Quadrotor Surveillance: Local Peak Seeking and Smooth Coverage Control

One of the earliest reasons quadrotor surveillance stopped feeling like a normal planning problem to me was simple: too many elegant formulations assumed I already knew the map I was supposed to discover. If the goal is to inspect regions whose importance is encoded in an unknown nonconvex utility function, then an optimizer that needs the whole function in advance is really answering a slightly different problem. That mismatch started to feel structural rather than technical.

The standard architectures all made sense on their own terms. Plan-then-track methods could produce collision-free waypoints, but the resulting references often ignored higher-order vehicle dynamics and created the familiar jitter between planner and controller. Nonlinear MPC was more principled in that regard because it could encode dynamics and actuator limits directly, but it paid for that elegance with computational cost and short effective horizons. More importantly, both families still leaned on having the objective available in advance. In this paper, MPC becomes a benchmark, not the core philosophy.

What changed the framing for me was the sensing assumption. If the vehicle can measure the local gradient of the utility function, then it should be possible to move toward important regions without reconstructing the whole field first. But plain gradient ascent was not enough. A gradient gives a direction, not necessarily a good reference for a quadrotor. The vehicle does not just need to know where to go. It needs a smooth, preferably twice-differentiable trajectory that can actually be tracked with its dynamics.

That was the real shift in the note. Instead of treating optimization as something that happens before control, I started using a continuous-time accelerated gradient law itself as the reference generator. The triple-momentum dynamics produce a smooth path using only local gradient information, and that reference can then be handed to a tracking layer. Once written this way, the optimizer is no longer an abstract search rule. It becomes part of the closed-loop motion design. That is what made the planner and controller feel less like separate modules and more like parts of the same system. The same smooth reference could then be tracked through backstepping or a flatness-based construction, so smoothness was not aesthetic. It was the bridge between online optimization and feasible flight.

But reaching one local maximum was still not the real mission. Surveillance means inspecting the surrounding high-value area and then continuing the search instead of getting trapped at the first attractive point. That is where the hybrid state machine became the real heart of the work. A more aggressive ascent mode helps the vehicle move through flat or ambiguous regions. A tuned local mode settles near a maximum. Then a spiral mode deliberately shifts the objective from peak seeking to area coverage. That was the moment the project stopped looking like online optimization alone and started looking like a surveillance controller.

The memory and restart logic pushed that idea further. The controller records previously visited maxima and their inspected radii, checks whether the current motion meaningfully points away from the recently covered region, and triggers new exploration when a spiral grows too large or the vehicle risks cycling through the same area again. That mattered because it turned local behavior into a repeatable mission policy. The drone was no longer just climbing hills. It was discovering, covering, leaving, and restarting in a structured way.

The simulations made the tradeoff clearer. Under relatively mild actuator limits, the hybrid planner combined with backstepping or corrected flatness tracks the reference quickly and can match or outperform nonlinear MPC while requiring far less computation. Under tighter tilt and body-rate limits, nonlinear MPC regains an advantage because it re-optimizes at every step with those constraints built in. I found that result helpful rather than disappointing. It showed that the contribution was not “MPC but better in every regime.” It was a different compromise: less model knowledge, less computation, smoother online references, and strong performance when the generated path remains trackable.

The large-map experiment is what makes the note feel like a research-origin piece to me. On a 1000 m × 1000 m environment with 14 peaks, the controller moves from local gradient climbing to repeated coverage without ever assuming full knowledge of the field, and the relevant regions are fully covered in about 100 minutes. Looking back, that is the lasting idea. Surveillance under unknown objectives should not be framed only as a precomputed trajectory problem. It can be built as a hybrid closed-loop behavior where local gradients provide online discovery, continuous optimization provides smooth motion, nonlinear tracking provides feasibility, and mission logic turns local peak seeking into full-area surveillance.