diff --git a/src/roboticstoolbox/mobile/PRMPlanner.py b/src/roboticstoolbox/mobile/PRMPlanner.py
index c9fcec047..13b579622 100644
--- a/src/roboticstoolbox/mobile/PRMPlanner.py
+++ b/src/roboticstoolbox/mobile/PRMPlanner.py
@@ -165,6 +165,8 @@ def _create_roadmap(self, npoints: int, dist_thresh: float | None) -> None:
         graph = self._graph
         if occgrid is None or graph is None:
             raise ValueError("no occupancy grid or graph")
+        if npoints > 0 and np.all(occgrid.grid):
+            raise NoPathError("occupancy grid has no free cells")
 
         self.progress_start(npoints)
 
@@ -246,6 +248,8 @@ def plan(
         :param dist_thresh: distance threshold, defaults to ``dist_thresh`` given
             to constructor
         :param animate: deprecated, animating the planning is not implemented
+        :raises NoPathError: points were requested but the occupancy grid has
+            no free cells
 
         Create a probabilistic roadmap.  This is a graph connecting points
         randomly selected from the free space of the occupancy grid. Edges are
diff --git a/tests/test_prm_free_space.py b/tests/test_prm_free_space.py
new file mode 100644
index 000000000..ca7f2e0ee
--- /dev/null
+++ b/tests/test_prm_free_space.py
@@ -0,0 +1,29 @@
+"""PRM planning on maps where rejection sampling cannot find free space."""
+
+import numpy as np
+import pytest
+
+from roboticstoolbox import NoPathError, PRMPlanner
+
+
+@pytest.mark.timeout(2)
+@pytest.mark.parametrize("inflate", [0, 1])
+def test_plan_rejects_maps_without_free_cells(inflate: int) -> None:
+    grid = np.ones((5, 7))
+    if inflate:
+        grid[2, 3] = 0
+    planner = PRMPlanner(grid, inflate=inflate, progress=False, seed=0)
+
+    with pytest.raises(NoPathError, match="no free cells"):
+        planner.plan(npoints=1)
+
+
+def test_plan_with_free_cells_builds_a_roadmap() -> None:
+    grid = np.ones((5, 7))
+    grid[1:4, 2:5] = 0
+    planner = PRMPlanner(grid, progress=False, seed=0)
+
+    planner.plan(npoints=5)
+
+    assert planner.graph.n == 5
+    assert all(not planner.occgrid.isoccupied(vertex.coord) for vertex in planner.graph)