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<title>GlobMP: Continuous-Time Constrained Motion Planning</title>
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<body>
<nav class="topnav"><a href="#method">Method</a><a href="#experiments">Experiments</a><a href="#multirobot">Multi-robot</a><a href="#steering">Steering</a><a href="#avoidance">Avoidance</a><a href="#maze">Maze2D</a><a href="#code">Code</a><a href="#contact">Contact</a></nav>
<header class="hero">
<h1>GlobMP</h1>
<div class="tag">Continuous-Time Motion Planning and Steering with Global Convergence</div>
<div class="btn-group">
<a class="btn" href="https://arxiv.org/abs/2610.30607" target="_blank" rel="noopener">Paper (arXiv)</a>
<a class="btn" href="https://github.com/GlobalMotionPlanning/GlobMP" target="_blank" rel="noopener">Code (GitHub)</a>
<a class="btn" href="https://huggingface.co/GlobalMotionPlanning/GlobMP" target="_blank" rel="noopener">Code and data (Hugging Face)</a>
</div>
</header>
<section id="method">
<div class="container">
<h2>Method</h2>
<p class="sub">Planning and steering as one continuous-time program</p>
<p class="t">GlobMP represents each motion as a piecewise polynomial, so every constraint, whether an obstacle, a separation between robots, or closeness to a learned policy's proposal, becomes a polynomial that must <b>stay nonnegative over the whole motion</b>, not only at sampled times. A <b>gradient projection</b> method alternates a step that lowers the smoothness cost with a restoration step that makes the curve feasible again. <b>Every iterate stays feasible</b>, and under mild assumptions the <b>cost approaches the global optimum</b> as the number of pieces grows.</p>
<figure style="max-width:900px"><video src="project_page/videos/method_anim.mp4" poster="project_page/posters/method_anim.jpg" autoplay muted loop playsinline controls preload="auto" style="width:100%;border-radius:12px;border:1px solid #e2e8f0;background:#fff"></video><figcaption>Two robots, A and B, planned jointly among ellipsoidal obstacles. Top: each robot's path. Bottom: clearance to each obstacle and to the other robot over time; below zero is a collision. (1) The direct paths collide. (2) Checking the constraints at 8 sample times misses collisions between them. (3) GlobMP's curves keep every clearance nonnegative over the whole motion.</figcaption></figure>
</div>
</section>
<section id="experiments" class="alt">
<div class="container">
<h2>Experiments</h2>
<p class="sub">Tightness and cost on synthetic instances</p>
<figure><img src="project_page/figs/fig_synth1.png" alt="Tightness and cost"/><figcaption>Clearance of the returned trajectory on one instance (a) and on all instances (b), and cost relative to GlobMP against the number of robots (c). Below zero is a violation.</figcaption></figure>
</div>
</section>
<section id="multirobot">
<div class="container">
<h2>Multi-robot experiments</h2>
<p class="sub">Robotarium, twelve robots, five scenarios, six planners (5&times; speed)</p>
<div class="mtabs"><button class="mbtn on" data-s="crossroom">Cross-Room</button><button class="mbtn" data-s="corridor">Conveyor</button><button class="mbtn" data-s="corridorbay">Corridor-Bay</button><button class="mbtn" data-s="shelf">Drop-Region</button><button class="mbtn" data-s="empty">Empty</button><button class="mbtn" data-s="all">All scenarios</button></div>
<div class="mgrid" id="mgrid"><div class="mcell"><video muted loop playsinline preload="metadata" data-m="CD"></video><div class="mname">CD</div></div><div class="mcell"><video muted loop playsinline preload="metadata" data-m="MMD-CBS"></video><div class="mname">MMD-CBS</div></div><div class="mcell"><video muted loop playsinline preload="metadata" data-m="PCD-SHD"></video><div class="mname">PCD-SHD</div></div><div class="mcell"><video muted loop playsinline preload="metadata" data-m="Final"></video><div class="mname">Final Proj.</div></div><div class="mcell"><video muted loop playsinline preload="metadata" data-m="DiRecT"></video><div class="mname">DiRecT</div></div><div class="mcell us"><video muted loop playsinline preload="metadata" data-m="GlobMP"></video><div class="mname">GlobMP (ours)</div></div></div>
