CSymPlan: Certified Symbolic Planning and Control for High-DOF Manipulators

Aditya Narendra; Ashok Kumar Saini; Mahathi Anand; Mahmoud Khaled; Fares J. Abu-Dakka; Abdalla Swikir

cs.ROAug 24, 2026

CSymPlan: Certified Symbolic Planning and Control for High-DOF Manipulators

Authors: Aditya Narendra, Ashok Kumar Saini, Mahathi Anand, Mahmoud Khaled, Fares J. Abu-Dakka, Abdalla Swikir

Organizations: Mohamed bin Zayed University of Artificial Intelligence (MBZUAI), Abu Dhabi, United Arab Emirates · Learning Systems and Robotics Lab, Technical University of Munich, Germany · Ludwig Maximilian University of Munich, Munich, Germany · New York University Abu Dhabi, Abu Dhabi, United Arab Emirates

Abstract

Robot manipulators are commonly engineered around a decoupled motion-generation stack: a planner computes a collision-free path and a lower-level controller tracks the resulting reference. This separation is computationally convenient, but it can produce references that are difficult to execute under actuator limits, tracking error, model mismatch, and small obstacle clearances. We present CSymPlan, a certified symbolic planning and control framework for high-DOF manipulators with two complementary implementations: an offline implementation that precomputes certified reach-avoid feedback policies for known workspaces; and an online implementation that synthesizes or updates symbolic policies at runtime from changing task and perception information using parallelization. The offline implementation reduces the manipulator dynamics to a sampled perturbed double-integrator model in operational space through feedback linearization, treats torque-realization errors, modeling inaccuracies, and measurement uncertainty as bounded disturbances, and refines the synthesized symbolic policy to the Franka FR3 through a quantization--lookup--torque realization pipeline. The online implementation uses the same abstraction and refinement interface, but replaces the precomputed policy table with a runtime pFaces request--synthesis--execution loop. In randomized simulated benchmarks and perception-driven Franka FR3 experiments, both implementations complete reach-avoid tasks with zero safety violations; whenever no certified action exists, the robot holds, replans, or stops safely instead of executing an uncertified command.

Figures & tables

Figure 1: Overview of CSymPlan. The offline implementation synthesizes a certified reach-avoid policy from a finite abstraction of sampled perturbed task-space dynamics and executes it through a quantization–lookup–torque pipeline. The online implementation uses the same abstraction and torque-realization interface, but calls pFaces online mode at runtime to synthesize or refresh the symbolic policy for the current target and obstacle sets.

Figure 2: Offline CSymPlan architecture. The upper row shows the one-time synthesis pipeline: task-space discretization, finite symbolic model construction, reach-avoid task specification, SCOTS-based policy synthesis, and export of a policy table for runtime query. The lower row shows the real-time execution pipeline: the robot state is measured and quantized, the precomputed policy is queried, the selected abstract input is refined through operational-space torque realization, and the resulting torque command is applied to the robot.

Figure 3: Online CSymPlan architecture. At each replanning instant, the robot senses the environment, updates the obstacle model and uncertainty bounds, maps the measured task-space state to an abstract cell, and sends the current state, target set, unsafe set, and horizon to the pFaces server. pFaces performs finite-horizon reach-avoid synthesis over the symbolic abstraction, returns a certified policy or command segment for the current state, and the robot refines the selected abstract input through operational-space torque realization. The lower loop illustrates the receding-horizon update: changes in the environment trigger map updates, new pFaces requests, and replacement of stale command segments.

Figure 4: Offline real-time execution architecture on the Franka FR3. Joint feedback is converted to task-space position and velocity, quantized, queried through the precomputed symbolic policy, and refined to joint torques at the control rate.

Method	Success (%)	Violation (%)	$t_{\mathrm{goal}}$ (s)	$L$ (m)	Smoothness	Effort	CPU/step (ms)
CSymPlan	100	0.0	2.3	1.25	0.90	1.05	0.05 / 0.08
RRT + tracker	76	10.0	3.9	1.42	1.25	1.18	120 / 240
LQR-RRT ⋆ + tracker	83	6.0	3.6	1.33	0.62	1.02	170 / 340
MPPI	95	4.5	2.5	1.17	0.52	0.98	18.1 / 19.0
Neural MPC	93	3.5	2.6	1.14	0.38	0.92	3.6 / 4.4

Table I: Offline simulated reach-avoid benchmarking in PyBullet across randomized trials and scenes. Metrics summarize reliability, efficiency, control quality, and online computation time.

