TIE: An Autonomous and Adaptive Terrestrial-Aerial Quadrotor

09/10/2021
by   Ruibin Zhang, et al.
Zhejiang University
0

This letter presents a fully autonomous robot system that possesses both terrestrial and aerial mobility. We firstly develop a lightweight terrestrial-aerial quadrotor that carries sufficient sensing and computing resources. It incorporates both the high mobility of unmanned aerial vehicles and the long endurance of unmanned ground vehicles. An adaptive navigation framework is then proposed that brings complete autonomy to it. In this framework, a hierarchical motion planner is proposed to generate safe and low-power terrestrial-aerial trajectories in unknown environments. Moreover, we present a unified motion controller which dynamically adjusts energy consumption in terrestrial locomotion. Extensive realworld experiments and benchmark comparisons validate the robustness and outstanding performance of the proposed system. During the tests, it safely traverses complex environments with terrestrial aerial integrated mobility, and achieves 7 times energy savings in terrestrial locomotion. Finally, we will release our code and hardware configuration as an open-source package.

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I Introduction

In recent years, unmanned aerial vehicles (UAVs) have attracted more and more attention in both academia and industry. Among them, quadrotors are most widely used due to their simple structure, high mobility, and vertical takeoff and landing (VTOL) capabilities. Moreover, progresses in autonomous navigation enable quadrotors to fly safely and aggressively in unknown cluttered environments with full autonomy[25, 26, 24], greatly expanding their application area.

However, quadrotor inherently suffers from bad power utilization (PU) because most of the energy is wasted on counteracting the body weight. This defect limits quadrotors’ use in long-distance missions such as search and rescue, delivery, and active exploration. In such missions, the mobility of quadrotors is necessary for traversing extreme terrain, while the relatively short endurance can hardly support quadrotors to complete the entire mission. In contrast, although unmanned ground vehicles (UGVs) cannot cross rugged terrains, they enjoy a much better PU because the driving force only needs to overcome friction, not support their own weight. To combine the advantages of both types of mobile robots, researchers propose various terrestrial-aerial vehicles [20, 3, 8, 17, 7, 23, 9, 10, 22, 2, 21, 11, 16, 14, 4, 6, 15, 18] (detailedly introduced in Sect.II-A). The locomotion modes of the vehicles can be dynamically altered depending on the need for better PU or higher mobility.

In this work, we customize a compact yet fully functional Two-wheeled terrestrIal-aErial quadrotor called TIE (as shown in Fig.1). Compared with the prototypes developed in previous works that share a similar structure [20, 9, 3, 8, 23, 17, 7], TIE possesses a smaller size, lighter weight, and longer hover duration. We also deploy adequate sensing and computing resources on TIE. Furthermore, careful engineering considerations are incorporated to balance its portability and robustness. The mobility of TIE is demonstrated in the video, in which it performs challenging tasks such as seamless locomotion transition, slope climbing, wall climbing, and rolling on rough ground.

Fig. 1: Diagram of TIE, a terrestrial-aerial quadrotor with two passive wheels deployed on each side of the frame. Its mobility and autonomy are exhaustively presented in the video available at https://youtu.be/QpZMRq7sXnM.
Fig. 2: Software architecture. The perception, planning, and control modules run parallelly using onboard sensing and computing resourcess.

The other focus of our work is autonomous navigation for terrestrial-aerial vehicles. At present, only Fan et al.[7] present a complete terrestrial-aerial navigation framework. However, it is deficient in motion planning and motion control. The planning method proposed by Fan et al.[7] cannot generate satisfactory trajectories due to the coarse path searching and the lack of trajectory optimization. Besides, it does not consider the nonholonomic constraint for terrestrial locomotion. As for motion control, the method of Fan’s[7] fixes the total thrust in terrestrial locomotion, limiting PU improvement. We effectively solve these problems in the proposed navigation framework. Firstly, we develop a motion planner that generates safe, smooth, and dynamically feasible terrestrial-aerial trajectories. The nonholonomic constraint is also properly handled. Then, we design a unified terrestrial-aerial controller which includes an adaptive thrust adjustment method to improve PU in terrestrial locomotion. The results show up to 7 times less energy consumption compared with aerial locomotion. Furthermore, we integrate self-localization and local map fusion modules in the proposed navigation framework for real-world applications.

