Autonomous micro-mobility vehicles (MMVs) such as wheelchairs, scooters, and bicycles have the potential to improve mobility access and support safe low-speed transportation in pedestrian-shared spaces. Achieving MMV autonomy will require realistic, predictable MMV motion. However, many existing autonomous vehicle stacks rely on simplified kinematic models that fail to capture key MMV characteristics such as tire slip, friction, and wheel layouts, limiting realism and gradient-based optimization. In this paper, we explore differentiable formulations of dynamics models for autonomous micro-mobility systems. We first construct DiffKBM, a differentiable version of the kinematic bicycle model (KBM). Then, we introduce DiffGM3, a differentiable formulation of the General Micro-Mobility Model (GM3), a unified tire-based dynamics formulation for micro-mobility vehicles that supports a wide range of MMV configurations. DiffKBM and DiffGM3 enable end-to-end differentiable optimization through MMV dynamics, making them suitable for integration into differentiable autonomy stacks. We evaluate these dynamics models in both open-loop and closed-loop settings: (1) open-loop trajectory matching, where DiffKBM and DiffGM3 are integrated as a dynamics layer within DiffStack and optimized to reproduce real-world MMV trajectories, and (2) closed-loop autonomous navigation, where DiffKBM and DiffGM3 are paired with a differentiable MPC controller in CrowdNav pedestrian scenarios. In the open-loop setting, DiffGM3 outperforms DiffKBM in reproducing trajectories with improvements in ADE and NLL across bicycle, scooter, and motorcycle modes, and reductions in planning loss for bicycle and motorcycle trajectories. We also find that, in closed-loop settings, DiffGM3 improves on DiffKBM's CrowdNav performance by producing 55% fewer collisions and a 75% lower discomfort frequency for the bicycle mode.
Figures & tables
Symbol
Description
Units
ℓ
Half contact length
m
R
Tire radius
m
γ
Camber angle
rad
μ
Coefficient of friction
-
cp
Tread element stiffness per unit area
N/m 2
TABLE I : Physical Parameters in the tire brush model.
Symbol
Description
Units
Fz
Normal load
N
Ω
Wheel angular velocity
rad/s
δ
Steering angle
rad
r
Vehicle yaw rate
rad/s
α
Slip angle
rad
TABLE II : Input Variables in the tire brush model.
Fig. 1 : DiffKBM implements wheelbase L as a learnable parameter in the steering component. The resulting turning rate θ˙ along with velocity are used in Euler integration to obtain the position. By making KBM end-to-end differentiable, we are able to tune L for an MMV with unknown wheelbase length.
Fig. 2 : DiffGM3 contains several differentiable components with sets of learnable parameters ρlean,ρtire , and ρVI . First, the steering control input δ is converted into tire-specific steering angles δi . This, along with the MMV’s previous longitudinal velocity vx , lateral velocity vy , and yaw rate r , is used to calculate tire velocities. Meanwhile, longitudinal and lateral accelerations, ax and ay , are used to transfer load among the tires, and the previous lean angle γ and roll rate γ˙ are used to determine the next lean angle. In addition to wheel angular velocity Ω , the results from these modules are inputs to the tire brush model, where forces and moments are computed. The outputs for each tire are integrated into the vehicle dynamics to obtain longitudinal, lateral, and yaw acceleration. Finally, the resulting position is calculated with Euler integration. This fully differentiable formulation allows gradients to backpropagate to each module so parameters can be tuned on MMV trajectory data.
Component
Optimized Parameters
Bicycle body
kalign , dyaw,droll , Iz , Ix
Tires (each wheel)
μ , cp , ℓ
TABLE III : DiffGM3 parameters optimized using IMPTC trajectories. Align gain kalign and damping coefficients dyaw,droll help to stabilize the MMV and reduce oversteering. Moments of inertia Iz , Ix , and tire parameters are tuned because they are not easily measurable.
Fig. 3 : Open-loop Trajectory Matching Comparison between the DiffKBM and DiffGM3 : (a) On bicycle trajectories, DiffGM3 is able to stay on path because it has learnable parameters to prevent overturning. However, in some cases, it stops before the goal as shown by the red arrow, leading to a higher goal cost in the planning loss function. (b) On the other hand, the DiffKBM reaches its goal but veers off the ground-truth straight path, as indicated by the red arrow. This is due to the DiffKBM’s lack of support for realignment in its formula for yaw. (c) For a scooter, DiffGM3 is able to steer the scooter to its goal while avoiding other agents. (d) On the same trajectory, the DiffKBM causes the ego agent to turn towards another agent and slow down, preventing it from reaching its goal.
↓ ADE (m)
↓ NLL
↓ Planning Loss
Mode
DiffGM3
DiffKBM
DiffGM3
DiffKBM
DiffGM3
DiffKBM
Bicycle
2.06±0.08
2.08±0.07
1.07±0.00
1.10±0.04
149.10±7.87
155.58±10.38
Scooter
1.45±0.01
1.61±0.02
1.23±0.19
1.28±0.17
142.75±2.09
119.57±3.01
Motorcycle
1.74±0.00
1.78±0.06
3.02±0.05
3.17±0.27
212.23±12.77
298.50±7.54
TABLE IV : Open-loop Trajectory Matching Evaluation Results: DiffGM3 outperforms DiffKBM in ADE (Bicycle: -1.16%, Scooter -9.84%, Motorcycle: -2.37%) and NLL (Bicycle: -3.02%, Scooter -2.05%, Motorcycle: -4.75%) on all modes. For planning loss, DiffGM3 outperforms DiffKBM on bicycle (-4.16%) and motorcycle (-28.9%) trajectories, but performs worse on scooters (19.39%).