Figure 5: Offline hardware experiment procedure and control-loop execution order.

Panel of Figure 6 — Figure 6: Offline Franka FR3 real-robot execution metrics across hardware trials. The panels show (a) end-effector position tracking error, (b) commanded joint-torque norm, and (c) measured joint-velocity norm. Curves show the mean and one-standard-deviation band over $N=5$ trials per scene.

Figure 7: Representative offline simulation scene. The robot starts at the blue marker and aims to reach the red marker. Green markers indicate a trajectory produced by CSymPlan through the certified safe set.

Panel of Figure 8 — Figure 8: Representative maze trajectories for offline CSymPlan and baselines. Dashed curves show reference paths where applicable and solid curves show executed end-effector trajectories from the same start to the same goal. Black regions are obstacles; a collision is counted when the end-effector footprint intersects an obstacle cell.

Figure 9: Representative Isaac Sim benchmark environments used for online evaluation: shelf/rack reach-avoid, point reach, 3D maze, and moving-obstacle under tasks.

Figure 10: Real-world online perception and simulation correspondence. Left: Franka FR3 hardware setup used for the online reach-avoid experiments. Middle: DNVblox voxel reconstruction obtained from depth sensing and used to form the runtime obstacle set. Right: corresponding Isaac Sim scene used for controlled online benchmarking.

Figure 11: Representative online real-world Franka FR3 task scenes. Left: dynamic-obstacle reach-avoid, where the robot moves from the red start region to the green goal region while avoiding a moving rod obstacle. Middle: maze traversal with dynamic walls, where the wall configuration is changed during execution and the controller replans from the updated obstacle set. Right: smooth static-maze traversal, where the robot follows a continuous path through fixed curved maze corridors from start to goal.

Metric	Definition	Interpretation
Success	$100N_{\mathrm{succ}}/N$	Trials that reach and hold the final target without leaving the safe set.
Violation	$100N_{\mathrm{viol}}/N$	Trials with collision, inflated-obstacle entry, workspace exit, or limit violation.
Safe stop / timeout	$100N_{\mathrm{stop}}/N$	Trials that terminate without collision because no certified action is available, a command becomes stale, or the task times out.
Safe resolution	$100(N_{\mathrm{succ}}+N_{\mathrm{stop}})/N$	Trials that either succeed or terminate conservatively without a safety violation.
Time to goal	$t_{\mathrm{goal}}$	Elapsed time from motion start to final target hold.
Path length	$\sum_{k}\left\lVert x_{k+1}-x_{k}\right\rVert_{2}$	Length of the executed end-effector trajectory.

Table II: Online evaluation metrics. The safe-resolution metric separates certified task failure from unsafe execution.

Panel of Figure 12 — Figure 12: Online hardware stability profiles over normalized execution time. (a) Mean end-effector tracking error with one-standard-deviation bands for the evaluated task families. (b) Mean obstacle clearance with one-standard-deviation bands for the dynamic tasks; the dashed horizontal line is the configured safety margin used to inflate the runtime obstacle set before pFaces synthesis.

Task family	Trials	Success (%)	Safe stop / timeout (%)	Violation (%)	Safe resolution (%)	$t_{\mathrm{goal}}$ (s)	$L$ (m)	$d_{\min}$ (cm)	pFaces mean / 95p (ms)
Shelf reach-avoid	50	98	2	0.0	100	$3.2\pm 0.5$	$1.31\pm 0.16$	$5.8\pm 1.4$	84 / 190
3D maze	50	94	6	0.0	100	$6.1\pm 1.1$	$2.12\pm 0.29$	$3.4\pm 0.8$	210 / 510
Moving obstacle	50	90	10	0.0	100	$4.8\pm 1.0$	$1.76\pm 0.25$	$4.6\pm 1.2$	170 / 430
All online simulation	150	94	6	0.0	100	$4.7\pm 1.5$	$1.73\pm 0.41$	$4.6\pm 1.6$	155 / 430

Table III: Representative online Isaac Sim task outcomes. Values are mean

\pm

standard deviation where applicable.