We perform sufficient experiments in challenging real-world environments to show the performance and robustness of the proposed robot system. During the tests, TIE plans safe and low-power trajectories in unstructured dense environments and accurately tracks these trajectories even when there are sharp turnings. We also compare our work with cutting-edge works. The results show that the proposed methods are superior in planning performance, controlling accuracy, and PU. Contributions of this letter are:

  • A lightweight and maneuverable quadrotor prototype that can seamlessly switch between terrestrial and aerial locomotion, and can carry sufficient onboard sensors and computing power.

  • An adaptive navigation framework that enables the proposed quadrotor prototype to traverse unknown cluttered environments with terrestrial-aerial integrated locomotion autonomously.

  • Presenting adequate real-world experiments and benchmark comparisons to validate the proposed robot system, as well as releasing source code and hardware configuration for the reference of the community.

Ii Related Work

Ii-a Terrestrial-Aerial Vehicle Design

Previous terrestrial-aerial vehicle designs can be divided into two categories according to whether the terrestrial locomotion is active or passive. Typically, the active ones use motor-driven wheels [22, 2, 11, 21] for ground locomotion. Because the dynamics and control of differentially driven wheeled mobile robots have been thoroughly studied, such design ensures the stability of terrestrial locomotion. Some other works include some novel deformable mechanisms [16, 14, 4] for locomotion mode switching. However, the above terrestrial-aerial vehicle designs need additional actuation and control systems for terrestrial locomotion or mode switching, which increase the vehicles’ payload and make the mechanical structure more complicated.

In contrast, the passive ones use wheels [20, 8, 3, 7, 17, 12, 1], cylindrical cages [9, 23] or spherical shells [6, 15, 18] that are driven by the multirotor thrust for terrestrial locomotion without introducing extra actuators or mechanisms. Among them, the cylindrical cage brings slip friction much bigger than the rolling one when turning, making it difficult to control the turning motion. The spherical shell makes the multirotor capable of omnidirectional rolling. However, this mechanism increases the instability of terrestrial locomotion, resulting in difficulties in the design of the control system. Also, the spokes of cages and shells block the view of the onboard cameras, which is hazardous for autonomous navigation. In brief, we can safely claim that the passive-wheeled quadrotor design is best suited for developing autonomous navigation systems.

Ii-B Autonomous Navigation for Terrestrial-Aerial Vehicles

As stated before, only a few researchers have worked on autonomous navigation for terrestrial-aerial vehicles. To the best of our knowledge, only Fan et al. [7] involve terrestrial-aerial motion planning. Firstly, it uses A* to search for a geometric path. Then, by adding a cost to nodes in the air, this method tends to search for a terrestrial path. Finally, a waypoint is selected along this path as the goal for a primitive-based local planner. It generates a set of minimum-snap trajectories, and scores each with a predefined cost to choose the best one. However, the path searching method is too coarse due to the lack of kinodynamic information. Also, since no post-refinement is applied to the trajectory in the local planner, its smoothness and dynamic feasibility cannot be guaranteed. Moreover, it does not consider the nonholonomic constraint in terrestrial locomotion.

Reference Size (mm) Weight (g) Hover Duration (min) Onboard Sensing Onboard Computing
Takahashi et al. [20]
Kalantari et al. [9] 7
Colmenares et al. [3] 350
Nakao et al.[17] 6400
Yamada et al. [23] 1360 8
Hada et al. [8] 1200 7
Fan et al. [7]
TIE
TABLE I: Hardware comparison. Notes: ”” means the corresponding parameter is missing in the paper.

On the other hand, several works [7, 3, 20, 1] present control systems for passive-wheeled terrestrial-aerial quadrotor designs. Fan et al.[7] and Colmenares et al.[3] propose cascaded control schemes similar to a general quadrotor controller. They both simply set the thrust as a constant value lower than the vehicle weight, so the PU cannot be improved dynamically. In fact, the total thrust can be flexibly adjusted because the ground support force partially shares the vehicle’s weight. Takahashi et al.[20]

propose a controller based on Linear Quadratic Regulator (LQR) with online parameter estimation. Nevertheless, no real-world trajectory tracking experiments are presented to validate the method’s efficacy. Atay et al.

