How to Perform Trajectory Planning for Robot Manipulator Assignment
Trajectory planning is one of the most critical stages in any robotics-related project or assignment involving robot manipulators. It determines how a robotic system moves from its initial position to the desired target location while adhering to constraints such as position limits, velocity limits, acceleration boundaries, and in some cases, jerk control. For students looking for help with MATLAB assignment related manipulator, understanding trajectory planning is not just about knowing the theory — it’s about translating that theory into precise simulations and executable motion commands that work in real-world scenarios. Although our primary focus here will be on manipulators, many of the principles discussed are also applicable to autonomous vehicles, aerial drones, and various other mechatronic systems that require controlled movement.
When we talk about trajectory planning, it’s important to see where it fits within the larger hierarchy of motion planning. At the highest level, we have task planning, which deals with defining the goals — for instance, instructing the robot to pick up an object from a conveyor belt and place it in a storage bin. Once that task is defined, path planning finds a feasible spatial route between the starting and ending positions, often represented as a sequence of waypoints. From there, trajectory planning comes into play, taking that spatial path and determining exactly how the robot will traverse it over time. Finally, trajectory following ensures the physical robot executes the planned movements accurately, typically via control systems that continuously monitor and adjust the robot’s motion.
A simple way to differentiate between path planning and trajectory planning is to remember that path planning focuses on “where to go” while trajectory planning focuses on “how to move there over time.” This distinction is vital for any student preparing a robotics assignment because confusing the two can lead to incorrect implementation in MATLAB or Simulink. In this blog, we will assume that the path has already been generated, typically as a list of waypoints, and our task will be to generate a suitable trajectory that allows the manipulator to follow those points in a safe and efficient manner.
Choosing Between Task Space and Joint Space for Your Trajectory
One of the first decisions in designing a trajectory is whether it should be defined in task space or joint space. This choice can significantly affect how the robot moves and how complex your MATLAB implementation becomes.
Task-space trajectories define motion in terms of the Cartesian position and orientation of a specific point on the manipulator, usually the end effector. In this approach, the interpolation between waypoints occurs in the physical workspace of the robot, meaning that the end effector moves in a way that appears smooth and natural relative to the environment. This method is ideal for applications where precise positioning in space matters, such as assembly, pick-and-place tasks, or surgical robotics. However, there is a trade-off: to follow a task-space trajectory, you often need to solve inverse kinematics (IK) at multiple points along the path. For assignments involving complex manipulators with many degrees of freedom, this can quickly become computationally heavy, especially if your IK solver is iterative or optimization-based.
Joint-space trajectories, on the other hand, define motion directly in terms of joint positions — angles for revolute joints or linear displacements for prismatic joints. This approach avoids the need for frequent IK computations since joint targets are explicitly defined, making execution faster and more straightforward in MATLAB. It also ensures that joint constraints are easier to check and enforce. However, the resulting end-effector motion might not be as intuitive or smooth in the Cartesian workspace, and there’s no guarantee that intermediate joint positions won’t violate workspace constraints unless checked carefully.
In practical assignment work, choosing between task space and joint space often depends on the priority: if the focus is on workspace accuracy and obstacle avoidance, task space is preferable. If the priority is fast computation and direct control of actuators, joint space is often the better choice.
Understanding the Types of Trajectories You Can Generate
Once the decision between task space and joint space is made, the next step is to decide the mathematical form of the trajectory. In MATLAB and Simulink, several well-established trajectory types are available, each with its strengths and limitations.
Trapezoidal velocity profiles are perhaps the most intuitive starting point. They consist of three distinct phases: constant acceleration, constant velocity, and constant deceleration. When plotted, the velocity curve forms a trapezoid, while the position curve has an S-shape. These profiles are easy to implement, simple to validate, and well-suited for scenarios where velocity and acceleration limits must be strictly adhered to. MATLAB’s trapveltraj function or the Simulink “Trapezoidal Velocity Profile Trajectory” block provides a straightforward way to implement this. In an academic assignment, using this method can demonstrate clear understanding of speed control while still being computationally efficient.
Another widely used approach is polynomial trajectories. Here, you interpolate between waypoints using polynomial functions of time. Cubic polynomials (third order) require four boundary conditions — position and velocity at both start and end points. Quintic polynomials (fifth order) require six boundary conditions — position, velocity, and acceleration at both ends. Polynomial trajectories excel in producing smooth acceleration and jerk profiles, which is important in delicate or high-precision tasks. MATLAB functions such as cubicpolytraj and quinticpolytraj make generating such trajectories straightforward. The trade-off is that validating these trajectories against physical constraints can be more challenging because control over peak velocity and acceleration is indirect.
