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An Adaptive Control Architecture for Slope and Terrain Compensation in Autonomous Navigation in Mediterranean Greenhouses
Fernando Cañadas-Aránega, Dirk Wollherr, José L. Guzmán, José C. Moreno, José L. Blanco-Claraco
TL;DR
Greenhouse robots can suffer navigation errors and failures when small ground variations alter wheel behavior and sensors cannot fully compensate. The paper characterizes greenhouse terrain and slope, then combines adaptive feedforward control with MPC-based trajectory tracking; simulations report reduced tracking error and control effort, with slightly increased SCI.
Problem
Small greenhouse ground variations can alter wheel angular velocity, causing localization losses and navigation failures that sensors may not fully compensate.
Method
The strategy characterizes common greenhouse soils, estimates slope with an IMU, and uses gain-scheduled adaptive feedforward control with MPC for trajectory tracking.
Results
The differential-drive robot achieves significant reductions in tracking error and control effort, while feedforward control slightly increases SCI.
Takeaways & Limitations
The approach improves navigation quality and reliability in narrow spaces and adverse Mediterranean greenhouse conditions.
Takeaways & Limitations
The study evaluates the approach in simulations and includes safety constraints for gravel-sand conditions where friction may be unfavorable.
Abstract
from arXiv · showhide
The ability to move stably over terrain with varying slopes and textures is essential for mobile agricultural robots operating in complex and dynamic environments such as greenhouses, where small terrain irregularities can lead to significant navigation errors. This article presents a novel terrain-adaptation strategy based on the carried payload, ensuring accurate and robust trajectory tracking. The proposed approach is based on: (i) the experimental characterization of the most common types of greenhouse soil, concrete, compacted sand, and gravel, and (ii) the direct measurement of terrain slope using the IMU, in order to estimate the force with which this angle affects the motor input. Based on this information, a cascade trajectory-tracking scheme has been designed, consisting of a model-based predictive controller (MPC) in the outer loop and a PI controller in the inner loop. The system incorporates an adaptive feedforward control through gain scheduling approach, capable of adjusting to disturbances caused by variations in slope and terrain type. Simulation results demonstrate that the differential-drive robot achieves a significant improvement both in error indices and in control signal efficiency, highlighting the effectiveness and robustness of the proposed approach.
1. Introduction
Greenhouse robots face navigation and control failures when limited space, heterogeneous terrain, and small surface variations disturb wheel motion. The paper proposes terrain- and slope-adaptive control to improve trajectory tracking and navigation stability.
- Small ground-surface variations can change wheel angular velocity, causing localization losses and potentially navigation failures.
- Different soils and slopes alter robot dynamics, stability, and low-level motor control in greenhouse environments.
- The proposed strategy combines soil characterization, IMU-based slope estimation, adaptive feedforward gain scheduling, and MPC for terrain-aware trajectory tracking.
- Simulation results report significant reductions in tracking error and control effort, improving navigation quality in complex environments.
- The paper is organized around the problem, control-scheme and parameter-identification methodology, results, and conclusions.
2. Experimental Setup
The experimental setup models a skid-steer agricultural robot and greenhouse in MVSim, incorporating motor, mass, friction, payload, soil, and slope effects. The simulation represents heterogeneous greenhouse sectors and terrain-induced disturbances relevant to control design.
- The simulation uses a 20 × 20 m greenhouse model with five 4 m navigation corridors flanked by tomato plants.
- MVSim provides physics-based tyre-ground friction models for analysing terrain disturbances and developing the control law.
- The AgriCobIoT I platform is represented as a four-wheel skid-steer robot with differential-drive state x(t) = [x(t) y(t) θ(t)] ∈ R3.
- The robot model includes viscous friction, wheel inertia, chassis and wheel masses, rotational vehicle inertia, dynamic friction, and damping.