[1] extend the works of [9, 20] by elaborating the specific dynamic model and developing a model-based control system. In addition, a thrust-optimization method is proposed. However, this work takes the pitch angle as one of the flat outputs of the controller, but fails to present the mapping from a given trajectory to the flat outputs, making this control system inapplicable to trajectory tracking.

Iii System Overview

Iii-a Robot Design

The main body of TIE is designed as a micro quadrotor with a diagonal wheelbase of 200mm. For terrestrial locomotion, we connect each passive wheel to a shaft fixed on the quadrotor, so that each wheel can rotate freely relative to the quadrotor. For strength and weight considerations, we use carbon fiber as the main structure of TIE, including the quadrotor frame, shafts, and wheels. Moreover, each passive wheel is made of two thin carbon plates fixed by nylon columns rather than a whole carbon plate, which further reduces weight while maintaining strength. The wheels, bearings, and shafts weigh 140g. The overall weight of the robot is 847.7g, including a 2300 mAh - 14.8 V battery that weighs 235g. It can hover up to 9 minutes in aerial locomotion with racing-drone brushless motors (T-Motor F2203.5 2850KV) and Gemfan 4023 propellers.

For autonomous navigation, we equip TIE with the following equipments onboard:

To make the electrical connections more integrated and stable, we also customize two printed circuit boards (PCBs) to connect the motors, electronic speed controllers (ESCs) and the above equipments. Detailed composition of TIE is shown in the exploded diagram Fig.3.

Fig. 3: The detailed composition of TIE. The serial numbers represent (1) onboard computer, (2) autopilot, (3) upper PCB, (4) upper quadrotor frame, (5) tracking camera , (6) power-supply PCB, (7) battery, (8) lower quadrotor frame, (9) tracking camera, (10) wheel, (11) bearing, (12) shaft.

As mentioned above, several previous works develop terrestrial-aerial vehicles with a similar structure to the proposed one [20, 9, 3, 8, 23, 17, 7]. We summarize and compare hardware specifications from these works in Tab.I. It is worth noting that the TIE has the smallest size, the longest endurance, and a relatively light weight. On the other hand, only TIE and the one developed by Fan et al. [7] carry both onboard sensing and computing resources, while TIE weighs only as much as the other.

Iii-B Software Architecture

The architecture of the proposed navigation framework is illustrated in Fig.2

. Firstly, Visual Inertial Odometry (VIO) is obtained from the tracking camera. We fuse it with the IMU onboard the autopilot by Extended Kalman Filter (EKF) to generate smoother UAV state estimation. On the other hand, the depth images from the depth camera are projected to the world frame as a point cloud. We then adopt a column-wise evaluation

[19] to extract ground points. When maintaining an occupancy grid map, these points are not used, in order to avoid situations that the flat ground is set to be occupied. We also compute and update a Euclidean Signed Distance Field (ESDF) by an efficient algorithm developed by Zhou et al. [25]. Afterward, the local planner searches for a kinodynamic path using the Fused VIO and the occupancy map. The resulted path is then optimized utilizing the gradient information obtained from the ESDF. The controller finally tracks the desired trajectory with both terrestrial and aerial locomotion. The experiments shown in Sect.VI-B validate the real-time performance of the proposed navigation framework.

Fig. 4: Illustration of the kinodynamic path searching method. Red curves represent the terrestrial motion primitives, while green curves are the aerial motion primitives. The method keeps planning aerial trajectories until an unavoidable obstacle appears.

Iv Safe Terrestrial-Aerial Motion Planning

The proposed terrestrial-aerial motion planner is built on Fast-Planner[25], which consists of a kinodynamic path searching method and a gradient-based spline optimizer. The path searching method is based on hybrid-state A* algorithm[5], which uses motion primitives instead of straight lines as graph edge in the searching loop. This work adds an extra energy consumption cost to the motion primitives whose destination is above the ground. Consequently, the path searching tends to plan terrestrial trajectories unless TIE encounters enormous obstacles and needs to fly over them, as shown in Fig.4.