A third option is spline trajectories, with B-splines being a common choice. Unlike time-based polynomials, splines are parameterized in space and shaped by control points. The resulting path does not necessarily pass through every control point but remains within the convex hull defined by them. This property is useful when designing paths that must stay within certain spatial limits. MATLAB’s bsplinepolytraj function allows for efficient creation of spline-based paths, making it possible to fine-tune shapes by adjusting control points without recalculating from scratch.
Managing Orientation Alongside Position in Trajectory Planning
For most real-world manipulator assignments, controlling the position of the end effector is not enough; its orientation must also be precisely managed. However, interpolating orientation is more complicated than interpolating position because rotations can wrap around, and certain representations like Euler angles can introduce singularities or ambiguities.
A robust solution is to represent orientation using quaternions and interpolate between them using Spherical Linear Interpolation (Slerp). Slerp provides the shortest rotational path between two orientations at a constant angular speed, avoiding issues like gimbal lock. In MATLAB, functions like rottraj handle pure rotational interpolation, while transformtraj can combine both position and orientation interpolation in a single function call.
Orientation trajectories can also benefit from time scaling techniques. For instance, applying a trapezoidal time-scaling profile to an orientation change ensures that the rotation starts and ends at zero angular velocity, with the maximum velocity reached midway through the segment. This results in smoother motion, which is particularly valuable when the manipulator is handling delicate objects or performing precision assembly.
Implementing a Practical Trajectory in MATLAB
Let’s consider a practical MATLAB example that combines translation, rotation, and time scaling. Suppose we want to move the end effector from a starting position at the origin to a point at coordinates (1, 2, 3) while rotating it according to specific Euler angles. By combining transformtraj with a trapezoidal velocity time-scaling function, we can produce a smooth and controlled trajectory:
T0 = trvec2tform([0 0 0]);Tf = trvec2tform([1 2 3]) * eul2tform([pi/2 0 pi/4],'ZYX');tTimes = linspace(0,1,51);tInterval = [0 5];
[s,sd,sdd] = trapveltraj([0 1], numel(tTimes));[T,dT,ddT] = transformtraj(T0, Tf, tInterval, tTimes, 'TimeScaling', [s; sd; sdd]);
plotTransforms(tform2trvec(T), tform2quat(T));
In this example, the trapveltraj function generates a time-scaling profile that controls the speed of the transformation. The transformtraj function then produces a trajectory that smoothly moves and rotates the end effector, while plotTransforms provides a visualization. This kind of MATLAB implementation not only makes the theory concrete but also serves as a strong deliverable for an academic assignment.
Moving from Simulation to Physical Implementation
Simulation in MATLAB and Simulink is an essential step, but the ultimate goal for many students is to implement their trajectories on real hardware. Before deployment, it is important to integrate the trajectory into a dynamic simulation model of the manipulator. This allows for testing under realistic physical conditions, including actuator limitations, load variations, and possible disturbances.
Once the trajectory is validated in simulation, additional checks should be performed to ensure that joint limits are respected, torque demands are within actuator capabilities, and there are no collisions with the environment or the robot’s own structure. MATLAB’s robotics and control toolboxes provide built-in functions to perform these checks efficiently.
For physical implementation, MATLAB’s real-time execution capabilities, along with hardware support packages, make it possible to send trajectory commands directly to the robot’s controller. This bridge between simulation and execution is what makes MATLAB such a powerful tool for students — the same code that was tested in simulation can often be reused with minimal modification for real-world execution.
Integrating Trajectory Planning with Low-Level Control
Trajectory planning does not exist in isolation; it is closely tied to the control strategies used to follow the planned path. For instance, the velocity profile generated during trajectory planning can be fed directly into the derivative term of a PID controller, improving tracking performance. Similarly, having acceleration information allows for feedforward control, which can significantly enhance the robot’s responsiveness and stability.
In more advanced assignments, model-based control methods such as computed torque control can be combined with planned trajectories to account for the dynamics of the manipulator. MATLAB and Simulink make it relatively straightforward to integrate such control strategies, enabling students to go beyond kinematics and explore dynamic control concepts.
Conclusion
Trajectory planning for robot manipulators is a complex but rewarding area of robotics engineering, especially in the context of university-level assignments where both theoretical understanding and practical MATLAB implementation are required. From choosing between task space and joint space, to selecting the right trajectory type, to managing both position and orientation, each decision shapes the performance and feasibility of the final motion. MATLAB’s powerful toolboxes provide a rich environment for simulating, validating, and deploying these trajectories, allowing students to focus on innovation while maintaining engineering precision.
By approaching trajectory planning methodically — starting with clear requirements, choosing appropriate mathematical models, simulating thoroughly, and finally deploying with robust control — students can create assignments that not only meet academic expectations but also reflect industry-grade engineering practices. Whether the end goal is a high-precision assembly task or a simple point-to-point move, mastering trajectory planning in MATLAB equips future engineers with skills that are directly transferable to professional robotics applications.