<figure id="mall" style="display:none;max-width:1000px"><video src="project_page/videos/robotarium_grid.mp4" poster="project_page/posters/robotarium_grid.jpg" muted loop playsinline preload="metadata" style="width:100%;border-radius:12px;border:1px solid #e2e8f0;background:#000"></video></figure>
</div>
</section>
<section id="steering" class="alt">
<div class="container">
<h2>Steering</h2>
<p class="sub">Steering tactile-reactive dexterous policies on a bimanual humanoid</p>
<p class="t">GlobMP steers the action chunks of a learned policy (GR00T N1.7, &pi;<sub>0.5</sub>) on a bimanual robot with two XHAND1 hands. A <b>meta-reasoner</b> picks the constraint blocks once per episode, and GlobMP returns a curve that <b>meets every block at every instant</b> while staying close to the policy.</p>
<div class="trow"><div class="tcard on" data-task="bag_box_1019"><video src="project_page/videos/steer_bag.mp4" poster="project_page/posters/steer_bag.jpg" autoplay muted loop playsinline preload="auto"></video><div class="tname">Bag into box</div></div><div class="tcard" data-task="handover_random_1007"><video src="project_page/videos/steer_handover.mp4" poster="project_page/posters/steer_handover.jpg" autoplay muted loop playsinline preload="auto"></video><div class="tname">Tissue-box handover</div></div><div class="tcard" data-task="tissue_random_1009"><video src="project_page/videos/steer_tissue.mp4" poster="project_page/posters/steer_tissue.jpg" autoplay muted loop playsinline preload="auto"></video><div class="tname">Pull a tissue</div></div><div class="tcard" data-task="pick_cup_full_empty_random_1014"><video src="project_page/videos/steer_cup.mp4" poster="project_page/posters/steer_cup.jpg" autoplay muted loop playsinline preload="auto"></video><div class="tname">Pick up a full or empty cup</div></div></div>
<div class="viewer"><div id="tp-title" style="text-align:left;font-weight:600;color:var(--navy-900);margin:4px 0 2px"></div>
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<select id="tp-task"><option value="bag_box_1019">Bag into box</option><option value="pick_cup_full_empty_random_1014">Pick up a full or empty cup</option><option value="handover_random_1007">Tissue-box handover</option><option value="tissue_random_1009">Pull a tissue</option></select>
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<button id="tp-play">&#9654; Play</button>
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<span id="tp-fr" class="sub"></span>
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<div class="tp-bar" style="display:none"><label><input type="checkbox" id="tp-shared"> same colour scale for all fingertips (0 to the episode's highest value)</label></div>
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<p class="sub" style="text-align:center">Force magnitude per fingertip (raw sensor units), above its resting value. Dashed lines: first and last frame with motion.</p>
</div>
<figure><img src="project_page/figs/fig7b_handover.png" alt="Steered motion planning, handover" style="width:100%;max-width:900px"/><figcaption>Steered motion planning, illustrated on the handover task: the meta-reasoner sets keep-out, keep-in and grip blocks once; GlobMP returns a smooth, collision-free curve close to the policy.</figcaption></figure>
<div style="max-width:860px;margin:18px auto 0;padding:26px 20px;border:2px dashed var(--slate-300);border-radius:14px;text-align:center;color:var(--slate-500)">Steered rollouts on the robot and real-robot results: coming soon</div>
</div>
</section>
