum walks on 1D lattice

We consider quantum walks with position dependent coin on 1D lattice $\mathbb{Z}$. The dispersive estimate $\|U^tP_c u_0\|_{l^\infty}\lesssim (1+|t|)^{-1/3} \|u_0\|_{l^1}$ is shown under $l^{1,1}$ perturbation for the generic case and $l^{1,2}$ perturbation for the exceptional case, where $U$ is the evolution operator of a quantum walk and $P_c$ is the projection to the continuous spectrum. This is an analogous result for Schrödinger operators and discrete Schrödinger operators. The proof is based on the estimate of oscillatory integrals expressed by Jost solutions.

math-ph↗

Dynamics of solitons for nonlinear quantum walks

We present some numerical results for nonlinear quantum walks (NLQWs) studied by the authors analytically \cite{MSSSS18DCDS, MSSSS18QIP}. It was shown that if the nonlinearity is weak, then the long time behavior of NLQWs are approximated by linear quantum walks. In this paper, we observe the linear decay of NLQWs for range of nonlinearity wider than studied in \cite{MSSSS18DCDS}. In addition, we treat the strong nonlinear regime and show that the solitonic behavior of solutions appears. There are several kinds of soliton solutions and the dynamics becomes complicated. However, we see that there are some special cases so that we can calculate explicit form of solutions. In order to understand the nonlinear dynamics, we systematically study the collision between soliton solutions. We can find a relationship between our model and a nonlinear differential equation.

quant-ph↗

Scattering and inverse scattering for nonlinear quantum walks

We study large time behavior of quantum walks (QWs) with self-dependent (nonlinear) coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on space-time estimate of (linear) QWs such as dispersive estimates and Strichartz estimate. Such argument is standard in the study of nonlinear Schrödinger equations and discrete nonlinear Schrödinger equations but it seems to be the first time to be applied to QW.

math-ph↗

Weak limit theorem for a nonlinear quantum walk

This paper continues the study of large time behavior of a nonlinear quantum walk begun in arXiv:1801.03214. In this paper, we provide a weak limit theorem for the distribution of the nonlinear quantum walk. The proof is based on the scattering theory of the nonlinear quantum walk and the limit distribution is obtained in terms of its asymptotic state.

math-ph↗

On nonlinear scattering for quantum walks

We study large time behavior of quantum walks (QW) with self-dependent coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on space-time estimate of (linear) QW such as Strichartz estimate. Such argument is standard in the study of nonlinear Schrödinger equations but it seems to be the first time to be applied to QW. We also numerically study the dynamics of QW and observe soliton like solutions.

math-ph↗

Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly

We consider inverse scattering problems for the three-dimensional Hartree equation. We prove that if the unknown interaction potential $V(x)$ of the equation satisfies some rapid decay condition, then we can uniquely determine the exact value of $\partial_ξ^α\hat{V}(0)$ for any multi-index $α$ by the knowledge of the scattering operator for the equation. Furthermore, we show some stability estimate for identifying $\partial_ξ^α\hat{V}(0)$.

math.AP↗

An inverse scattering problem for the Klein-Gordon equation with a classical source in quantum field theory

An inverse scattering problem for a quantized scalar field ${\bm ϕ}$ obeying a linear Klein-Gordon equation $(\square + m^2 + V) {\bm ϕ} = J \mbox{in $\mathbb{R} \times \mathbb{R}^3$}$ is considered, where $V$ is a repulsive external potential and $J$ an external source $J$. We prove that the scattering operator $\mathscr{S}= \mathscr{S}(V,J)$ associated with ${\bm ϕ}$ uniquely determines $V$. Assuming that $J$ is of the form $J(t,x)=j(t)ρ(x)$, $(t,x) \in \mathbb{R} \times \mathbb{R}^3$, we represent $ρ$ (resp. $j$) in terms of $j$ (resp. $ρ$) and $\mathscr{S}$.

math-ph↗

On the life span of the Schrödinger equation with sub-critical power nonlinearity

We discuss the life span of the Cauchy problem for the one-dimensional Schrödinger equation with a single power nonlinearity $λ|u|^{p-1}u$ ($λ\in\mathbb{C}$, $2\le p<3$) prescribed an initial data of the form $\varepsilonφ$. Here, $\varepsilon$ stands for the size of the data. It is not difficult to see that the life span $T(\varepsilon)$ is estimated by $C_0 \varepsilon^{-2(p-1)/(3-p)}$ from below, provided $\varepsilon$ is sufficiently small. In this paper, we consider a more precise estimate for $T(\varepsilon)$ and we prove that $\liminf_{\varepsilon\to 0}\varepsilon^{2(p-1)/(3-p)}T(\varepsilon)$ is larger than some positive constant expressed only by $p$, $\mathrm{Im}λ$ and $φ$.

math.AP↗

Inverse scattering for the nonlinear Schrödinger equation with the Yukawa potential

We study the inverse scattering problem for the three dimensional nonlinear Schroedinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of the scattering states. Our result is applicable to reconstructing the nonlinearity of the semi-relativistic Hartree equation.

math.AP↗