- Friction simulator model: MVSim decomposes each wheel’s total force into longitudinal and lateral components and imposes a per-wheel friction limit Frmax = µ mpw g before slippage.
- Payload, soil type, and terrain slope: The setup varies payload, slope, and soil-dependent friction, damping, and rolling coefficients; payload conditions are 0 kg and 70 kg.
- Payload, soil type, and terrain slope: Gravel sand is treated as a critical sector because it increases skidding likelihood and safety risk under unfavorable ground conditions.
- Terrain slope as a disturbance: Slopes act as disturbances by changing speed and introducing resistive torque whose magnitude depends on inclination and total robot mass.
3. Proposed adaptive control approach
The proposed architecture compensates for payload, terrain, and slope disturbances through cascade control, online slope-force estimation, and adaptive feedforward gain scheduling.
- The architecture combines an inner motor-speed PID loop with an outer MPC loop for trajectory tracking and motor-speed reference generation.
- The main contribution estimates wheel force caused by terrain slope and adapts the feedforward compensator gain to disturbance conditions.
- The disturbance model includes friction, rolling resistance, gravity, and damping, using soil type, payload, slope angle, and wheel speed.
- Slope-effect simulations identify the static gain Ks(s, p) from changes in slope torque to changes in motor angular velocity across payloads and terrain types.Tests include slopes between (-5,5)% and a maximum payload of mpl = 70 kg, including combined slope and terrain changes.
- The feedforward gain is calculated as Kff(s, p) = Ks(s, p)/Km and scheduled according to payload and terrain type.The gain-scheduling values and friction parameters are summarized in Table 2.
- The MPC velocity and acceleration constraints are modified in real time using βmpc = Frmax/Flongmax · 0.9 to account for friction-related force limits.The factor 0.9 represents the stated 10% safety coefficient associated with ISO 3691-4.
4. Results
The simulations compare cascade control with and without adaptive feedforward compensation across same- and different-terrain tests. The proposed approach improves trajectory-tracking performance, with clearer gains under slope and terrain perturbations, while constrained operation reduces friction demand.
- Simulation setup: The simulations evaluate the cascade architecture with and without adaptive feedforward compensation in same- and different-terrain tests.A 0.01 s sampling interval and five-step forecast horizon were used; Figure 5 presents the graphical results.
- Tracking performance: The proposed approach produces noticeable performance improvements, with clearer slope-compensation gains when both perturbations are present.Sector-transition improvements are described as modest, whereas combined slope and terrain effects show a clearer improvement.
- Tracking performance: The adaptive feedforward action slightly increases control effort while considerably reducing tracking error and improving navigation.Table 3 reports SAE and SCI comparisons, with the final columns summarizing improvement indices.
- Constraint adaptation: A 17.4% friction reduction satisfies the constraints and prevents violation of the friction threshold.The adjustment adds a 10% safety margin in hazardous areas and is illustrated in Figure 6.
5. Conclusion
The work presents a gain-scheduled adaptive control strategy for trajectory tracking under varying payloads, terrain types, and slopes. Simulations report reduced tracking error and SAE, while SCI increases only slightly, supporting more reliable navigation in the tested greenhouse setting and adverse conditions.
- Conclusion: Gain scheduling combines an adaptive feedforward compensator with MPC to adjust robot control dynamics under varying payloads, terrain types, and slopes.The stated objective is to improve trajectory tracking and reduce localization and navigation failures on heterogeneous soils.
- Conclusion: The differential-drive robot achieves significant tracking-error reductions in the confined greenhouse test environment.The reported results characterize the approach as effective and robust within that test environment.
- Conclusion: The method reduces SAE during trajectory tracking, while feedforward control may slightly increase SCI relative to its precision and stability gains.The conclusion frames the SCI increase as minimal compared with the reported gains.
- Conclusion: The robot can navigate more reliably in narrow spaces and adverse conditions typical of Mediterranean greenhouses.This practical outcome is stated as previously not possible in the paper’s conclusion.