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"applications/steering/xhand_data/bag_box_1019/episode_0100_20261019_032016/viewer.mp4"}, {"label": "ep 0101_20261019_032347", "T": 690, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0101_20261019_032347/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0101_20261019_032347/viewer.mp4"}, {"label": "ep 0102_20261019_034330", "T": 701, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0102_20261019_034330/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0102_20261019_034330/viewer.mp4"}, {"label": "ep 0103_20261019_035851", "T": 702, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0103_20261019_035851/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0103_20261019_035851/viewer.mp4"}, {"label": "ep 0104_20261019_040657", "T": 710, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0104_20261019_040657/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0104_20261019_040657/viewer.mp4"}, {"label": "ep 0105_20261019_040745", "T": 711, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0105_20261019_040745/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0105_20261019_040745/viewer.mp4"}, {"label": "ep 0107_20261019_040931", "T": 712, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0107_20261019_040931/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0107_20261019_040931/viewer.mp4"}, {"label": "ep 0108_20261019_041017", "T": 712, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0108_20261019_041017/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0108_20261019_041017/viewer.mp4"}, {"label": "ep 0110_20261019_041156", "T": 704, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0110_20261019_041156/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0110_20261019_041156/viewer.mp4"}, {"label": "ep 0111_20261019_041242", "T": 679, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0111_20261019_041242/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0111_20261019_041242/viewer.mp4"}, {"label": "ep 0112_20261019_041325", "T": 711, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0112_20261019_041325/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0112_20261019_041325/viewer.mp4"}, {"label": "ep 0114_20261019_041506", "T": 711, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0114_20261019_041506/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0114_20261019_041506/viewer.mp4"}, {"label": "ep 0116_20261019_041641", "T": 695, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0116_20261019_041641/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0116_20261019_041641/viewer.mp4"}, {"label": "ep 0117_20261019_041723", "T": 711, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0117_20261019_041723/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0117_20261019_041723/viewer.mp4"}, {"label": "ep 0118_20261019_041806", "T": 694, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0118_20261019_041806/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0118_20261019_041806/viewer.mp4"}, {"label": "ep 0119_20261019_041849", "T": 703, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0119_20261019_041849/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0119_20261019_041849/viewer.mp4"}, {"label": "ep 0121_20261019_042017", "T": 711, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0121_20261019_042017/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0121_20261019_042017/viewer.mp4"}, {"label": "ep 0125_20261019_042250", "T": 711, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0125_20261019_042250/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0125_20261019_042250/viewer.mp4"}, {"label": "ep 0126_20261019_042351", "T": 598, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0126_20261019_042351/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0126_20261019_042351/viewer.mp4"}, {"label": "ep 0127_20261019_042436", "T": 711, "durl": "applications/steering/xhand_data/bag_box_1019/episode_0127_20261019_042436/viewer.json", "vurl": "applications/steering/xhand_data/bag_box_1019/episode_0127_20261019_042436/viewer.mp4"}]}, "lut": "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"};