Task family	Replans / trial	Buffer underruns / trial	Stale rejects / trial	Dominant safe-stop cause
Shelf reach-avoid	$5.8\pm 1.6$	0.1	0.2	Timeout near shelf lip or conservative grid boundary.
3D maze	$13.5\pm 3.7$	0.8	1.1	No winning action in a narrow passage for the requested horizon.
Moving obstacle	$16.2\pm 4.5$	1.2	1.6	Obstacle update invalidates the currently buffered segment.
All online simulation	$11.8\pm 5.8$	0.7	1.0	Certified hold, re-request, or timeout without collision.

Table IV: Representative online Isaac Sim replanning and buffer statistics.

Task	Trials	Success	Safe stop	Violation	Safe resolution	$t_{\mathrm{goal}}$ (s)	$d_{\min}$ (cm)	Stop cause
High-speed reach	10	10 / 10	0 / 10	0 / 10	10 / 10	$2.3\pm 0.3$	–	none
Dynamic-obstacle reach-avoid	10	9 / 10	1 / 10	0 / 10	10 / 10	$4.4\pm 0.8$	$5.1\pm 1.6$	no certified action
Dynamic maze	10	8 / 10	2 / 10	0 / 10	10 / 10	$7.0\pm 1.5$	$3.5\pm 0.9$	stale / no solution
All hardware	30	27 / 30	3 / 30	0 / 30	30 / 30	$4.6\pm 2.1$	$4.3\pm 1.5$	certified stops

Table V: Representative online Franka FR3 task outcomes with DNVblox perception. Values are mean

\pm

standard deviation where applicable.

Task	Tracking error mean / max (cm)	pFaces mean / 95p (ms)	DNVblox age mean / 95p (ms)	Replans / trial	Underruns / trial	Stale rejects / trial
High-speed reach	1.1 / 3.2	65 / 150	–	$4.1\pm 1.0$	0.0	0.0
Dynamic-obstacle reach-avoid	1.6 / 4.8	135 / 330	70 / 125	$11.8\pm 3.2$	0.4	0.8
Dynamic maze	2.1 / 6.0	260 / 680	85 / 150	$18.7\pm 5.0$	1.7	2.1
All hardware	1.6 / 6.0	153 / 410	78 / 139	$11.5\pm 6.4$	0.7	1.0

Table VI: Representative online Franka FR3 runtime statistics.

Method	Success (%)	Violation (%)	Safe stop / timeout (%)	Safe resolution (%)	Solve mean / 95p (ms)	Comment
CSymPlan online	94	0.0	6.0	100.0	155 / 430	Certified actions; no-solution cases become safe stops.
NMPC	91	3.3	5.7	96.7	38 / 74	Fast deterministic optimization, but no symbolic winning-set certificate.
MPPI	88	5.3	6.7	94.7	22 / 31	Aggressive sampling-based behavior with lower clearance near obstacles.
RRT-Connect + tracker	74	9.3	16.7	90.7	210 / 460	Plan–then–track mismatch in dynamic scenes.
CBF-QP	83	1.3	15.7	98.7	3.1 / 6.5	Very fast local safety filter, but can get stuck in maze-like tasks.
Neural MPC	86	6.0	8.0	94.0	1.4 / 2.2	Fastest runtime, but weaker safety under distribution shift.

Table VII: Representative online simulation baseline comparison aggregated across shelf, maze, and moving-obstacle tasks.

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Changes in a robot's observations do not automatically imply changes in the task it is solving, but language-conditioned manipulation systems often fail to separate the two. If an object moves, for example, the locations at which actions should be executed may change while the underlying manipulation plan remains valid. We introduce Sequential Planning via Anchored Robotic Keypoints (SPARK), which separates a task's symbolic plan from its execution-time perceptual grounding, and we experimentally isolate whether a fixed symbolic plan can survive substantial changes to the scene through execution-time re-grounding. SPARK represents the task as a symbolic behavior tree whose object references are grounded to current 3D observations during execution, allowing the robot to update where actions are performed while preserving the plan. Runtime verification then enables local recovery and renewed grounding, only resorting to a new plan if necessary. To test the separation between plan and perceptual-grounding, we perform a set of manipulation experiments with a fixed plan while moving objects during execution. Under a 10 cm displacement, verification and adaptation maintain

66.7\%

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Abstract

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