876 research outputs found
Velocity constrained trajectory generation for a collinear Mecanum wheeled robot
While much research has been conducted into the generation of smooth trajectories for underactuated unstable aerial vehicles such as quadrotors, less attention has been paid to the application of the same techniques to ground based omnidirectional dynamically balancing robots. These systems have more control authority over their linear accelerations than aerial vehicles, meaning trajectory smoothness is less of a critical design parameter. However, when operating in indoor environments these systems must often adhere to relatively low velocity constraints, resulting in very conservative trajectories when enforced using existing trajectory optimisation methods. This paper makes two contributions; this gap is bridged by the extension of these existing methods to create a fast velocity constrained trajectory planner, with trajectory timing characteristics derived from the optimal minimum-time solution of a simplified acceleration and velocity constrained model. Next, a differentially flat model of an omnidirectional balancing robot utilizing a collinear Mecanum drive is derived, which is used to allow an experimental prototype of this configuration to smoothly follow these velocity constrained trajectories
Temporal Logic Motion Planning with Convex Optimization via Graphs of Convex Sets
Temporal logic is a concise way of specifying complex tasks. But motion
planning to achieve temporal logic specifications is difficult, and existing
methods struggle to scale to complex specifications and high-dimensional system
dynamics. In this paper, we cast Linear Temporal Logic (LTL) motion planning as
a shortest path problem in a Graph of Convex Sets (GCS) and solve it with
convex optimization. This approach brings together the best of modern
optimization-based temporal logic planners and older automata-theoretic
methods, addressing the limitations of each: we avoid clipping and passthrough
by representing paths with continuous Bezier curves; computational complexity
is polynomial (not exponential) in the number of sample points; global
optimality can be certified (though it is not guaranteed); soundness and
probabilistic completeness are guaranteed under mild assumptions; and most
importantly, the method scales to complex specifications and high-dimensional
systems, including a 30-DoF humanoid. Open-source code is available at
https://github.com/vincekurtz/ltl_gcs
Optimal Control for Kinematic Bicycle Model with Continuous-time Safety Guarantees: A Sequential Second-order Cone Programming Approach
The optimal control problem for the kinematic bicycle model is considered
where the trajectories are required to satisfy the safety constraints in the
continuous-time sense. Based on the differential flatness property of the
model, necessary and sufficient conditions in the flat space are provided to
guarantee safety in the state space. The optimal control problem is relaxed to
the problem of solving three second-order cone programs (SOCPs) sequentially,
which find the safe path, the trajectory duration, and the speed profile,
respectively. Solutions of the three SOCPs together provide a sub-optimal
solution to the original optimal control problem. Simulation examples and
comparisons with state-of-the-art optimal control solvers are presented to
demonstrate the effectiveness of the proposed approach.Comment: 8 pages, 5 figure
Nonlinear Model Predictive Control for Constrained Output Path Following
We consider the tracking of geometric paths in output spaces of nonlinear
systems subject to input and state constraints without pre-specified timing
requirements. Such problems are commonly referred to as constrained output
path-following problems. Specifically, we propose a predictive control approach
to constrained path-following problems with and without velocity assignments
and provide sufficient convergence conditions based on terminal regions and end
penalties. Furthermore, we analyze the geometric nature of constrained output
path-following problems and thereby provide insight into the computation of
suitable terminal control laws and terminal regions. We draw upon an example
from robotics to illustrate our findings.Comment: 12 pages, 4 figure
Constrained Reachability and Trajectory Generation for Flat Systems
We consider the problem of trajectory generation for constrained differentially flat systems. Based on the topological properties of the set of admissible steady state values of a flat output we derive conditions which allow for an a priori verification of the feasibility of constrained set-point changes. We propose to utilize this relation to generate feasible reference trajectories. To this end, we suggest to split the trajectory generation problem into two stages: (a) the planning of geometric reference paths in the flat output space combined with (b) an assignment of a dynamic reference motion to these paths. This assignment is based on a reduced optimal control problem. The unique feature of the approach is that due to the specific construction of the reference paths the optimal control problem to be solved is guaranteed to be feasible. To illustrate our results we consider a Van de Vusse reactor as an example
Efficient Motion Primitives-Based Trajectory Planning for UAVs in the Presence of Obstacles
The achievement of full autonomy in Unmanned Aerial Vehicles (UAVs) is significantly dependent on effective motion planning. Specifically, it is crucial to plan collision-free trajectories for smooth transitions from initial to final configurations. However, finding a solution executable by the actual system adds complexity: the planned motion must be dynamically feasible. This involves meeting rigorous criteria, including vehicle dynamics, input constraints, and state constraints. This work addresses optimal kinodynamic motion planning for UAVs in the presence of obstacles by employing a hybrid technique instead of conventional search-based or direct trajectory optimization approaches. This technique involves precomputing a library of motion primitives by solving several Two-Point-Boundary-Value Problems (TPBVP) offline. This library is then repeatedly used online within a graph-search framework. Moreover, to make the method computationally tractable, continuity between consecutive motion primitives is enforced only on a subset of the state variables. This approach is compared with a state-of-the-art quadrotor-tailored search-based approach, which generates motion primitives online through control input discretization and forward propagation of the dynamic equations of a simplified model. The effectiveness of both methods is assessed through simulations and real-world experiments, demonstrating their ability to generate resolution-complete, resolution-optimal, collision-free, and dynamically feasible trajectories. Finally, a comparative analysis highlights the advantages, disadvantages, and optimal usage scenarios for each approach
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