const dec=s=>Uint8Array.from(atob(s),c=>c.charCodeAt(0));
const gunzip=async s=>new Uint8Array(await new Response(new Blob([dec(s)]).stream().pipeThrough(new DecompressionStream('gzip'))).arrayBuffer());
const LUT=dec(D.lut), FN=["thumb","index","middle","ring","pinky"], HN=["left","right"];
const COL=["#e6194b","#3cb44b","#4363d8","#f58231","#911eb4"];
const sel=document.getElementById("tp-ep"), vid=document.getElementById("tp-video"), sl=document.getElementById("tp-slider"),
fr=document.getElementById("tp-fr"), grid=document.getElementById("tp-grid"), tl=document.getElementById("tp-time"),
play=document.getElementById("tp-play"), shared=document.getElementById("tp-shared"), rate=document.getElementById("tp-rate");
const taskSel=document.getElementById("tp-task");
function fill(){sel.innerHTML="";D.items=D.index[taskSel.value];D.items.forEach((it,i)=>{const o=document.createElement("option");o.value=i;o.textContent=it.label;sel.appendChild(o);});}
fill();
const DEF={bag_box_1019:"0103_20261019_035851",handover_random_1007:"0050_20261007_095616",tissue_random_1009:"0050_20261009_114442",pick_cup_full_empty_random_1014:"0085_20261014_214907"};
taskSel.onchange=()=>{vid.pause();fill();const i=Math.max(0,D.items.findIndex(x=>x.label.includes(DEF[taskSel.value]||"zzz")));sel.value=i;load(i).then(()=>{vid.play().catch(()=>{})});};
const tiles=[];
HN.forEach((h,hi)=>{const row=document.createElement("div");row.className="tp-hand";row.innerHTML=`<div class="h">${h} hand</div>`;
FN.forEach((f,fi)=>{const t=document.createElement("div");t.className="tp-tile";
const c=document.createElement("canvas");c.width=12;c.height=10;
const lab=document.createElement("div");lab.innerHTML=`<b style="color:${COL[fi]}">${f}</b>`;
const v=document.createElement("div");v.className="v";t.append(lab,c,v);row.appendChild(t);
tiles.push({ctx:c.getContext("2d"),img:c.getContext("2d").createImageData(12,10),v});});
grid.appendChild(row);});
let cur=null, frame=0;
async function load(i){
const it0=D.items[i]; const it=Object.assign({},it0,await (await fetch(it0.durl)).json()); const T=it.T;
const maps=await gunzip(it.maps), force=new Float32Array((await gunzip(it.force)).buffer);
const fmax=new Float32Array(10), gmax=[0];
for(let t=0;t<T;t++)for(let k=0;k<10;k++){const o=(t*10+k)*120;for(let p=0;p<120;p++){const z=maps[o+p];if(z>fmax[k])fmax[k]=z;}}
for(let k=0;k<10;k++){gmax[0]=Math.max(gmax[0],fmax[k]);fmax[k]=Math.max(fmax[k],5);}
let fM=0;for(let x of force)fM=Math.max(fM,x);
cur={it,T,maps,force,fmax,gmax:Math.max(gmax[0],5),fM:Math.max(fM,10)};
const pk=document.getElementById("tp-peak"); let rows="<tr><th>fingertip</th><th>left peak |F|</th><th>right peak |F|</th><th>left mean |F|</th><th>right mean |F|</th></tr>";
for(let k=0;k<5;k++){const st=h=>{let m=0,sum=0;for(let t=0;t<T;t++){const v=force[t*10+h*5+k];if(v>m)m=v;sum+=v;}return [m.toFixed(1),(sum/T).toFixed(1)];};
const L=st(0),R=st(1);rows+=`<tr><td><b style="color:${COL[k]}">${FN[k]}</b></td><td>${L[0]}</td><td>${R[0]}</td><td>${L[1]}</td><td>${R[1]}</td></tr>`;}
pk.innerHTML=rows;
const M=Object.entries(it.meta||{}).map(([k,v])=>`${k}: <b>${v}</b>`).join(" · "), a=it.act;
document.getElementById("tp-title").textContent="Touch data \u00b7 "+taskSel.options[taskSel.selectedIndex].text+" \u00b7 "+sel.options[sel.selectedIndex].text;document.getElementById("tp-meta").innerHTML=`${it.label} · ${T} frames (${(T/30).toFixed(1)} s)`+(M?" · "+M:"")+(a?`<br>idle at start: ${a[0]} frames (${(a[0]/30).toFixed(1)} s) · idle at end: ${T-1-a[1]} frames (${((T-1-a[1])/30).toFixed(1)} s)`:"");
vid.src=it.vurl; sl.max=T-1; frame=0; drawTimeline();
let tot=new Float32Array(T);for(let t=0;t<T;t++){let q=0;for(let k=0;k<10;k++)q+=force[t*10+k];tot[t]=q;}