In trajectory optimization, we reparameterize the generated trajectory as a degree uniform B-spine with control points

. Note that in terrestrial locomotion, we assume that TIE moves over flat ground, so that the vertical motion can be omitted. We then classify the control points above the ground as

, and the rest as . Each terrestrial control point is two-dimensional, i.e., . To refine the trajectory, we firstly adopt the following cost terms from [25]:

(1)

where is the smoothness cost designed as an elastic band cost function. is the collision cost based on the ESDF gradient information. and are dynamical feasibility costs that limit velocity and acceleration. are weights for each cost terms. Due to the convex hull property of the B-spline, the above cost terms only constrain the control points for safety and dynamical feasibility. We refer the readers to [25] for detailed formulations.

Fig. 5:

Diagram of the reference frames: inertial frame (I), body-fixed frame (B), and terrestrial frame (T). T is also a body-fixed frame with z-axis parallel to that of I, both pointing in the opposite direction of the gravity vector. Thus, T is separated from B by the rotation

along y-axis.

In terrestrial locomotion, the velocity of TIE is limited to be parallel with the yaw angle due to the nonholonomic constraint. Therefore, if the trajectory is too curved, huge tracking errors will occur during turning. To resolve this, we enforce a cost on to limit the curvature of the terrestrial trajectory. The curvature at is defined as , where , and . Therefore, this cost can be formulated as

(2)

where is a differentiable cost function with specifying the curvature threshold:

(3)

The derivation of the gradient can be found in [5]. Note that may be segmented into several subsets by intermediate aerial control points, the curvature of the endpoints are not taken into consideration. In general, the overall objective function is formulated as follows:

(4)

The optimization problem is solved by a non-linear optimization solver NLopt555https://nlopt.readthedocs.io/en/latest/.

After motion planning is done, a setpoint on the generated trajectory is selected according to the current timestamp, and then sent to the controller as a reference state in the inertial frame (defined in Fig.5). An aerial setpoint includes the yaw angle and 3D position, velocity, and acceleration (). A terrestrial one includes the yaw angle and 2D position and velocity (). For consistency, and are both set to be parallel with the velocity. If the current setpoint is in a different locomotion mode than the previous one, an extra trigger will be sent to the controller for the locomotion switch.

V Unified Terrestrial-Aerial Motion Control

This section manifests the proposed controller, which adopts a cascaded architecture for both terrestrial and aerial locomotion. The reference frames are defined in Fig.5. The estimated state obtained from onboard VIO is denoted as , including the position, velocity, orientation (parameterized by Euler angles ) and its derivation (). As for the locomotion switch, When take-off is desired, the controller immediately switches to aerial mode without a slow transition process. During landing, the controller commands TIE to land smoothly with a constant speed, avoiding a sudden impact that may cause VIO divergence.

V-a Aerial Controller

The aerial controller is shown in Fig.6. It takes the reference state from motion planning as the input. The position control module computes the position and velocity error using a proportional controller, and combines them with the reference term to generate a desired acceleration . is firstly used to generate the desired thrust , and then used together with to calculate the desired attitude leveraging the differential-flatness of quadrotors. The detailed equations of attitude calculation can be found in [13]. The inner attitude control and body-rate control generate the attitude derivations

and the desired moment

, respectively. These two modules are performed on the onboard pilot using PX4 open-source firmware666https://github.com/PX4/PX4-Autopilot.

Fig. 6: The cascaded controller for aerial locomotion.

V-B Terrestrial Controller

Fig.7 illustrates the terrestrial controller, which owns a similar architecture to the aerial one. The attitude controller is executed by the onboard autopilot as well. The terrestrial controller’s tracking performance is shown in Fig.8.

1) Yaw Control: The desired yaw is calculated according to the current position error between and , which is defined as . When the norm of is relatively small, is taken as the reference term which points along the trajectory’s tangent direction. However, if the norm is larger than a threshold, is calculated to be parallel with for error correction. The corresponding equations are shown as follows:

(5)

where is the position error threshold. and are the x-axis and y-axis value of , respectively.

2) Adaptive Thrust Control: The desired total thrust is adaptively controlled according to the magnitude of current desired turning angle, defined as . As mentioned before, position tracking error accumulates when TIE is turning due to the nonholonomic constraint. To reduce the tracking error, we dynamically adjust the thrust so that it produces a maximal yaw acceleration large enough to make TIE finish the turning in a short period , which is set as in experiments. Since is small, almost remains constant, and the yaw kinematics can be derived:

(6)

Due to the nonlinearity of the inner attitude controller, we obtain the relationship between and by experimental fitting, given as

(7)

where is a normalized value between 0 and 1, and the dimension of is . can be solved from Equ.6 and Equ.7. Also, is ensured to be lower than hover thrust.