Fig. 4 : Overview of the DiffMPC pipeline integrated with DiffKBM or DiffGM3 . At each timestep, the environment provides a state estimate xt , which is passed to the optimizer with the goal position and surrounding pedestrian states pedst . The optimizer proposes a control sequence u0:T−1 and uses either DiffKBM or DiffGM3 parameterized by learnable parameters ρKBM or ρGM3 to roll out predicted future states x0:T . A cost function is defined with learnable cost weights ρC . Because both the dynamics and the cost function are differentiable, gradients can be back-propagated through the prediction and cost modules to enable end-to-end learning of MMV dynamics parameters. The first control action u0 is applied to the environment, and the process repeats in a receding-horizon loop.
Model
↑ Success Rate
↓ Collision Rate
↓ Incomplete Rate
↓ Nav. Time (s)
↓ Discomfort Freq.
↑ Avg. Min Dist
DiffKBM Bicycle
0.62
0.38
0.00
4.02
0.08
0.13
DiffGM3 Bicycle
0.64
0.17
0.19
5.13
0.02
0.12
DiffGM3 Scooter
0.63
0.13
0.23
6.14
0.03
0.13
DiffGM3 Wheelchair
0.60
0.23
0.17
6.30
0.03
0.12
DiffGM3 Tricycle
0.67
0.23
0.17
4.82
0.04
0.11
TABLE V : Closed-loop Pedestrian Crowd Navigation Performance Comparison between DiffGM3 and DiffKBM: DiffGM3 prioritizes safety and demonstrates significantly fewer collisions across all vehicle configurations relative to DiffKBM. Specifically, in the baseline comparison between the two bicycle models, DiffGM3 produces 55% fewer collisions, with a 3% better success rate. DiffGM3’s incomplete rate and slower navigation time can be explained by its tendency to avoid collisions by veering away from the goal, resulting in situations where the vehicle is unable to arrive at the goal within the time limit. This also explains why DiffGM3’s discomfort frequency is 50% - 75% better than DiffKBM’s across all modes. Moreover, DiffKBM’s faster navigation times are primarily the result of collisions ending the scenario early.
Fig. 5 : Closed-loop Navigation in Pedestrian Crowds Comparison between DiffGM3 Bicycle and DiffKBM: We show two unique scenarios each for DiffGM3 and DiffKBM. Longer pedestrian paths reflect the longer navigation time taken by the MMV to avoid moving pedestrians to reach its goal. Scenario 1: DiffGM3’s route reflects its ability to use real-world kinematics to avoid pedestrians when necessary, while DiffKBM’s simple kinematics forces it to attempt to fit right in between two pedestrians, resulting in a collision. Scenario 2: While both models reach the goal, DiffGM3’s longer route demonstrates less discomfort and higher minimum distance from pedestrians relative to DiffKBM’s direct route.
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Shouma Amano, Takuya Azumi
Saitama University · Academic Association (Graduate School of Science and Engineering) Saitama University
Developing autonomous mobile robot systems typically requires either extensive, platform-specific data collection or relies on simplified abstractions, such as unicycle or bicycle models, that fail to capture the complex kinodynamics of diverse platforms, ranging from wheeled to tracked vehicles. This limitation hinders scalability across evolving heterogeneous autonomous robot fleets. To address this challenge, we propose Cross-vehicle kinodynamics Adaptation via mobility Representation (CAR), a novel framework that enables rapid mobility transfer to new vehicles. CAR employs a Transformer encoder with Adaptive Layer Normalization to embed vehicle trajectory transitions and physical configurations into a shared mobility latent space. By identifying and extracting commonality from nearest neighbors within this latent space, our approach enables rapid kinodynamics adaptation to novel platforms with minimal data collection and computational overhead. We evaluate CAR using the Verti-Bench simulator, built on the Chrono multi-physics engine, and validate its performance on four distinct physical configurations of the Verti-4-Wheeler platform. With only one minute of new trajectory data, CAR achieves up to 67.2% reduction in prediction error compared to direct neighbor transfer across diverse unseen vehicle configurations, demonstrating the effectiveness of cross-vehicle mobility knowledge transfer in both simulated and real-world environments.
Tong Xu, Chenhui Pan, Xuesu Xiao
Department of Computer Science, George Mason University
We present a learning-enhanced motion planner for differential drive mobile manipulators to improve efficiency, success rate, and optimality. For task representation encoder, we propose a keypoint sequence extraction module that maps boundary states to 3D space via differentiable forward kinematics. Point clouds and keypoints are encoded separately and fused with attention, enabling effective integration of environment and boundary states information. We also propose a primitive-based truncated diffusion model that samples from a biased distribution. Compared with vanilla diffusion model, this framework improves the efficiency and diversity of the solution. Denoised paths are refined by trajectory optimization to ensure dynamic feasibility and task-specific optimality. In cluttered 3D simulations, our method achieves higher success rate, improved trajectory diversity, and competitive runtime compared to vanilla diffusion and classical baselines. The source code is released at https://github.com/nmoma/nmoma .