let mx=0;for(const x of tot)mx=Math.max(mx,x);let f0=0;for(let t=0;t<T;t++){if(tot[t]>0.4*mx){f0=Math.max(0,t-30);break;}}
frame=f0;vid.addEventListener("loadedmetadata",()=>{vid.currentTime=(f0+0.5)/30;},{once:true});draw(f0);
}
function drawTimeline(){
const r=tl.getBoundingClientRect(), dpr=window.devicePixelRatio||1; tl.width=r.width*dpr; tl.height=r.height*dpr;
const g=tl.getContext("2d"); g.setTransform(dpr,0,0,dpr,0,0); g.clearRect(0,0,r.width,r.height);
const css=getComputedStyle(document.documentElement), ML=48, W=r.width-ML-6, H=r.height/2, {T,force,fM}=cur;
const step=[1,2,5,10,20,50,100,200,500].find(s=>fM/s<=4)||500, top=Math.ceil(fM/step)*step;
cur.ML=ML; cur.W=W;
for(let h=0;h<2;h++){const y0=h*H+14, y1=(h+1)*H-6, Y=v=>y1-v/top*(y1-y0);
g.fillStyle=css.getPropertyValue("--faint");g.font="11px sans-serif";g.textAlign="right";
for(let v=0;v<=top;v+=step){g.strokeStyle=css.getPropertyValue("--line");g.lineWidth=1;g.beginPath();g.moveTo(ML,Y(v));g.lineTo(ML+W,Y(v));g.stroke();g.fillText(v,ML-6,Y(v)+4);}
g.textAlign="left";g.fillText(HN[h]+" hand: force magnitude |F| (sensor units)",ML+4,h*H+11);
for(let k=0;k<5;k++){g.strokeStyle=COL[k];g.lineWidth=1.4;g.beginPath();
for(let t=0;t<T;t++){const x=ML+t/(T-1)*W, y=Y(force[t*10+h*5+k]);t?g.lineTo(x,y):g.moveTo(x,y);}g.stroke();}}
if(cur.it.act){g.strokeStyle="#888";g.setLineDash([4,3]);g.lineWidth=1;cur.it.act.forEach(f=>{const x=ML+f/(T-1)*W;g.beginPath();g.moveTo(x,0);g.lineTo(x,r.height);g.stroke();});g.setLineDash([]);}
cur.tlimg=g.getImageData(0,0,tl.width,tl.height);
}
function draw(t){
frame=t; const {maps,force,fmax,gmax,T}=cur;
for(let k=0;k<10;k++){const tile=tiles[k], d=tile.img.data, o=(t*10+k)*120, s=shared.checked?gmax:fmax[k]; let m=0;
for(let p=0;p<120;p++){const z=maps[o+p]; if(z>m)m=z; const li=Math.min(255,Math.round(z/s*255))*3;
d[p*4]=LUT[li];d[p*4+1]=LUT[li+1];d[p*4+2]=LUT[li+2];d[p*4+3]=255;}
tile.ctx.putImageData(tile.img,0,0); tile.v.textContent=`${m} / ${force[t*10+k].toFixed(1)}`;}
sl.value=t; fr.textContent=`frame ${t+1}/${T} · ${(t/30).toFixed(2)} s`;
if(cur.tlimg){const g=tl.getContext("2d"), dpr=window.devicePixelRatio||1; g.setTransform(1,0,0,1,0,0); g.putImageData(cur.tlimg,0,0);
const x=(cur.ML+t/(T-1)*cur.W)*dpr; g.strokeStyle="#111";g.lineWidth=1.5*dpr;g.beginPath();g.moveTo(x,0);g.lineTo(x,tl.height);g.stroke();}
}
const fromVideo=()=>Math.min(cur.T-1,Math.max(0,Math.floor(vid.currentTime*30+1e-3)));
function tick(){ if(!vid.paused){draw(fromVideo()); requestAnimationFrame(tick);} }
function seek(t){ t=Math.max(0,Math.min(cur.T-1,t)); vid.currentTime=(t+0.5)/30; draw(t); }
play.onclick=()=>{ if(vid.paused){ if(frame>=cur.T-1)seek(0); vid.playbackRate=+rate.value; vid.play(); } else vid.pause(); };
vid.onplay=()=>{play.textContent="❚❚ Pause"; requestAnimationFrame(tick);};
vid.onpause=vid.onended=()=>{play.textContent="▶ Play"; draw(fromVideo());};
vid.onseeked=()=>{ if(vid.paused) draw(fromVideo()); };
rate.onchange=()=>vid.playbackRate=+rate.value;
sl.oninput=()=>{vid.pause(); seek(+sl.value);};
tl.onclick=ev=>{const r=tl.getBoundingClientRect(); vid.pause(); seek(Math.round((ev.clientX-r.left-cur.ML)/cur.W*(cur.T-1)));};
shared.onchange=()=>draw(frame);
sel.onchange=()=>{vid.pause(); load(+sel.value).then(()=>{vid.play().catch(()=>{})});};
document.addEventListener("keydown",e=>{ if(e.target.tagName==="INPUT"&&e.target.type==="range")return;
if(e.key==="ArrowRight"){vid.pause();seek(frame+1);} else if(e.key==="ArrowLeft"){vid.pause();seek(frame-1);} });
window.addEventListener("resize",()=>{drawTimeline();draw(frame);});
const i0=Math.max(0,D.items.findIndex(x=>x.label.includes("0103_20261019_035851")));sel.value=i0;
load(i0).then(()=>{vid.muted=true;vid.play().catch(()=>{});});
})();
</script>
<script>
(function(){const T=document.getElementById("tp-task"),C=[...document.querySelectorAll(".tcard")];
function mark(task){C.forEach(c=>c.classList.toggle("on",c.dataset.task===task));}