Fig. 7: The cascaded controller for terrestrial locomotion.

3) Attitude Calculation:

It generates the desired attitude . We firstly calculate the desired attitude in inertial frame and obtain by coordinate transformation. Among them, has been computed in the yaw controller, and remains zero due to the assumption that TIE moves on flat ground. The following equations give the derivation of . Firstly, we compute the x-axis value of the desired acceleration in terrestrial frame (denoted as ) based on and the velocity error with a feedback control law:

(8)

where is the integral velocity tracking error. , and are constant gains. Then, can be calculated with the following dynamics equation. In this work, we do not take into account external forces such as the rolling friction.

(9)

where is the total mass of TIE, and is the scale parameter.

Fig. 8: Tracking performance of the terrestrial controller in the office traversing experiment (Demonstrated in Sect.VI-B). The results show that the planned trajectory and the desired attitude are closely tracked by the proposed terrestrial controller during the whole experiment.

Vi Results

Fig. 9: Comparison of different methods when tracking a lemniscate trajectory. This is the result when velocity limit is .
Method
Comp.
Time(ms)
Inte. of Acc.
Success
Rate(%)
Mean Max Std
Proposed 20.55 77.83 139.69 23.25 96
Fan’s [7] 44.62 227.82 368.51 52.69 78
TABLE II: Terrestrial-Aerial Planning Comparison
Velocity Method (m) (m)
Colmenares’s [3] 0.147 0.0404 0.3736
Fan’s [7] 0.147 0.0600 0.4608
Proposed 0.147(Average) 0.0158 0.0946
Colmenares’s [3] 0.153 0.0973 0.6690
Fan’s [7] 0.153 0.0358 0.2725
Proposed 0.153(Average) 0.0225 0.1015
Colmenares’s [3] 0.171 0.1339 0.5293
Fan’s [7] 0.171 0.0474 0.3005
Proposed 0.171(Average) 0.0338 0.1894
TABLE III: Terrestrial Controller Comparison

Vi-a Benchmark Comparisons

Fig. 10: Experiment in a large office. TIE moves about 100m with terrestrial-aerial locomotion, and the average velocity is about .

To demonstrate the superiority of the proposed navigation framework, we conduct benchmark comparisons against the previous works on terrestrial-aerial navigation in two-folds: the terrestrial-aerial planning and the terrestrial controller.

1) Comparison of Terrestrial-Aerial Planning: We conduct comparisons between the proposed planning method and Fan’s [7]. Specifically, each algorithm runs for 50 times independently in a simulation environment with 80 randomly deployed obstacles. We only compare planning methods and do not include terrestrial-aerial motion controllers in the simulation tests. The distance between the starting and goal positions is . We also set up a huge barricade between the starting and goal positions, requiring the robot to fly over it. All the computations are done on a 2.9 GHz processor with 16 GB RAM. The velocity and acceleration limits are set as and . As shown in Tab.II, the proposed planner finds trajectories with less computing time, better smoothness (integral of the squared acceleration), and higher success rate. Firstly, our planner both refines the trajectories’ smoothness and dynamical feasibility, which are not considered in Fan’s [7]. In addition, the motion-primitive based method in Fan’s [7] is time-consuming and incomplete, which may fail to generate feasible trajectories when facing complex environments, resulting in a low success rate even with a higher computing time. Therefore, our method outperforms Fan’s [7] in both time efficiency and planning performance.

2) Comparison of Terrestrial Controller: We compare the proposed terrestrial controller with method[3, 7] in real-world environments. Only the outer translation control is compared because it is our focus, and the inner attitude control of all methods is executed by the autopilot. During the comparison, TIE uses each controller to track a lemniscate trajectory with different velocities. Since method[3, 7] set the desired thrust to be constant, we first test our method, then calculate the desired average normalized thrust (denoted as ) and assign it to method[3, 7]. The average and maximal trajectory tracking error and are compared. As shown in Tab.III and Fig.9, the proposed method achieves lower and with the same in every case. With the adaptive thrust control, the proposed controller generates a larger thrust to make TIE pass through sharp turnings faster, thereby reducing the tracking error. In contrast, method[3, 7] requires a large thrust at all times to achieve the same tracking performance, which greatly increases energy consumption.

