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arxiv: 2605.13748 · v1 · submitted 2026-05-13 · 💻 cs.RO · cs.SY· eess.SY· math.OC

Recognition: unknown

TinySDP: Real Time Semidefinite Optimization for Certifiable and Agile Edge Robotics

Ishaan Mahajan , Jon Arrizabalaga , Andrea Grillo , Fausto Vega , James Anderson , Zachary Manchester , Brian Plancher
Authors on Pith no claims yet

Pith reviewed 2026-05-14 18:04 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SYmath.OC
keywords semidefinite programmingembedded optimizationmodel predictive controlrobot motion planningconvex relaxationreal-time controlquadrotor navigationcollision avoidance
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The pith

TinySDP is an embedded semidefinite programming solver that runs real-time model predictive control with explicit collision-avoidance certificates on microcontrollers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents TinySDP as the first SDP solver built specifically for resource-constrained embedded hardware. It folds positive-semidefinite cone projections into a cached-Riccati ADMM iteration and adds a post-hoc rank-1 certificate that turns each relaxed solution into a concrete geometric guarantee. On hard benchmarks such as cul-de-sac passages and moving-obstacle avoidance, the resulting controller produces collision-free trajectories up to 73 percent shorter than prior local planners. The same solver is shown to run at real-time rates on a Crazyflie quadrotor, proving that semidefinite relaxations can be enforced inside tight embedded timing loops.

Core claim

TinySDP integrates positive-semidefinite cone projections into a cached-Riccati-based ADMM solver and pairs the solver with an a posteriori rank-1 certificate that converts each relaxed solution into explicit geometric guarantees at every time step, thereby enabling real-time model-predictive control on microcontrollers for nonconvex obstacle constraints.

What carries the argument

Cached-Riccati ADMM iteration that incorporates positive-semidefinite cone projections, combined with an a posteriori rank-1 certificate that extracts explicit geometric guarantees from the relaxed solution.

If this is right

  • Collision-free navigation succeeds in cul-de-sac and dynamic-obstacle scenarios that cause local planners to fail.
  • Paths are up to 73 percent shorter than those produced by state-of-the-art baselines.
  • Semidefinite constraints are enforced at real-time rates on agile embedded platforms such as the Crazyflie quadrotor.
  • The same framework directly supports model-predictive control with nonconvex geometric obstacle constraints.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same solver structure could be applied to other nonconvex constraints that admit SDP relaxations, such as attitude or contact constraints.
  • Certification at every step makes the controller suitable for safety-critical edge deployments where formal guarantees are required.
  • Because the method is built around cached Riccati structure, it may scale to multi-robot coordination problems that share the same quadratic cost.

Load-bearing premise

That the positive-semidefinite projections inside the cached ADMM loop remain fast enough on microcontrollers while the rank-1 certificate reliably converts relaxed solutions into correct geometric constraints.

What would settle it

A run on the Crazyflie in which either the solver exceeds the real-time deadline or the generated trajectory collides with an obstacle in the cul-de-sac benchmark.

Figures

Figures reproduced from arXiv: 2605.13748 by Andrea Grillo, Brian Plancher, Fausto Vega, Ishaan Mahajan, James Anderson, Jon Arrizabalaga, Zachary Manchester.

Figure 1
Figure 1. Figure 1: Front (top) and side (bottom) views of the Crazyflie running TinySDP online to avoid a moving arm. Left to right: [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Dynamic moving-gap benchmark. Time-lapse com￾parison of TinySDP (blue) against RPCBF (red) and the linearized baselines (green, purple). TinySDP anticipates the moving obstacle, deviating early to maintain clearance. The zero-margin baselines (light green, light purple) fail to antici￾pate the motion and collide. The tuned baselines (dark green, dark purple) achieve safety only by using impractically large… view at source ↗
Figure 4
Figure 4. Figure 4: 3D dynamic obstacle avoidance extension. TinySDP navigating two dynamic 3D sphere scenarios: Sweeping Barrier (top) and Vertical Gate (bottom). The two rows provide complementary views of the same 3D motion, while the columns show the approach, midpoint, and end of the maneuver. The white dotted path indicates the direct start-to-goal line, which would intersect the obstacle field. TinySDP extends naturall… view at source ↗
Figure 5
Figure 5. Figure 5: Evolution of the Rank-1 certificate as the Crazyflie [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on resource-constrained embedded systems. To address this gap, we introduce TinySDP, the first semidefinite programming solver designed for embedded systems, enabling real-time model-predictive control (MPC) on microcontrollers for problems with nonconvex obstacle constraints. Our approach integrates positive-semidefinite cone projections into a cached-Riccati-based ADMM solver, leveraging computational structure for embedded tractability. We pair this solver with an a posteriori rank-1 certificate that converts relaxed solutions into explicit geometric guarantees at each timestep. On challenging benchmarks, e.g., cul-de-sac and dynamic obstacle avoidance scenarios that induce failures in local methods, TinySDP achieves collision-free navigation with up to 73% shorter paths than state-of-the-art baselines. We validate our approach on a Crazyflie quadrotor, demonstrating that semidefinite constraints can be enforced at real-time rates for agile embedded robotics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces TinySDP, the first SDP solver for embedded systems, which integrates positive-semidefinite cone projections into a cached-Riccati-based ADMM solver and uses an a posteriori rank-1 certificate to convert relaxed solutions into geometric guarantees for real-time MPC in robotics with nonconvex obstacles. It reports up to 73% shorter collision-free paths than baselines in benchmarks like cul-de-sac and dynamic obstacle avoidance, and validates the approach on a Crazyflie quadrotor for real-time performance.

Significance. If the performance claims and certificate reliability hold, this work would significantly advance certifiable optimization-based control for resource-constrained embedded robotics, enabling safer agile navigation where local methods fail.

major comments (2)
  1. [Abstract] Abstract: The quantitative claim of 'up to 73% shorter paths' is presented without error bars, full experimental protocol, or implementation details, making it difficult to assess the robustness of the benchmark improvements.
  2. [Abstract (a posteriori rank-1 certificate)] Abstract (a posteriori rank-1 certificate): The paper relies on the a posteriori rank-1 certificate to provide explicit collision-free guarantees from relaxed SDP solutions, but provides no analytic bound on the tightness for nonconvex obstacle constraints or coverage of failure cases where the relaxation admits higher-rank solutions or duality gaps; this is load-bearing for the collision-free navigation claims.
minor comments (1)
  1. [Abstract] The abstract mentions 'challenging benchmarks, e.g., cul-de-sac and dynamic obstacle avoidance scenarios' but does not specify the exact baselines compared against.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard convex optimization assumptions plus the domain-specific premise that the described ADMM structure will be tractable on microcontrollers; no new physical entities are introduced and no free parameters are explicitly fitted in the abstract.

axioms (1)
  • domain assumption Positive-semidefinite cone projections combined with cached Riccati recursions inside ADMM remain computationally feasible at real-time rates on resource-constrained microcontrollers.
    This assumption underpins the claim of real-time performance on embedded hardware.

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