C.forEach(c=>c.onclick=()=>{T.value=c.dataset.task;T.dispatchEvent(new Event("change"));mark(c.dataset.task);});
T.addEventListener("change",()=>mark(T.value));mark(T.value);})();
</script>
<section id="avoidance">
<div class="container">
<h2>Obstacle avoidance</h2>
<p class="sub">Collision-free motion in end-effector space (D3IL avoiding-v0)</p>
<p class="t">A planar end-effector must reach the goal while avoiding pillars. GlobMP is the projection step of DiRecT's diffusion sampler, compared with ten diffusion planners over 100 rollouts each.</p>
<figure style="max-width:760px"><video src="project_page/videos/avoiding_rollouts.mp4" poster="project_page/posters/avoiding_rollouts.jpg" autoplay muted loop playsinline controls preload="auto" style="width:100%;border-radius:12px;border:1px solid #e2e8f0;background:#fff"></video><figcaption>GlobMP rollouts on avoiding-v0 (seed 0, 100 episodes: 95 safe, 98 reach the goal), replayed in the simulator. Blue: test-time constraints. The robot runs four rollouts, then all 100 paths appear, safe in navy and violating in red.</figcaption></figure>
<figure><img src="project_page/figs/d3il_c_page.png" alt="(c) safety rate against task success" style="width:100%;max-width:800px;border:1px solid #cbd5e1"/><figcaption>Safety rate against task success, 100 episodes per method. Only the upper right both reaches the goal and avoids.</figcaption></figure>
</div>
</section>
<section id="maze" class="alt">
<div class="container">
<h2>Maze2D</h2>
<p class="sub">Safe navigation in a nonconvex maze (D4RL maze2d-large)</p>
<p class="t">A point robot crosses a nonconvex maze while avoiding keep-out regions. GlobMP picks a corridor by breadth-first search and enforces the keep-outs in continuous time; GlobMP is deterministic, the ten baselines run 10 episodes each.</p>
<figure style="max-width:900px"><video src="project_page/videos/maze2d_broad.mp4" poster="project_page/posters/maze2d_broad.jpg" autoplay muted loop playsinline controls preload="auto" style="width:100%;border-radius:12px;border:1px solid #e2e8f0;background:#fff"></video><figcaption>Broad setting. Dark stretches marked &times; are inside a keep-out; the badge counts runs that entered one.</figcaption></figure>
<figure style="max-width:900px"><video src="project_page/videos/maze2d_narrow.mp4" poster="project_page/posters/maze2d_narrow.jpg" autoplay muted loop playsinline controls preload="auto" style="width:100%;border-radius:12px;border:1px solid #e2e8f0;background:#fff"></video><figcaption>Narrow setting, with six keep-outs.</figcaption></figure>
</div>
</section>
<section id="code">
<div class="container">
<h2>Quick Start</h2>
<p class="sub">Code on GitHub and Hugging Face</p>
<pre><code>git clone https://github.com/GlobalMotionPlanning/GlobMP.git
cd globmp
pip install -e .
python -m pytest globmp/tests # about 10 s on one CPU core</code></pre>
</div>
</section>
<section class="alt">
<div class="container">
<h2>BibTeX</h2>
<pre><code>@misc{amiri2026globmp,
title={Continuous-Time Motion Planning and Steering with Global Convergence},
author={Amiri, Mohsen and Didari, Sima and Ataee Tarzanagh, Davoud and Moon, Hankyu and Kwon, Yeongdae},
year={2026},
note={Equal contribution: Amiri, Didari, Ataee Tarzanagh}
}</code></pre>
</div>
</section>
<section id="contact">
<div class="container">
<h2>Contact</h2>
<div class="contact">
<div class="people">Mohsen Amiri<sup>&dagger;</sup><br>Sima Didari<sup>&dagger;</sup><br>Davoud Ataee Tarzanagh<sup>&dagger;</sup><br>Hankyu Moon<br>Yeongdae Kwon</div>
<div class="where"><b>Samsung SDS Research America</b><br>Mountain View, CA, USA<br><span class="eq">&dagger; equal contribution</span><br><br><a href="https://github.com/GlobalMotionPlanning/GlobMP/issues" target="_blank" rel="noopener">Questions and issues on GitHub</a></div>
</div>
</div>
</section>
<footer>GlobMP &middot; Samsung SDS Research America</footer>
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