Vi-B Experiments

To demonstrate the autonomy and performance of the entire robot system, we perform extensive autonomous tests in various complex environments (as shown in Fig.11). Except for several waypoints, no prior information of the environments is given. The unknown dense environments and limited onboard vision make the experiments challenging.

Fig. 11: The real-world experimental scenes. a) The complex maze. b) The scene for comparison between terrestrial and aerial locomotion. c) Terrestrial winding tunnel. d) Aerial winding tunnel.

1) Walking out of a Complex Maze:

Fig. 12: The thrust curve of both terrestrial and aerial locomotion. Note that the sharp drop in the air thrust curve is due to landing.

In this experiment, TIE has to navigate a complex maze with tremendous obstacles, sharp turnings, and an unavoidable barricade. The velocity limit is set to be . It turns out that TIE manages to walk out of this maze, and it remains in terrestrial locomotion except when it flies over the unavoidable barricade. This result is as expected because terrestrial locomotion is preferable due to better PU.

2) Flying vs Rolling: This experiment presents quantitative PU comparisons between terrestrial and aerial locomotion. The experimental scene is complicated as well because of tortuous paths and a great many obstacles. However, it is set to be passable for both terrestrial and aerial locomotion. In the experiment, TIE passes through the environment in terrestrial and aerial locomotion with the same velocity limit , respectively. The normalized thrust curve is depicted in Fig.12. The average thrust is in terrestrial locomotion and in aerial locomotion. That is, TIE passes this challenging test in both locomotion modes, but requires about only a quarter as much thrust in terrestrial locomotion as in the aerial one. We also experimentally measure that the corresponding energy consumption ratio is approximately . This result highlights the great advantage of terrestrial locomotion in PU.

3) Moving through Winding Tunnels: We perform aggressive flight and rolling tests in this experiment to present the proposed system’s high mobility even in autonomous navigation. Two winding tunnels are set for the flight and rolling test, respectively. The end of each tunnel is outside TIE’s sensing range, so TIE needs to replan in time and turn quickly to pass the test. As a result, TIE can travel back and forth through the tunnels with a velocity up to in aerial locomotion and in terrestrial locomotion. The results are comparable with state-of-the-art autonomous quadrotor systems in [25, 26, 24].

4) Traversing a large Office: The last experiment is conducted in an unknown office with a size over . It is full of cluttered objects, leaving only narrow passages, which brings difficulties to motion planning. What is more, the lighting and terrain condition around the office does not remain the same, posing a huge challenge to the perception and the terrestrial controller of the system. In order to test both terrestrial and aerial navigation, We set up a take-off waypoint halfway and keeps TIE flying after it passes this waypoint. It turns out that TIE safely traverses the office in terrestrial-aerial integrated locomotion. The executed trajectories are shown in Fig.10. This experiment strongly demonstrates the robustness of the proposed system.

In conclusion, the above experiments verify the excellent performance of the proposed robot system from all aspects. It maintains the high maneuverability of a quadrotor while incorporating low-power terrestrial locomotion and can flexibly switch locomotion modes according to environmental changes. Moreover, the system’s robustness makes it capable of both aggressive locomotion and long-time navigation even in unknown dense environments. More details are included in the video.

Vii Conclusion

Terrestrial-aerial vehicles possesses distinct advantages because they combine both the mobility of UAVs and the long endurance of UGVs. However, there are no representative works on the autonomous navigation of these vehicles. To fill this gap, we present an autonomous quadrotor system that can safely navigate in unknown cluttered environments with terrestrial-aerial hybrid locomotion. Based on the design of a lightweight terrestrial-aerial quadrotor, we propose an adaptive navigation framework which mainly consists of a safe motion planner and a unified motion controller. We carry out challenging tests to show the proposed system’s robustness and superiority.

For future work, we will pay attention to motion planning on uneven terrain. On the other hand, we will consider the exogenous forces in the controller, so as to further improve the control accuracy and energy savings.

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